Games - Strategy and Tactics

Terraforming Mars: Breathing Filters--and Minimum Requirements

2019-01-30T00:02:00.000-07:00

Breathing Filters

Tags	Science
Add. Req	Min.: Oxygen 7%
Card List Cost	11
Costs	Actual	Normalized	Max Norm	Min Norm
Req. Cost	0	0	0	0
Effect Cost	0	0	0	0
Final Card Cost	14	9	9	9

Value
VP Value	26	26	26	26
Income Value	0	0	0	0
Final Profit(Loss)	12	12	12	12

ROI	85.71%	85.71%	85.71%	85.71%
Breakeven Turn	Immediate

Notes

Breathing filters, like Trans-Neptune Probe(TNP), is a fairly simple card, but with 1 minor addition: the minimum requirement of Oxygen of 7%. However, Breathing Filters provides a much greater return.

Requirements

Important Oxygen Levels per Turn

Mins & Maxes

Many cards have either minimum or maximum requirements. These requirements can either be "Eventual" requirements or "Optional" requirements. Of these two requirements, a card can have either a Minimum (min) or a Maximum (max) of these requirements.

"Eventual" Requirements are one of the three requirements for Terraforming Mars: Water, Oxygen, or Temperature. These are Eventual requirements because they will eventually be met as they are required to win the game.

"Optional" Requirements are any requirement other than those needed to win the game and may include have a certain number of Tags in play, a certain number of cities, or some other special requirement.

Minimum Eventual Requirements (MinER) Cost Calculation

Important Ocean Levels per Turn

Cards with Minimum Eventual Requirements are not much of a requirement in terms of calculating cost. A MinER will eventually occur, so the card can be played. The major effect of an MER is the card may be delayed in being played, but the play is eventual (thus the name of the card). This effect may cause the card to either not generate as much as expected depending on when the requirement's average play occurs.

Maximum Eventual Requirements (MaxER) Cost Calculation

Cards with a MaxER are a true requirement. These cards must be played before the requirement is met, or the card is reduced to a value of zero. For cost purposes, the card's value is assumed to be only if the card is played before meeting this requirement.

Optional Requirements

Optional requirements are based on the probability an event occurs. For example, if a card requires one Science Tag, it is necessary to calculate the probability of a science tag being played. Grabbing these cards early is risky as the additional card may not occur and the 3mC spent on keeping the card may be lost. For calculation purposes the cost is based as a percentage probability the card may be played.

Important Temperature Levels per Turn

For some requirements (namely Venus levels), this number is a rough estimate as data collection on it is incomplete at this time.

Terraforming Mars:Trans-Neptune Probe (and Template Explanation)

2019-01-27T17:13:00.001-07:00

Trans-Neptune Probe

Tags	Science, Space (Base)
Add. Requirement	-
Card List Cost	6
Costs	Actual	Normal	Ma	Min
Req. Cost	-	-	-	-
Effect Cost	-	-	-	-
Final Card Cost	9	9	9	9

Value	Actual	Normal	Max	Min
VP Value	13	13	13	13
Income Value	-	-	-	-
Final Profit(Loss)	4	4	4	4

ROI	44.44%	44.44%	44.44%	44.44%
Breakeven Turn	Immediate

Explanation of Card Template

Tags: Lists the tags found on the card. Generally, tags will be considered to have a value of "0". Instead, they will impact the cost of cards (explained when that becomes necessary). The card's set will also be displayed here.

Add. Requirements: Additional requirements based on the card.

Card List Cost: The cost of the card as listed on the card

Costs/Value: Costs are measured in 4 types
Actual- This is the cost as measured from the card (not normalized).
Normal- Normalized costs are the cost normalized to a standard cost of 13. This is explained in earlier articles.
Max-The maximum normalized value possible. This valued is found if the card is played as early as possible for those cards which have an income per turn.
Min-This is valued as if the card were played as late as possible.

Req. Cost-This is the calculated cost based on the card's requirements.

Effect Cost-Some cards have an ongoing, or effective, effect which has some cost calculated here.

VP Value-VP Value is the measured increase based on Victory points.

Income Value- Measures the value of the card based on its income. As mentioned in earlier articles, this is the income based on an average play of the card.

Final Profit/Loss-This is the card's final (initial) gain or loss from playing the card.

ROI (Return on Investment)- This is the card's calculated return based on the card's cost. For those mathematically inclined, this is found using the following formula: [Gain-Cost]/Cost.

Breakeven- This is either how many uses, or how many turns, are needed for the card to pay for itself.

Any notes for the card will appear after This point.

Notes
Trans-Neptunian Probe is arguably the simplest of cards, and the reason it was chosen first. It has no requirements, generates 1VP, and has 2 tags. That is all there is to it. How does it fare against other cards? A question for future articles...

Going Forward

The cards in TM will be broken up by set, effect, and complexity. It is hoped to display two or three cards at a time in an article.

Terraforming Mars: Standard Projects: City

2019-01-17T01:43:00.003-07:00

Standard Projects

All Standard Projects were used to determine the value of a VP and form the "Actual" cost/value for a given item. However, here we will evaluate each individually to determine the value of the City Standard Project.

City

A city may be created for 25mc. In return, it will generate 1mc per turn, plus a bonus resource if placed on particular areas of Mars. Looking at the lowest cost can provide some insight into the value of the basic city. For this analysis, the city will be built on a non-benefit tile and not adjacent to a greenery tile.

A city built on Turn 1 will provide a maximum of 10mc. Thus, the final "value" of a city is -15mc if not built on a special tile. If built on an "average" turn, it will generate only 4.5mc.

Cost: 25

Production: 1mc

Max Value: -15mc

Avg Value: -21.5mc

Building Locations

The first thing to improve the value a city is to look at the specific locations on Mars. The best location will vary depending on the map. The maps were evaluated in an earlier article, providing an average return.

Map

Basic: +2.82mc

Hellas: +2.78mc

Elysium:+2.95mc

For all intents and purposes, it is possible to say the value is 3mc.

Greenery Value

The city value at 2 greenery tiles is 11.

Every Greenery tile adjacent to a city provides that city with a 1VP bonus. The maximum possible is 6. Thus, the value of a city increases more based on the greenery tiles. The chart below shows the breakdown of value based on the number of surrounding greenery tiles.

The break even point for getting one's money back on the standard project occurs just over the 2 Greenery mark. Therefore, a city must be adjacent to at least 3 Greenery tiles to turn a 'profit'.

General Statement

Looking at just the city value without any other terms, can lead to some poor decision making. Many times it is necessary to review the overall board positioning and other strategic considerations. That said, its important to understand the absolute basic value of the city to truly understand the depth of the decision being made.

Corporate Bonus

Corporations will be looked at in depth later, but it is important to mention a particular corporation when speaking of cities, Tharsis Republic. Tharsis Republic grants a double income for placing a city and an additional 3mc immediately. Adding in all the benefits, Tharsis building a city on turn 1 will generate a 1mc benefit to the player of Tharsis. Overall, this is minimal in comparison to other options available to the player.

Turn 1-Tharsis
Cost to Build	-25
Regular Income	+10
Tharsis Income	+10
Tharsis bonus mc	+3
"Average" map	+3
Final Value	+1

Perhaps most important, Tharsis can begin to benefit from even a single Greenery tile. However, its important to realize the basic value drops off twice as fast for Tharsis than for other corporations. If Tharsis builds a city on turn 2, it will generate a return of -1mc. The chart below compares the value of building a city by turn for a basic player, and for a Tharsis player.

Tharsis vs non-Tharsis player city value comparison by turn

Conclusions

Building a city using Standard Projects on turn one is an expensive operation. The action by itself will probably not return a profit. Tharsis Republic will see a 1mc return for if the city is built on Turn 1, but typically there are much better investments to be made.

Adjacent Greenery tiles increase the value of a city dramatically. Therefore, it is the placement of greenery tiles which better dictates the value of a city rather than the income returned from the city.

Without additional cards and/or effects, a city on Mars is not practical. However, as soon as a city can be placed adjacent to 3 Greenery tiles, it becomes instantly profitable. Even on turn 10, a city adjacent to 3 greenery tiles breaks even instantly.

From an efficiency standpoint, placing a city is generally not a good decision without adjacent greenery tiles. Even then, there are typically more efficient options available than the Standard Project to generate VP. As the cards will show, most players can perform better decisions than placing a city down.

Tharsis Republic can consider placing a city down adjacent to a greenery tile a profitable decision until turn 8 of the game. After that, there is a minor loss of ROI if it is a single greenery tile. Placing a tile next to 2 greenery tiles will always return a profit to Tharsis, but the amount will differ based on the game turn.

This analysis looks at placing Standard Project city from an efficiency standpoint (i.e. mc/VP). Viewed in this light, placing city is mostly loss unless placed next to 3 or more Greenery tiles. However, Strategic considerations (such as map access, blocking opponents, etc.) may override this advice, but it is necessary to understand the value the player is giving up when to properly place a value on that strategic city placement.

Terraforming Mars: A New View of the Map

2018-12-23T00:00:00.000-07:00

Using the spaces determined by the previous valuations, each of the maps is shown below. Each space on the maps was calculated and given a color. The darker the green color the more points the location is worth.

All values show the Normalized values for the locations

NOTE: All images are of the Terraforming Mars Boardgame. They were graphically designed by Isaac Fryxelius, and he did an excellent job on them

Original Map

The Original map has a total potential value of 172.25 MC worth of locations, within an average of 2.82 MC per space. Most of this is concentrated along the equatorial belt, with ocean tiles essentially splitting access to half of these spaces. This makes locations which may be built in ocean tiles (Mohole, Protected Valley, etc.) particularly valuable as they permit a player to cross these ocean locations granting access to the entire belt.

Mineral locations are clumped into three main areas. To the North and South Iron deposits exist. Titanium is only available on three locations, and not in any great quantity.

Cities may be built almost at any location and have access to resources. City placement is relatively easy and blocking/expansion of cities may take place just about anywhere. This leaves lots of open area to build in while the oceans in the middle effectively separate the two areas of the board.

Elysium map

Elysium is the richest of the maps, having both the most number of spaces with benefits and the largest single benefit locations ont he map. Two of the locations have a value of 9 or more. Like the Original Map, Elysium's main locations are on the equatorial belt, but the oceans do not as effectively break up the map.

The large bodies of water on the right hand side of the map effectively block expansion to the center of the map for those grabbing the "3-card" spot. It can be effective to take this location, but some other method of getting to the center of the map needs to be devised. Titanium is slightly more plentiful, and iron is much more plentiful than in the Original. Still, the total value difference between the maps is only 8.25MC, but the large value locations are definitely worth taking.

Despite this map being more plentiful in minerals and plants, placing cities is slightly more of a challenge. The lower portion of the map is a large wide open area, while the upper portion is broken up by all the ocean tiles. While most would choose to focus on the center or edges of the map to maximize resource gains, city scoring in these areas is severely restricted.

Hellas Map

Hellas poses an interesting challenge. Despite having fewer total resources, albeit not by much, it isn't effectively broken up. furthermore, some of the south pole locations offer heat, the only map to provide this benefit. Oceans on this map are either on the edge or in one large 7 hex structure just ot the right hand side.

Mineral deposits are more plentiful, while plants are more rare than the other maps, as befits the south pole. Being the South Pole of Mars, the plant locations are all on the upper edges. Furthermore, the most valuable spot on the board is arguably in the worst potential position and, though it provides a great benefit, it raises the cost of any actions there by 6. This means settling the South Pole requires a greater overall income, although the benefit is probably worth it.

Since the oceans are on edges or in one big area, this leaves the map wide open for settlement. Titanium locations are primarily on the edges of the map, while iron exists in a large clump in the center of the board. This large clumping of iron breeds competition for locations in the center of the map, despite having more total overall room to expand.

Terraforming Mars: Production Valuations

2018-12-20T02:14:00.000-07:00

Production Issues

Producing resources in Terraforming Mars occurs at the beginning of every generation after the first. Two complications arise when calculating Production in Terraforming Mars.

First, the longer a game of Terraforming Mars runs, the more of a resource will be generated through production. Since the average game was calculated, the best thing is to standardize on an 'average' game. So, 10 generations (turns) is the number to use in calculating production for comparison purposes. As more players enter the game, the number of turns will decrease, but 10 provides a common baseline for most 2-4 player games.

Second, total output will differ based on when the production begins. Started at the beginning of a game, Production will generate the greatest returns. If Production is started on the last turn, it provides no benefit (plant's excepted).

Minimum Production

For evaluative purposes, Awards and Milestones will be ignored. This makes the minimum Production for all resources 0mc, except plants. Plants may be spent to boost final scores at End Game (if they total 8). Thus, plants will have one extra generation of production if produced on the last turn of the game.

Maximum Production

For all resources, except plants and Electricity, the maximum production is 9 turns of production. Thus, generating 1mc per turn will yield 9mc in total. Remember, production on Turn 1 is impossible as no production will occur until the start of Turn 2.

Plants receive a maximum of 10 turns of production since they may be used the turn after the game ends in an end game condition style mechanism (described in Minimum Production above). During this last turn, a plant can only be spent for 1VP since there is no oxygen. Both of these have minor impact on plant calculations, but they are factored into the table below.

Electricity takes an extra turn before become usable heat.

Electricity Production has an additional built-in delay of 1 turn. This is because electrictity becomes Heat on the turn after it is generated. Thus, an Electricity production on Turn 1 will become Heat on Turn 3. This delay means electricity production has only 8 turns of useful maximum production.

Average Production

For most resources, average production occurs for roughly 4.5 turns (9/2). Plants will undergo 5 turns of production (10/2), while electricity will experience 4 turns of production before becoming heat.

Value of Production

The value of production is calculated for Maximum and Average production. Minimum production is always 0, so it isn't worth noting. Multiplying out the production, and assuming every resource is efficiently spent on generating VP (e.g. every amount generates a VP), the following values are calculated for each Resource Production:

	Actual		Normalized
Production	Max	Average	Max	Average	Return
Money	9	4.5	9	4.5	1
Electricity	11	5.5	13	6.5	1.181818
Heat	15.75	7.875	14.625	7.3125	0.928571
Iron	18	9	18	9	1
Plant	28.75	14.375	16.25	8.125	0.565217
Plant-oxy	28.75	15.8125	30.875	16.25	1.073913
Titanium	27	13.5	27	13.5	1

Actual and Normalized Resource production values

Summary

The Return of all Production values didn't change, except for Plants which generate oxygen. This dropped slightly from 1.13 to 1.07. This is due to the last turn of production being worth just slightly less. Still, it remains above 1, which indicates it is still a good option.

When looking at Totals output, Plant production is always the best purchase by a long shot, especially when Normalized to VP values. Titanium and Iron make a second and third "best" investment, but this is only if the Titanium and Iron can be converted directly into VP.

With Production values and resource values determined, it is now time to begin evaluating the "worth" of elements in the game.

Terraforming Mars: Valuing Resources

2018-12-16T00:44:00.000-07:00

Resources

The goal of this post is to normalize the cost of all resources for comparison purposes.

Normalized & Actual Cost of Resources

Calculating the Actual value of a resource requires looking at that Resources Standard Project cost and dividing by its conversion rate (typically 8). Similarly, the Normalized cost is the VP cost (13) divided by the resources conversion rate.

Money (mc)

Money is the easiest to calculate, as it is the basis of all analysis, 1mc=1mc. This is both the Normalized and the Actual cost for money.

Steel & Titanium

Iron and Steel are worth 2mc and 3mc. This is because Iron and Steel may be traded 2 to 1 and Titanium 3 to 1 when play Buildings or Space tags, respectively. For this to work, we will assume every token of generated either resource is also spent.

Normalized Heat & Energy

It takes 8 Heat to generate one Temp increase (1VP).Thus, Heat and Energy have the same "normalized" cost of 1.625mc.

Plants

8 Plants will generate 1 Greenery tile. This will provide either 1 or 2 VP depending on if Oxygen will increase or not. With Oxygen, the Normalized value of Plants becomes 3.25mc, and without Oxygen it is the same as Heat or Energy, 1.625mc.

Cards (Patents)

It costs 3mc to keep a card in a player's hand. Therefore, if a card is generated it "saves" the player spending 3mc to keep the card. A card's value will differ depending on the card, but all cards can be sold for 1mc. Thus, the card's least value can be calculated as 1mc. If, after calculating a card's effectiveness, it is less than the value of selling a card, it would be best to sell the card.

Summary

In this post the value of individual resources were determined. From this, the calculated values for each resource are as follows:

Resources	Actual Cost	Normalized	Effectiveness
Plant w/oxy	2.875	3.250	1.130
Plant-no oxy	2.875	1.625	0.565
Heat	1.750	1.625	0.929
Electricity	1.375	1.625	1.182
Card (traded)	3.000	1.000	0.333
Iron	2.000	2.000	1.000
Titanium	3.000	3.000	1.000
Money	1.000	1.000	1.000

The most surprising result of this analysis is the most effective move possible is to gain Energy, although no cards offer this. This is because of the reduced cost in comparison to Heat. Next post will concern with calculating Production values of various resources.

Terraforming Mars: What a Game Looks Like

2018-12-12T00:00:00.000-07:00

Charting a Game

(Pre-Note: Information I have is limited to 3 & 4 Player games. I am looking for data on 5-Player games, and if your interested in helping me collect data, please contact me at: cfolmar@gmail.com. I'd like to create a library of Game Plays and share the results after a period of time. If enough interest, I'll create a sheet to download and record game plays with instructions).

Having determined the magical 13MC/VP, it's time to look at what a game actually 'looks' like. This is important to determine how long a game of Terraforming Mars lasts. It also shows an interesting trend.

Any individual play will differ based on a number of factors: corporation chosen, card draw, player experience, set chosen, etc. The focus of these individual factors is for later blog posts. For this analysis, however, we will look at the total VP given out to all players each turn. We will also only look at the Terraform Rating gained from working towards one of the main End Game conditions. So, for example, if during Turn 1 Player A increased Oxygen 1 Step and Player B increased the Temp 1 Step, then Turn 1 earned a 2 VP total (just to different players).

This may seem a strange and arbitrary way of looking like at a game, but the insights are amazing.

3-Player Game

We start with a four 3-player games (graph below). The important thing to see is how the games ended from Generation 10 to 12. More can be seen, but we will dissect it more later in the post.

3-Player Games

4-Player Game

Next we look at 4 player games. Here the games end from Generation 9 to Generation 12. Still, despite the somewhat shorter games, for which there is a reason we will go into later, we can see the beginning of a definite patter. To make it more obvious we will take the average of the 3 and 4 player games and compare them.

Comparison: 3v4 Player Game

The games above may seem to have no pattern, but when we average the games together, and compare these averages, we see a definite pattern. I've included an average of the 3-player and 4-player games as a reference in the graph below.

Here we can see the general outline of a game take shape. The game starts with an initial rush of Terraform Rating increases, immediately followed by a slight dip in turn 2. We can begin our analysis here on a relatively turn by turn basis.

Turn 1 - Initial Grabs: Turn 1 sees a player's jockeying to get some early initial TR. This can provide a boost to income in later turns, and (as we'll see), an boost early is significant. I suspect much of these initial boosts are also related to the Heat bonuses on the Temperature chart at the 3 position.

Turn 2, 3, 4-Economy Setup: These turns see players grab a few additional TR, but money is in
shorter supply as they are now dependent on 'self generated' income and not on the initial income. This is also where most players begin focusing on building their economy. This may be either to supplement their gains from Turn 1 (focusing on Heat production), or building resource mining operations.

Turn 5, 6, 7 (& 8)-Milestone Grabs: Here we see real activity occurring. In particular there are three points of interest.

First, the economies built from turns 1-4 have come to fruition. Players actively begin grabbing TR at a rapid rate. These are not haphazard, however, and lead to the second indicators.

The Second point is the "Turn 5/6 Plateau" in 4-player games or, in 3-player games, the "Turn 5/7 dips". I suspect this is caused as players begin to snatch up the Milestones. In both types of games this would be a reduction in total income of 24MC. However, in the 3-player games the removal of the MC effect is more pronounced.

Lastly, there is the Peak. In 4 player games this peak is more pronounced and definitely occurs around Turn 8. In the 3-player games, given the smaller total economy of all the players, the curve occurs around turn 8 and 9, but is still present. This is also when players hit those Upper Level Environment Bonuses (Free Temp & Ocean). Even if not grabbed, another player may rush to get the last Ocean in place to prevent an opponent from getting the full benefit, which has the same net effect on our graph.

Turn 8, 9, 10, 12 - Decline and Game End
Typically by Turn 8 the TR purchases are in decline. Instead, players have changed to focus on grabbing the Awards, which are a big drain on the overall economy (-22 MC to purchase first two awards, -42 to purchase all 3 awards). In the end, there are only a few TR left to grab so player's position to maximize their score by purchasing Settlements next to Greenery, blocking opponent's, or pursuing VP maximizing cards.

Conclusions

Looking at the games, most 3 and 4 player games follow a definite pattern (although anomalies exist: keep reading if interested below). Although there is enough variation in the game to keep it interesting and challenging. Understanding the flow of a game will assist in recognizing what to expect in the game.

Lastly, it is important to recognize that most games end around the 10 Turn mark. Some finish earlier, some later, but a good game length is 10 Turns. This will become the standard used in calculating values in later blog posts.

Interesting Anomaly

Look at the graph of a 3-player game below which is somewhat anomalous:

First, There is a huge initial TR grab on Turn 1. Second, the game was over by Turn 10, with almost no plateau, although one huge dip in Turn 7. Except for the Initial Turn 1 Grab, it looks like a fairly standard, if short, game.

The reason for this game is because of 2 of the corporations chosen by players and both choosing a similar strategy. The Corporations were Credicor and Teractor. Both of these have high initial MC (57 & 60 respectively). Both players decided to take no cards and, instead, just purchase Temp increases. These two players accounted for 8 of the 9 TR in the first turn (4 each). The 9th was purchased by the 3rd player. The two of them continued to purchase TR throughout the game until Turn 5. Around Turn 4 they switched to Oceans, and used ocean placement plants to power Greenery tiles.

Both players seemed in competition (the third player was never really in the running) until Turn 6. At that point Teractor switched strategies. While Credicor would continue purchasing Oceans and Heat, Teractor purchased Greenery outright and grabbed the Gardner milestone. On Turn 7 both players switched to Cities to try and gain the Mayor Milestone, which explains the sudden drop of TR. Teractor, due to Turn order, managed to beat Credicor to that milestone again, although Credicor did burst forth on Temp claimed Terraformer, it was too late.

At first glance, this game appears to defy the "average" game described earlier in the article. However, on closer examination we can see the same overall pattern. Except for the dip on Turn 6 and 7, this more closely resembles a 4 player game than a 3-player game. This is due to the players opting for the same strategy with two corporations with unusually high initial incomes.

Terraforming Mars: Cost of a VP

2018-12-09T00:00:00.000-07:00

What to Buy

Last post looked at how VP are scored and their cost. Summarizing the results below:

Item	Number	Points each	Ind. Cost(MC)	Total Cost(MC)
Ocean	9	1	9	162
Temperature	19	1	14	266
Oxygen	14	2	23 (with greenery)	322
Totals	42	56		750

Next step is to determine the money value of a VP. The goal here is to achieve two things:

"Normalize" the cost of all the cards to give an accurate determination of the card's values, which let's us determine...
Which action is relatively "best" to take in terms of earning VP.

To start the evaluation, a baseline needs to be created. For this, imagine a game played with two simple rules:

Only permit Standard Projects,
Only spend mc to end the game. (greenery, Temperature and Water).

How much would each VP cost? This provides a good starting point to determine the value of each card, resource, and even the location of map board spaces.

Weighted Average

To figure this out, use a technique called weighted average (or Weighted Arithmetic Mean).

One wrinkle in Terraforming Mars is Greenery tiles. Greenery tiles provide 2 VP instead of 1 VP. Thus, a greenery tile will yield slightly better on average VP than, say, Temperature. Overall, its not difficult to figure out (the values are already in the graph above). To do so, divide the Total Cost (750) by the Total VP (56).

This yields: 13.39 MC/VP!

But, what about...

The number above assumes purchasing every VP earned throughout the game. Terraforming Mars has a little "bonus" system which changes things up a bit. If Temperature is increased first, an Ocean tile gets placed for "free". Similarly, increasing Oxygen first yields a "free" Temperature. These bonuses change the amount of money spent. In fact, there are four scenarios to figure out:

Least Efficient Terraforming: Pay for everything.
Semi-Efficient Terraforming 1: Pay for All Heat, 8 of 9 Oceans, and All Oxygen
Semi-Efficient Terraforming 2: Pay for All Oxygen, All Oceans, and 18 of 19 Heat
Most Efficient Terraforming: Pay for all Oxygen, 18 of 19 Heat, and 8 of 9 Oceans

Doing an analysis on each scenario creates the following table:

Least Efficient:	13.39
Least Semi-Efficient:	13.07
Most Semi-Efficient:	12.91
Most Efficient:	12.28
Average:	12.915

Normalized vs Actual Cost

To simplify analysis, a value of 13mc will be used as the baseline cost for a single VP. This is the "Normalized Cost", where everything is measured from this "normalized" value of 13mc/VP.

"Actual Cost" is how much something would cost to normally generate. For example, while 1 Temperature has a "Normalized Cost" of 13mc, the "Actual Cost" for Temp is 14mc as indicated on the Standard Project's Chart.

Effectiveness

From these two costs it is possible evaluate a "Return" rating, which is simply the Normalized Cost divided by the Actual Cost. In a manner of speaking this is the "return on investment" for performing a specific action. Looking at the Standard Projects which generate Victory Points, we have the following chart:

	Actual Cost	Normalized	Return
Greenery (w/ oxygen)	23	26	1.13
Greenery (no oxygen)	23	13	0.57
Temperature	14	13	0.93
Water	18	13	0.72

1 Greenery may be played to generate Oxygen, or after Oxygen is maxed, thus the two entries.

The greater an Action's Return, and with no other external considerations, the more valuable the Action. Thus, from the chart, and with no other factors affecting it, Greenery when the Oxygen is not capped provides the greatest Return than all the other options. If one had 28mc to spend and could only spend it on Standard Projects, it would be smarter to purchase a Greenery tile than all other options listed.

Summary

We learned the following from the above:

Cost of a VP = 13mc
"Actual Cost" is the stated cost to perform an Action
"Normalized Cost" is the cost evaluated against the accepted cost of a VP.
"Return" is a measure of relative value of an Action, with the better actions having higher Return, if no other considerations exist.

Terraforming Mars: Reaching the End Game Condition

2018-12-02T00:00:00.000-07:00

Making Mars Habitable

The first step to understanding Terraforming Mars is understanding the Terraform Rating (TR). There are three basic ways to increasing the TR of a player:

Increasing Oxygen from 0% to 14% (each Step is 1%)
Increasing the Temperature 2 degrees from -30°C to +8°C (each Step is 2°C)
Placing an Ocean tile onto an Ocean space (each Ocean is a Step)

Each increase of a Step increase of one of the above increases the player's Terraforming Rating 1 step. Terraforming provides two things for a player. First, it is the player's base "score". Second, at the start of a Generation (a round of Terraforming Mars) it provides the player with some base income. Unlike most games, a player's Terraform Rating begins at 20.

Breaking Down the Steps

Ocean Steps

There are 9 Ocean tiles which need to be placed on the board. Placing an Ocean tile on the board typically grants some other benefit based on where the Ocean is placed. The Standard Project to add an Ocean costs 18MC.

Temperature Steps

Temperature increases along the track on the right hand size of the board. There are 19 Steps of Temperature, but three particular Steps provide additional bonus. At -24°C (Step 3) and at -20°C (Step 5), the player's Heat Production increases. At the 0°C mark (step 15) the player also gets to place a free Ocean tile, if there is an Ocean available.

There are two means of increasing Temperature, Heat and Standard Projects. The Standard Project cost for Temperature is 14MC.

The second way is to spend Heat. As the game progresses from Generation to Generation players gain Heat equal to their Heat production. Once a player has collected 8 Heat, they may trade that Heat into 1 Temperature increase.

Oxygen Steps

Oxygen is tracked along the top on the Oxygen track. There are 14 steps of Oxygen, but Step 8 grants a benefit of bumping up Temperature 1 Step as well, if available. Oxygen is typically increased by placing Greenery tiles. Every Greenery tile adds 1 Step when it is placed on the board. Greenery tiles are added either through the Standard Project (cost 23MC) or by trading in 8 'Plants'.

Plant production works similar to Heat. You gain Plants based on a player's Plant Production each generation. When a player has collected 8 plants, they may be traded in for a Greenery tile.

Greenery Tiles

Despite their expense, Greenery tiles offer an additional benefit. Every Greenery tile on the board gives the player who placed it an additional VP at the End of Game Scoring. Thus, although they cost 23 MC, they provide the player with 2 VP: one for the Oxygen increase and one for End Game Scoring.

Bringing It Together

Terraforming Mars ends once all the above Steps are met. Thus, in a game, there is a minimum number of VP available to the players:

Item	Number	Points each	Ind. Cost(MC)	Total Cost(MC)
Ocean	9	1	9	162
Temperature	19	1	14	266
Oxygen	14	2	23 (with greenery)	322
Totals	42	56		750

Yes, there are 42 Steps to Terraform Mars (which answers some questions). Using just Standard Projects, this gives us 750MC to put them into play, and will yield a total of 56 VP to be divided among the players.

This is the starting point for analysis of the game's economy, which we will perform in our next post.

Terraforming Mars - Up Next

2018-11-25T17:41:00.001-07:00

Terraforming Mars

Been...a long time. But, I've decided to do similar analysis to Through The Ages on a different game: Terraforming Mars. This will be a card by card analysis, as well as the map, and a little statistics.

Terraforming Mars is a fantastic game, one I have played almost 50 times last year alone. This year I've easily matched that many games, if not exceeded it.

I plan on releasing one article a week (more when able). Usually it takes me awhile to compile the game results. After that, I need to get a format down and then I can usually replicate it fairly quickly.

On a related note, I plan on changing how the blog interfaces with the spreadsheets and charts. Originally, I embedded the sheets and graphics from Google, but overtime the links broke. So, I'm going to screenshot and capture the images, so the blogs will work regardless of Google's changes.

About Terraforming Mars

Terraforming Mars (TM) is designed by Jacob Fryxelius. The object of the game is to...well...Terraform Mars. Each player takes on the role of a corporation whose goal is to make the Red Planet habitable. The players run, and improve, the economy of their corporation to better achieve the goal of Terraforming Mars into a Habitable planet, earning

Habitable, not comfortable.

Players gather cards (called "Patents") and pay for these patents. Typically, each patent is a more efficient means of increasing some resource, or one of the "Resource Steps". The catch is every Patent costs 3mc to keep (yes, it is officially "Megacredits" and has it's own symbol, but I'm going to use 'mc' to identify it as I can't get the TM currency symbol to appear easily where I need it).

Game End

The game ends when the planet's Oxygen is moved up by 14 steps (0% to 14%), Heat is increased by 19 steps (-30C to +8C), and 9 Ocean tiles are placed. Each of these "steps" gives the player who increased it an increase of 1 Terraform Rating (TR) and increases their income by 1mc.

Points are tallied based on Patents played, ending Terraform Rating, tiles placed, Awards and Milestones gained. The player with the highest points wins, and ties are decided on the player's remaining Megacredits. If you haven't played Terraforming Mars yet, I highly recommend it

PS: It is available on Steam and, except for a few bugs, works great.

What to cover next...

2017-06-19T12:09:00.000-06:00

I'm debating on where to start next. I'm think I will finish off the Here I Stand (HIS) Strategy blogs which I started. I've since played several dozen games of HIS since my hiatus. There have been many great games out there since.

So, what game do you feel I should work on next? Give your feedback in the comments or feel free to email me.

Back at it

2017-05-30T22:47:00.000-06:00

Been some time (years actually), but I'm restarting this blog again. going to give it another go and see what happens.

Dominion I - Tracking Score ()

2017-05-30T22:44:00.000-06:00

This blog post is brought to you by another contributor and friend of mine: "Sapphire Harp".

One of the most important things about playing Dominion competitively is knowing the score. In Dominion, the leading player is based on who has the most victory points in their deck. You aren't permitted to look at any player’s decks during the game, so this is hidden information - but it’s easily knowable. In every game, all players start with three victory points and will show all other players whenever they purchase more. It’s a simple matter to keep track, especially if you use a notepad to write on.

The advantage of keeping track is being able to make smarter decisions towards the end of the game. One of the players is going to decide when the game ends by buying either the last Province or by buying the last card of one type ,once two other purchase options are sold out. If one player has a major advantage in a game, knowledge of the score won’t help change the outcome. However, if you’re contemplating buying that last Duchy and your opponent is two to four points ahead of you, knowing the score can make a big difference!

Keeping track of the score can also be a good method of evaluating your strategy, if you are less concerned about winning this particular game. Knowing the score moment to moment will let you see when your opponent is pulling ahead of you. It can also give a sense if they’re making poor decisions and getting lucky draws, or if their strategy is a superior one. Maybe you’re using an over complicated approach and buying too many action cards, while they quietly pick up VPs every three or four turns.

Dominion - Main VP cards

Whether you want to keep track of the score or not usually depends on how important winning that specific game is to you. If you’re playing with friends, I strongly recommend against it unless you all enjoy one-upmanship. If you’re in a competition playing Dominion for prizes, I would anticipate every player keeping close track - either mentally or on paper. And I find using a scratch pad is a more accurate way to keep track, which is important because the games you really want to win will often be decided by a small number of points.

Ultimately, deciding whether to keep detailed track of the score or not should be based on how tolerant your other players are to the delay. You could easily be performing addition instead of making decisions when your turn starts, so the other players will have to wait while you’re calculating. It isn't conducive to a good time, so it’s important to streamline the process if possible.

At first I kept running totals, but eventually switched to a simpler method I now prefer. The total number of points accumulated isn't important, in itself. All you actually need to know is who’s in the lead and by how much. To do this I use individual
columns for each player. When a player gains victory points, I write that digit in their column. When all players have gained an equal number of points, I cross out all of those digits together.

For example, I buy a Duchy and an Estate, so I’d either write a ‘4’ or a ‘1’ and a ‘3’ in my column. My first opponent buys four Estates for no understandable reason, so I’d probably write a ‘4’ in his column, but might write ‘1’ four times. My second opponent buys a Province, but already has two Curses in his deck. I put a ‘6’ in his column in addition to the two ‘-1’s I've already written there. Then, because we've all changed scores by a matching value, I cross all of these digits out.

Scoring Sample: At this point, everyone has
accumulated 4 points so simply start over at 0

I believe it presents a smaller mental demand than totaling scores as you go, as well as being faster to write. It isn't going to keep the other player’s waiting more than a couple seconds. Additionally, it keeps you thinking about the score in terms of the cards, themselves. A player might be nine points ahead of you, but it could be because they have a Province and a Duchy, or it might be because they have a Duchy and six Estates. These two possibilities represent very different levels of challenge from your opponents and it’s good to know which is occurring.

Not totaling also offers a little flexibility if your current game involves cards which change in value over time. Gardens are a frequent problem for keeping track. Dukes from the Intrigue expansion present another. In these games, I would use ‘G’s and ‘D’s to keep track of those purchases. Crossing them out isn't an option since your Garden’s value will not match your opponent’s. I usually didn't keep exact track of deck sizes in Garden games, but you might find it important enough to do it.

As for Dukes, it should be relatively easy to know the value of your opponent’s deck if you use exact values when writing down digits on your pad. In that situation, you can look at their column and see how many ‘3’s there are, whether crossed out or not. That count will be the value of their Dukes. Also, once all of the Duchies are purchased, the Dukes become a fixed value for the rest of the game. At least, it’s highly unlikely a Duchy will be discarded at that point.

This is the best and quickest method I've come up with for tracking the score of Dominion. If you choose to give it a try, your mileage may vary, but I believe this style has a considerable amount of advantages. You will want to adopt and adjust to find the practices that work best for you. And it will change from game to game, depending on what your card selection turns out to be.

New Dominion Post!

2014-08-04T22:05:00.000-06:00

Hello Everyone:

Starting next week I have a guest blogger writing Dominion posts for me. The contributor is a good friend of mine and, obviously, a fellow gamer. I plan to post these new offerings on Friday mornings starting 8/15. We have a set of 5 blogs written and going through final editing.

If you have a suggestion or would like to contribute, please email me! If you have a favorite game you'd like to discuss in depth, drop me a line. I give credit where it is due and want this blog to grow in popularity. Just drop a line to: cfolmar@gmail.com.

Thank you and thanks to my first contributor: Sapphire Harp!

HIS-English: Assault of Scotland

2014-07-27T23:14:00.000-06:00

Goal: Scotland

Attacking and defeating Scotland is possible on the first turn. It is not difficult, but it does require the expenditure of several command points. The goal is to capture Edinburgh as quickly as possible. The required steps for this plan are as follows:

General Plan

During negotiations with France, DO NOT offer an alliance with France. You cannot declare war on Scotland if allied with France.
Spring Deploy troops from London to Berwick.
Move both navies to the North Sea (2 cp).
Play English Home Card to Declare war on Scotland.
Move troops to Edinburgh and lay siege to it.

York vs Berwick

It is possible to launch an attack from either York or Berwick. If launched from Berwick, it will be necessary to spend at least 1 cp for a mercenary and then spend 1 cp to move into Edinburgh. The other option is to Spring Deploy to York and move all troops to Edinburgh. This also takes 2 cp of movement.

The Berwick approach is the better option. Both options require 2 cp, but replacing the York regular infantry would cost 2 cp whereas the loss of the mercenary effectively brings the player back to their starting pieces.

Average Losses & Winning the Combat

On average, it takes 9 dice rolls to eliminate the units in Edinburgh. Mustering enough troops to reach these 9 dice rolls will require at least 8 troops. With only three cards, and the 4 cp required to lay siege to Edinburgh, getting the additional 5 cp of troops needed to meet this in one die roll is highly unlikely. Therefore, England will need to combat Scotland at least twice.

England can expect between 2 and 4 losses. Therefore, England should begin the invasion with at least 2 mercenaries, with 3 being preferable.

Benefits and Challenges

If successful, England conquers Scotland and controls Edinburgh. This gains them one Key and an additional card draw per turn. Given Edinburgh's remoteness, it is unlikely anyone will be able to retake Edinburgh. This makes conquering Scotland an attractive target for England.

The worst case for England is if France intercedes on Scotland's behalf. In this case, the French could spend resources tying up England in a War in England. This essentially places England in the unenviable position of fighting a war both on their island and near Calais.

HIS - English - Turn 1

2014-03-19T00:30:00.000-06:00

Scotland, New World, or Preparation?

On the first turn, the English player cannot use their Home Card to advance their marriage. This leaves the question of "Marriage" for the next turn. Still the player needs to decide on Scotland, the New World or simply Preparation.

Given the few cards the player has to begin with, it is necessary to choose one of the three and then focus on that goal till it is achieved.

Goal: Scotland

Scotland is Light Blue Minor Power
in the Game

Attacking and defeating Scotland is possible on the first turn. It is not difficult, but it does require the expenditure of several command points.

Rewards

2 VP with the new Key,
Immune to the "Scots Raid" card (which is loss of English troops), BlueSecure the Northern Border from a possible French activation of Scotland later,
An additional Card Draw.

Challenges

Not having enough Command Point cards in hand,
Revolt in Ireland will disrupt English Troops,
France could decide to intervene and actually attempt an early war with England,
Scots Raid,
Gout,
Poor Die Rolls will leave the Scottish in place.

Goal: New World

New World

Exploring the New World can grant some Victory Points and cards. Both of these are items which England needs. There are three ways to complete this goal: Conquer, Exploration and Colonization. Each has unique benefits and risks.

Rewards

Permanent Victory Points

Conquer (1-2 VP)
Exploration (1-4 VP)

Potential of additional card

28% - Colonization
83% Conquer

Challenges

"Loss" of spent command points for no gain

Colonization (2CP): 17%
Exploration (3 CP): 33%
Conquer (4 CP): 72%

with Smallpox: 42%

Delayed through card play

Exploration
Colonization

If the New World is chosen, Conquering is the least likely opportunity for England. If successful, however, the reward is both a Card and permanent Victory Points. This costs a whopping 4 Command Points, however.

Goal: Preparation

Preparing England

Preparation consists of simply building up your forces. This should consist of building both a naval force and land troops. Both of these types of units should be placed in Calais. The most "safe" strategy, it does permit the player to focus on a Marriage/New World for the following turn.

Benefits

Gain military units

Challenges

Revolt in Ireland can delay, but not stop, the build up.

Review

Of the strategies, the most likely to succeed is the capture of Edinburgh. If disrupted, however, it can leave England fighting a war on its island. However, France is already at war with two other forces, and if either the Hapsburgs or the Papacy can be convinced to attack France, France will most likely ignore England.

France may also opt to ally with Scotland, thus providing France one of its two keys needed to gain another card. If Scotland holds without France's assistance, France can find itself in a better position.

If going the Preparation route, it is recommended to spend the Home Card on an Exploration and a Colonization action. The potential gains generally outweigh the potential risks in a long term gain. In this scenario, England should hold one card for the following turn.

HIS - English - Overview

2014-03-05T00:30:00.000-07:00

The English

The English are the Red forces in Here I Stand. Like the Ottomans, the English have a few fairly straight forward decisions to make. Unlike the Ottomans, the English decisions begin on the first turn and greatly impact their ability to achieve various goals. Forutnately for beginning players, the initial decisions are "cut and dry" and only occur after other events in the game happen. In my opinion, this makes the English one of the more "Strategically effective" factions to play, but still easy enough for new players to grasp the various areas of play.

Strengths

The English are the most versatile of the nations, capable of amassing an army for military conquest, explore the New World, and even actively participate in the Protestant Reformation. This flexibility permits them to garner points in a variety of ways, but none so potentially quickly as the "Creation of an Heir".

The English Home Card, King Henry VIII, grants the powerful ability to declare war against a Power outside of the diplomacy phase. However, it is also the only way the English King has of achieving a suitable Heir to the throne.

Weaknesses

The English have several serious shortcomings. Like the Ottomans, their starting position on the "island nation" is a liability, but it is also a benefit. The island nation is unlikely to be attacked"by an enemy nation, but it is relatively easy to blockade the English ports, preventing the creation of large armies. Fortunately, the English can raise an almost unbeatable navy, but at great expense in Command points.

Again similar to the Ottomans, the English have a "War Card" worry, which can cripple their plans, particularly if it comes out early. The worst timing is if it comes out on Turn 1 or 2, just after the player declares war using their Home Card. It is only 4 troops, but 4 troops is enough to halt an English offensive in its tracks.

"Fortress England": Difficult to Assail, Difficult to Leave

The last major weakness of the English is their lack of cards. The English player, more so than any other player, is tempted to go in all avenues for Victory Points. The New World and its riches await, Conquering Scotland seems a necessity, and the player still needs to go for an Heir. Later, there is the Protestant Reformation to support. All of these require cards, however, and the English player is extremely limited in this regard. Therefore, the English player needs to focus on one or two

"The Heir Issue"

English Home Card

Historically, King Henry VIII's desire for a male heir drove many of the events, decisions, and (ultimately) changed the history of not only England, but of the world. Representing this, the English player's additional concern is about acquiring a male heir to the throne. There are two major impacts on the English player's game revolving the quest for an heir: Victory Points and Successors. This is an important enough discussion it will be handled in a later post.

Home Card

The English Home Card is one of the most powerful cards in the game. Not only does it grant the ability to advance the Marriage marker, but it also grants the ability to declare war during the Action Phase. The use of the English home card can seriously disrupt the plans of any of their nearby neighbors. The Spanish and French players must be particularly aware of a build up of English forces in Calais, as they represent a potential threat which should not be ignored.

Through The Ages - Cards - Alex Randolph

2013-06-28T00:30:00.000-06:00

This is a series of blogs written about each card in Through The Ages. To find more, simply click on "Cards" label.

Alex Randolph (Sid Meier)

History

This card is named Sid Meier in later version of the game. However, I will defer to my version of the game and will bio Alex Randolph.

Alexander Randolph was born May 4, 1922 and died May 10, 2004. He spoke four languages fluently and was an avid game designer. Although born in the United States of America, he traveled extensively and lived in many countries.

Alex Randolph created several well known games, and pioneered several game mechanics which are now considered 'everyday'. His games include: Twixt, Raj, Sagaland (Enchanted Forest), InKognito, and Breakthru. It is almost impossible to list all the games he had created here. However, he is recognized as one of the world's most prolific game designers, with his games having been on the selection list for the Spiel des Jahres award no less than 10 times, among numerous other awards.

Alex Randolph's philosophy involved games as a very human activity. Games define the human animal. It is human nature to create a way to describe the universe and to simulate them. To him, games are the mechanism by which humans simulate this.

However, it is also a feedback loop: the games influence the animal. Games are what permit us to describe the universe, but they also end up shaping our culture. Given the same core game, different cultures will modify the rules differently, eventually creating two distinct games. These games then may become popular, imprinting and reinforcing a style of thought on those that play the game.

Game Stats

Alex Randolph is the most popular Age III leader. Statistics seem to support choosing him as an Age III leader, given such a high win ratio.

Opinions

Randolph provides a significant boost to culture at a time when science resources are waning in importance. The four rounds of science which Alex could generate can add up to 12 culture at the loss of 4 science. And that is the gain/cost per lab! This is a significant gain fora marginal cost and one which shouldn't take much thought. Of all the Age III leaders, Alex Randolph is the only one which can be played without any hesitation with regards to the situation.

Through The Ages - Albert Einstien

2013-06-24T00:30:00.000-06:00

This is a series of blogs written about each card in Through The Ages. To find more, simply click on "Cards" label.

Albert Einstein

History

One of the most unique minds to inhabit our planet was born in Ulm, Germany in 1879: Albert Einstein.
He was a talented musician in the piano and violin. Hus family moved to Switzerland and Italy, and he graduated High School in 1896 in Switzerland. His grades were good enough to graduate in all subjects except mathematics and science, at which he excelled with maximum scores. He applied for ETH Zurich for advanced training later that year at the age of 16.

His goal was to attain a teaching position when he graduated, but he failed in that endeavor. His classmate secured him a position at the Patent Office in Bern, Switzerland. His specialty was evaluating patents for electromagnetic devices. Many of these patents involved synchronization of timing devices using electronic signals, items which become important in his "thought experiments" when he wrote his papers.

In 1905, still at the patent office, Einstein was a landmark year. He published 4 papers that year, one of which covered the equivalence of Energy and mass. By 1908, Einstein was a recognized scientific leader. It took another 7 years before Einstein finished the "General Theory of Relativity", but experimenters were quick to confirm the accuracy of his findings. For his efforts, Einstein was given the Nobel Prize in 1921.

Einstein's equations unlocked a several secrets of the universe. His equations permitted the development of television, lasers, and modern electronics. It also unlocked atomic power, both its peaceful and military applications.

His personal life was one fraught with successes and failures as well. He was married twice and had three children. Einstein died April 18, 1955 in Princton, New Jersey. Albert Einstein's name is recognized worldwide and has become synonymous with "genius" in many cultures. His legacy lives on as mathematicians, physicists, and philosophers try to complete the work he started by unraveling the mysteries of light, matter, and energy.

Game Stats

Albert Einstein grants a great boost to both science and culture. This late in the game Einstein's science will only be of benefit for a very short period of time. Einstein has a (relatively) high first place rate, this may be the effect of already acquiring a successful culture engine rather than contributing to it greatly. Still, Einstein's ability to get critical technologies out in a short time may contribute to additional bonus cards.

Opinions

I view Einstein, like most Age III leaders, as extraneous. If he appears early in Age III, he might be worth the two actions required to bring him out. Einstein's boost may be critical for completing some Age III technologies before time runs out and adjust final Bonus scoring. Still, if he appears late in the game, actions may be better spent on other things.

Through The Ages - Cards - Mahatma Gandhi

2013-06-22T11:52:00.000-06:00

This is a series of blogs written about each card in Through The Ages. To find more, simply click on "Cards" label.

Mahatma Gandhi

History

Mohandas Karamchand Gandhi was born October 2, 1869 in Probandar, India. At 13 he married a woman one year his senior in an arranged marriage. Growing up he loved stories of an ideal life, truth, and justice.

In 1888 he traveled to England and studied law. After completing his studies he failed at opening a law practice in Bombay for being too shy in court. In 1893 he traveled to South Africa for rich Indian Muslims, but once there he found himself facing both rich Indians and those who were indentured servants. During that time he was thrown off of trains, beaten, and subjected to other indignities for being "Indian" in a "British Colony". Never during his stay, did Gandhi raise a fist in anger, but instead would focus on civil disobedience through non-violent means.

Upon his return to India in 1914, Gandhi brought his non-violent civil disobedience to free his people from British rule and discriminatory practices. Gandhi joined the Indian National Congress and advocated for self-rule of the Indian nation. He attempted to alleviate restrictions on the poor farming class, promoted the education of women, end caste discrimination, and remove religious intolerance. Through his actions he rallied other Indians to rebel, not in violence, but through peaceful sit-ins, resigning from positions of power, and boycotts. For his efforts Gandhi was jailed several times, but eventually India was freed from British rule.

After a lifetime serving his people, Gandhi managed to get India its self-rule. He sat on the council which drew up the new nation's constitution. He taught Indians to view other Indians as equals, and he removed the barrier for women to be educated. Having achieved so much, freeing a nation and a people, the one hurdle Gandhi could not overcome was the religion. He attempted to reconcile the Muslims and Hindus, and for his efforts he was assassinated by a fanatic Hindu on January 30, 1948.

Gandhi's legacy lives on. India remains a country under its own rule. Gandhi inspires the oppressed and the weak that change the world around them through non-violent means and by leading a virtuous life.

Game Stats

Gandhi has horrible game statistics. His first place wins tie with Bach at 10%, with the only leader worse than him being Alexander the Great. Despite these statistics, Gandhi is a popular leader, being the 3rd most popular for his Age and appearing in 60% of the games! This makes him the most popular "bad" leader in the game.

Opinion

Gandhi is a losing player's leader. His popularity stems from his ability to prevent culture loss from Wars and Aggressions late in the game. Generally speaking, in many games, the player with the weakest military becomes the target of most other players in the game. They use their advanced military to steal culture from this weakest player. The result is the weaker player gets weaker, with the other players getting stronger. As we have seen, these usually don't affect the outcome of the game in Culture Points as Wars and Aggressions only count for less than 10% of the Winner's score (http://gamesstrategyandtactics.blogspot.com/2012/01/through-ages-part-x-culturewhere.html). However, most of that 10% of culture comes in Age III of the game (http://gamesstrategyandtactics.blogspot.com/2012/03/through-ages-part-xviii-military.html). Gandhi is merely a last ditch effort for a losing player to slowdown their culture loss.

In the 10% of games he won, however, Gandhi is an interesting character. The player with Gandhi went into Age III with a high culture generation engine and a weak military. Gandhi arrived early and the player took and played him immediately. The effect in this case was to prevent the militarily strong players from robbing the lead player of culture. The lead player could then concentrate on simply generating even more culture.

Unfortunately, such a strategy seems highly unlikely, only occurring in 10% of games.

Through The Ages - Cards - Rock & Roll Icon/Elvis Presley

2013-06-17T00:30:00.000-06:00

This is a series of blogs written about each card in Through The Ages. To find more, simply click on "Cards" label.
Elvis Presley (Rock & Roll Icon)

Rock & Roll Icon was later
renamed Elvis Presley

History

Elvis Presley (Rock & Roll Icon) was born January 8, 1935 in Tupelo, Mississippi. He learned to play the guitar from his uncles and a pastor. At 13 his family moved to Memphis, Tennessee. His teenage years were spent learning more about music, which seemed to predominate his thoughts.

In 1953 Elvis auditioned at several bands and record companies. He was usually told he did not have the voice for singing. He eventually found his way to Sam Phillips, who was looking for person capable of blending the musics of white and black. On July 5, after a failed night of trying to find the right "sound", Elvis suddenly jumped up and started "acting the fool" while singing. The members of the band joined in and Elvis Presley's singing career was born. Elvis' musical styling made his music difficult to get played on radio as the style was different than any other existing music types. Within a few short years, however, Elvis' music skyrocketed.

In 1958 Elvis was drafted into the military. When he was released from service in 1960's he found, much to his shock, that his music career was not over. He also returned from service with a taste for amphetamines. He would go on to make 31 movies and would release over 711 recordings.

Elvis' music styling combined Rhythm and Blues, Gospel, and "Hillbilly", as Country & Western was known in the 1940s and 1950s. Now referred to as "Rockabilly", a forerunner to modern rock music.

Game Stats

The statistics of the Rock & Roll Icon are average at best. Of the Age III culture leaders, he is the easiest to use.

Opinions
Elvis Presley, the Rock & Roll Icon, like most Age III leaders, is a last ditch effort to boost culture. From the statistics, he is not particularly effective. In general, it is probably better to concentrate on a good Age II leader and build wonders than plan on switching to Elvis. However, Elvis can assist in a happiness issue, which could be beneficial if it combines with some Age III bonus events.

Through the Ages - Card - Nikola Tesla/Bill Gates

2013-06-14T00:30:00.000-06:00

This is a series of blogs written about each card in Through The Ages. To find more, simply click on "Cards" label.

NOTE: Bill Gates replaced Nikola Tesla in a later edition of the game. The card effects are identical, only the image and name were modified. I wrote a brief biography of both. And, just to satisfy curiosity, I have the version with Nikola Tesla!
Nikola Tesla/Bill Gates

Bill Gates
History

Bill Gates was born in October of 1955. He is a leader and innovator in business, primarily focused on electronic computing environments. Bill Gates' founded the company Microsoft, which is the world's largest software company in the world. Through his leadership Microsoft came to dominate the personal computer market, and within a decade came to dominate the business world.

The Microsoft Windows Operating System runs the vast majority of computers in the world. By making the operating system relatively inexpensive, capable of running on inexpensive hardware, and allowing the free market to dictate which programs would be successful and which would not, Microsoft has shaped today's business world. Over its history Microsoft has been both criticized for its anti-monopoly techniques, but also praised for keeping certain computing environments free, namely the Internet browser market.

Bill Gates lives on (as of the time of this writing), so it is difficult to judge what his final impact on history will be, but as of now he is one of the most influential and powerful business leaders in the world.
Nikola Tesla
Nikola Tesla (10 July 1856 - 7 January 1943) was a Serbian physicist, mechanical engineer, and futurist who emigrated to the United States to work with Thomas Edison. Tesla is most famous for developing an alternating current (AC) system which functioned well. AC current allows us to use electrical power in our housing in a safe way.

Nikola Tesla experimented with X-Rays, vacuum tubes, radio signals and electricity. Much of today's modern inventions are based on Tesla's inventions and patents. Whereas most scientific discoveries, and many of the famous scientists of the past, were based on discoveries, Tesla's work focused on inventions. Tesla made practical use out of theories.

Despite a mechanical and electrical genius, Tesla was a poor businessman. He would become so focused on a given project he would forget all other responsibilities, and his business would collapse. Although he achieved astounding success in creating inventions, including later patents on tilt rotor aircraft using turbine engines, his business life was a disaster and he died impoverished.

Game Stats

BG/NT is only the second AGE III leader. The card's ability turns labs into an ore production center. Unfortunately, by the time Age III occurs, the time frame is so short there is little time to use the ore gained.
Opinions

BG/NT should greatly boost ore output, but given the short length of Age IV, the player needs to capitalize on it to maximize culture point production. For this reason, BG/NT is great for finishing a Wonder or boosting to some of the high end buildings. Expect the game to end shortly, however, so BG/NT will not be in play long.

Through The Ages - "Where the Data Came From" comment and response

2013-06-12T00:30:00.000-06:00

Shangliang Jiang asked where I received my data from. The full comment is below:

"This is a really cool website! I haven't finished reading all your posts yet but the Robespierre post made me think.

What are your thoughts on the extensions? Also, I was curious how you got your data.

Thanks!"

My response is below, and it describes where my data comes from:

"I'm glad your enjoying it.

The extensions are interesting changes and keep the game fresh. I don't believe all of the cards are as equally balanced in TtA, some Wonders are significantly better than the base set. That said, they are fun to play, which is the most important part of the game to me!

As for my data, I have one blogs on it from January 2012: http://gamesstrategyandtactics.blogspot.com/2012/01/through-ages-increasing-sample-size.html

Originally I used 20 games, then I increased it to 100. Not a whole lot changed with the increased set, mostly some minor jockeying for position, but there were a few changes.

The data game from the games played from Board Game Online (http://www.boardgame-online.com/) completed games. Each game was parsed and uploaded to a database turn by turn, action by action. Being a SQL Master, I further broke down the data into usable portions for analysis. Data was chosen randomly with the following conditions:
* No game had the same 4 players
* No individual player appeared in more than 3 games
* I did not participate in any of the games
* No game had a player resign
* Games had to be played to completion.

I'd like mention a special call out to a friend of mine, Brian Kowalski. Brian and I pored over different ideas of manipulating the data and discussing the results. He had some good insights, and we were both surprised by some of the statistics.

Thank you for reading and commenting!"

See, if you comment, or help me out, I will mention you. From this point forward you will be showered with riches, fame, and glory! Well, your will get mentioned on the page!

Through The Ages - Cards - Winston Churchill...Wait, I already covered him

2013-06-10T00:30:00.000-06:00

This is a series of blogs written about each card in Through The Ages. To find more, simply click on "Cards" label.
Winston Churchill

He is the next leader on the list. But, I already detailed him in this post here: http://gamesstrategyandtactics.blogspot.com/2012/03/through-ages-card-winston-churchill.html

So, that makes this the shortest card blog I have written to date. (In fact, he is the reason I began writing about all the leaders after a question from a reader!)

Through The Ages - Cards - Isaac Newton

2013-06-07T00:30:00.000-06:00

This is a series of blogs written about each card in Through The Ages. To find more, simply click on "Cards" label.
Isaac Newton

History

Born 25 December 1642, Isaac Newton would become one of the renown scientists of all times. He was born 3 months after the death of his father. At the age of 3 his mother remarried, leaving him to be raised by his maternal grandmother. After the death of her second husband, his mother returned and attempted to turn the now grown Isaac Newton into a farmer.

Accepted to the The Kings School, Newton would make great strides in mathematics and physics. By the time he graduated he had a formalized solution for generalized binomial theorem, established the foundations of what would become calculus, formulated basic properties of optics, and the development of the Law of Gravitation.

Newton's genius was widely recognized during his life. So much so he received special dispensation from the King to hold the Lucasian Professor of Mathematics, a position which normally required he be an ordained Anglican priest. Newton's views on religion differed widely from accepted doctrine, and he could not reconcile accepting becoming ordained for the sake of the Professorship. The King accepted his argument, and the dispensation was granted.

Newton would go on to further extend his theory of gravity to celestial mechanics. He stated the Three Laws of Mechanics and established the basis of cubics in analytic geometry. As a reward for his service, Newton was made Master of the Royal Mint, a position which required little work and a steady paycheck. However, Newton took the appointment seriously and gave up scientific exploration in exchange on changing the English coining standards and stopping forgers. Like many of his endeavors, he was successful. In 1717 Newton managed the transfer of the English economy from a silver to a gold standard. For his efforts, Newton would become the second scientist granted knighthood.

Newton died in his sleep on 27 March 1727.

Game Stats

Isaac Newton is the most popular leader in the game. His ability to increase science is seen as a critical skill by players. However, he also has an exactly 50% chance of coming the top 2 or coming in the bottom 2 positions.
Opinions

Another leader whose strength may be slightly overrated? My opinion of Newton is he is not as successful as another Age II leader: Robespierre. Overall, I believe the two will bring the same "gains" in science, but Robespierre (and his new government) will yield more civil actions than Newton in the long run. Furthermore, Robespierre will increase military actions.

The key to Robespierre's use lies in timing of government changes. Manage a single change of government, and make it during Age II when Robespierre is in play. This saves science and gains increased actions. Statistically, there is a slight advantage to Newton coming first, but the overall gains of coming 1st or 2nd goes to Robespierre.

Games - Strategy and Tactics

Terraforming Mars: Breathing Filters--and Minimum Requirements

Breathing Filters

Notes

Requirements

Mins & Maxes

Minimum Eventual Requirements (MinER) Cost Calculation

Maximum Eventual Requirements (MaxER) Cost Calculation

Optional Requirements

Terraforming Mars:Trans-Neptune Probe (and Template Explanation)

Trans-Neptune Probe

Explanation of Card Template

Going Forward

Terraforming Mars: Standard Projects: City

Standard Projects

City

Building Locations

Greenery Value

General Statement

Corporate Bonus

Conclusions

Terraforming Mars: A New View of the Map

Original Map

Elysium map

Hellas Map

Terraforming Mars: Production Valuations

Production Issues

Minimum Production

Maximum Production

Average Production

Value of Production

Summary

Terraforming Mars: Valuing Resources

Resources

Normalized & Actual Cost of Resources

Money (mc)

Steel & Titanium

Normalized Heat & Energy

Plants

Cards (Patents)

Summary

Terraforming Mars: What a Game Looks Like

Charting a Game

3-Player Game

4-Player Game

Comparison: 3v4 Player Game

Conclusions

Interesting Anomaly

Terraforming Mars: Cost of a VP

What to Buy

Weighted Average

But, what about...

Normalized vs Actual Cost

Effectiveness

Summary

Terraforming Mars: Reaching the End Game Condition

Making Mars Habitable

Breaking Down the Steps

Ocean Steps

Temperature Steps

Oxygen Steps

Greenery Tiles

Bringing It Together

Terraforming Mars - Up Next

Terraforming Mars

About Terraforming Mars

Game End

What to cover next...

Back at it

Dominion I - Tracking Score ()

New Dominion Post!

HIS-English: Assault of Scotland

Goal: Scotland

York vs Berwick

Average Losses & Winning the Combat

Benefits and Challenges

HIS - English - Turn 1

Scotland, New World, or Preparation?

Goal: Scotland Scotland is Light Blue Minor Power in the Game

Attacking and defeating Scotland is possible on the first turn. It is not difficult, but it does require the expenditure of several command points.

Goal: Scotland

Scotland is Light Blue Minor Power
in the Game

Goal: New World

New World

Goal: Preparation

Preparing England