Fish N Chips

talking showdowns

2009-10-23T19:23:03+02:00

It's been a little while since last time. This will be a short post on a subject that might seem trivial, but is easy to ignore. The question is "how does showdowns influence the evaluation of your play?". This is easier explained by an example than by abstract questions, so here we go:

$2/$4 No Limit Hold'em - 6 players

Hero (BB): $400
UTG: $400
MP: $208
CO: $1076
BTN: $475.75
SB: $400.00

Your read before this hand is that villain is an aggressive reg who is capable of firing multiple barrels. He also has a tendency to get too tricky with his stronger hands.

Pre Flop: ($6.00) Hero is BB with 9 8
4 folds, SB raises to $16, Hero calls $12

Flop: ($32) 8 6 3 (3 players)
SB bets $22, Hero calls $22

Turn: ($76) J (2 players)
SB bets $58, Hero calls $58

River: ($192) K (2 players)
SB checks, Hero checks

When the river hits you decide you will call a last barrel too, as you think your opponents range constitutes of more than enough bluffs. K is seemingly also a good card to bluff. To your surprise he checks. You check back and take down the pot with your pair of eights.

Final Pot: $192.00
BB shows Q T
Hero shows 9 8

Hero wins $192.00

This hand might seem trivial, but my question is: Do you pat yourself on the back because your "read" was correct (he didn't have anything...), or give yourself a smack because your opponent didn't act in the way you expected? The fact that he gave up with nothing probably means that his betting-range on the river must be more heavily weighted towards value. In turn your decision about calling his hypothetical river-bet probably was wrong. If you look at it this way your opponent actually won the leveling war, by not making an incorrect bluff. I think most people ignore this and just move on to the next hand without adjusting their read. It's of course not as black and white as this. Maybe your opponent would sometimes bluff and sometimes not, in this exact spot? At least I hope I have managed to give you something new to think about...

Relevant posts/articles:
decision making
value and polarized ranges
practical introduction to game theory

learning from your mistakes...

2009-09-05T20:18:32+02:00

Played some small stakes NLH today. I thought this hand was kind of hilarious. My miss-click prob ended up winning me $125 instead of $15. Well, we just got it in flipping, but the point is what happened pre-flop :). When I 4-bet in position it might be an idea to make the bet even smaller (100-125bb deep) than I've done before (usually I raise a 10-12bb 3-bet to about 24-26bb), as it gives a 5-bet bluff a worse prize and also can induce calls from his (semi-)bluffs. If he shove all of his value-range (TT+, AK and AQs+ maybe?) and just calls with hands like 42s and T7s, it can't be that bad. In addition I can see him 3-bet/folding hands like AJo and KQo in this spot (if they are a part of his range at all), as they would be too though to play oop. It kind of becomes a "value-bluff" with hands like AJo, Ato, KQo, KJo and KTo. Sometimes you get folds from better hands and sometimes calls by worse. Another pshycological point is that the smaller you can get away with making your 4-bets, the more it frustrates a habitual 3-better. The "head expotion factor" as David Benefield named it...

NL Holdem $1(BB)

silverdemon2 ($117)

NoSash ($124)

GroundStorm ($248)

Klovnen ($196)

eyes7475 ($111)

silverdemon2 posts (SB) $0.50

NoSash posts (BB) $1

Dealt to Klovnen Th As

fold,

Klovnen raises to $3

fold,

silverdemon2 calls $2.50

NoSash raises to $12

Klovnen raises to $21

fold,

NoSash calls $9

Villain was LAGy (3-bet a ton) and I had a nice nitty image. To call here is a bad idea. Even if villains range is wide ATo plays terrible, especeally with another player in the pot. I decided to turn it into a bluff as it got some nice blockers and my image was sick tight at the time. I typed in $26, but for some reason the amount jumped back to the minimum before I hit the raise button. I think the ideal bet amount is somewhere in-between though, maybe $23-24 in this case and $22-23 if 100bb deep. This balance better with your value 4-bet range too. The good pot/implied odds he get is just an illusion, as I will not stack off often enough. I will also be able to push him of the best hand a decent amount of the time when he flops a little bit of something.

FLOP ($45) Tc 6s 7c

NoSash checks

Klovnen bets $16

NoSash raises to $103 (AI)

Klovnen calls $87.55

TURN ($252) Tc 6s 7c 7s

RIVER ($252) Tc 6s 7c 7s Ad

The 1/3 pot bet size is standard in 4-bet pots 100bb deep, as you easily get the money in anyway. In addition such a bet can induce a bluff-raise and gives you a good prize on your own bluffs (or build a bigger pot before picking it up on the turn). 125bb deep $18 would have been a better amount, to leave about a pot-sized bet on the turn. It's no point in being afraid of giving odds to a draw, as aggressive players will push rather than call (after all, I will bet here as a bluff too). In many ways this is a very good example of the "threat of future betting", as I basically risk a small amount to put my opponent to a decision for his whole stack.

NoSash shows 4c 3c

(Pre 40%, Flop 47.8%, Turn 27.3%)

Klovnen shows Th As

(Pre 60%, Flop 52.2%, Turn 72.7%)

Klovnen wins $249

notes - abbreviations

2009-09-05T17:47:27+02:00

Just thought it would be an idea to scramble down some of the abbreviations I often use. Maybe some of you will find them useful for your own note taking:

F (fold), X (check), B (bet), R (raise)
ip (in position), oop (out of position)
3B (3-bet)FD
FD (flush draw)
SD (straight draw)
PC (pot control)
OPT (overplay top pair; thinking in absolute hand strength)
1BM (one barrel monkey)
DNB (do not bluff (him))
RNFV (round number for value + variants: NRNV, RNFB, NRNB)
GHR (good hand reader)
BHR (bad hand reader)
ET (easily tilted)

The rest of the note taking is based on the same system. For example min check-raise flop with KJ on a K76 flop and bet 6 turn, would be "mXC KJ K76, B 6". After getting used to it, it gets quite intuitive.

plo: pre-flop (part 2)

2009-09-05T09:04:16+02:00

In part one we tried to get a broad picture of the relative strength of different type of PLO hands. In the two next parts we will look at more specific situations, talk about playability and 3- and 4-bet pots. Hopefully this will give you a better understanding of some of the dynamics in PLO, and give you some useful tools to analyze pre-flop situations on your own.

Playability

Even more so than in NLH the playability of a hand increases in value as stacks gets deeper. The single biggest mistake most new players do is to overplay bad AA** and KK** when stacks are deep. Bad aces constitutes of those who aren't suited and can't make good two-pair hands, such as AcAdjh3h or AhAsQc6d. A hand like AhAs7h2d is also considered weak, even though one of the aces is suited. It's true that all these hands have an equity advantage against any non-aces hand. Nevertheless double and single suited rundowns, like KQJT, KQT9, QJT9 and so on, might have greater value. With these hands you can flop a lot of draws and continue on a wide variety of flops and turns, a statement that seldom holds true for bad AA**. Most of the time you will feel "lost" with AA** when you doesn't flop a set. Pre-flop equity is of course important, but you should be cautious with putting a lot of money in pre-flop with AA** as other hands often catch up and are easier to play. If stacks are shallow, this does of course not matter, and getting the money in as fast as possible with any AA** is correct. As a general rule; if you can get in about 1/3 of your stack with AA** pre-flop then go for it.

A hands playability is determined by how many flops and turns it profitably can peel, trying to catch up if behind. An example would be AsQdJcTs on a Td8s2c flop. On this board you can continue on any 9, T, J, Q, K or spade, knowing that you at least got outs to the nuts. With a hand like AcAdQs2h you might already be drawing slim, and there are not many turns you can withstand a lot of pressaure on. Another sort of hand with a lot of playability are connected nut-flush hands, such as AcTs9d8c. The nut flush draw has a lot of power in PLO. It never got less than 25% equity (against a set) on an unpaired board, and is even a favorite against a 13 out wrap. Having a pair in your hand raises your equity with 5-10% depending on your opponents hand and blockers he might have. I would suggest you go to propokertools.com and run some equities to get a feel for how the nut flush draw, with or without a pair, runs against other hands such as sets, two-pairs and wraps.

3-betting

In NLH you find a lot of 3-betting. You have a lot of fold-equity in this case, so you do it both as bluffs and for value. This doesn't really hold true in PLO, where you seldom will get a fold after 3-betting. So in PLO you should 3-bet for value and to create profitable post-flop spots in position. You should never 3-bet garbage hands, but rather semi-connected hands that want a heads-up pot. In today's games most players seem to automatically put you on AA** when you 3-bet, so 3-betting a hand like T976ds or 6543ds in position to isolate, will also have the benefit of being able to represent AA** on A-high boards. This is another reason to just flat bad AA** as well, as both plays add some deception to your game. You should be considerable more Conservative with 3-betting oop.

4-betting

Against aggressive habitual 3-betters you should in addition to 4-betting AA** start to 4-bet premium rundowns such as double suited AKQTds and JT98ds. Premium KK** are also good candidates, like KKJTds or KK97ds. Be aware that this is a suicidal strategy against the wrong opponents though. As stacks get deeper (200bb+) it's probably a good idea to stop 4-betting at all out of position. This also include premium AA**. Playing big pots oop deep, with a narrow range of hands, is just not profitable. You are better of keeping the pots as small as possible before the flop. This does of course not mean that you should go into a passive shell. Post-flop you are free to come out with the guns blazing again!

Calling 3-bets

Since position is such a big factor in PLO and the equities difference between hands so small, you should call most 3-bets ip. it's fine to let some hands go until you feel more comfortable in 3-bet pots. To fold 40-25% of your hands is not a terrible leak. Some good players profitably manage to call about 90% of their hands ip, something that tells you a lot about the difference between PLO and NLH. Hand's you should let go are unconnected off-suite hands. It's also worth noting that the worst kind of hand you can have against aces are hands including an A and a lower pair (for example AJJ8). Oop you should be tighter, the power of position can't be over emphasized.

Calling 4-bets

3-betting ip is a very powerful tool and you should increase your 3-betting frequency as your game improve. Some players will fold a lot to your 3-bets and some players will call and fold the flop, while others mitht fight back with thinner holdings. Be aware of your opponents tendencies! To learn to handle players who 4-bet light, it's necessary to do some math. In our next part (and last about pre-flop play), we will take a closer look at these situations.

Relvant articles/posts:

plo: introduction

plo: preflop (part 1)

decision making

plo: pre-flop (part 1)

2009-09-02T20:30:00+02:00

Pre-flop is maybe not the most important or interesting street in PLO, but it's still the foundation of the game, the place where you start to plan out your hand. For the NLH player it's important to note that no PLO hand is a huge favorite over another. A superb hand like AAKK only has 67.85% equity against a random hand. Compared to hold'em AA is a 85,2% favorite against a random hand. This fact encourage the players to be more active pre-flop. It's kind of meaningless to talk about PLO hands in terms of a hand chart, if not impossible. The most important thing is to understand the relative value of different hands and in what situations they play well. Most of the discussion that follows assume the players got around 100bb stacks or a little bit deeper.

Since the equities run so close in omaha, there are different successful pre-flop strategies used by strong players. Most strong players tend to play between 20% and 30% of their hands, but there are exceptions (notably some super LAGs). The most important thing is to set yourself up for profitable post-flop spots. All hands are drawing hands in omaha. In hold'em hands like AA or KK are usually still the best hand by the river unimproved. This is not the case in omaha, AA** usually has to improve to win a showdown. Roughly speaking AA** resembles a hand like 33 more than AA in NLH. The exception is if you can get the stack-to-pot ratio really low. If you for example get in 1/3 of your stack preflop, bare AA** is an easy shove on all but the worst flops. We categorize hands by what they are most likely to draw to post-flop. Here are the basic elements:

Pairs (AAKK): Build sets and boats
Suites: (AA**ds) Build flushes
Connected cards (JT98): Build straights

Bigger is better

In a general sense, PLO is a high card game. You want to build nut straights, flushes and boats. Premium hands combine the elements above, while at the same time drawing to the nuts. Examples are AATJds and JT98ds. In general hands consisting of cards T and higher (not trips of course...), belong in the premium had category. Bellow follows a table of the top 30 hands. Being suited or double suited adds a lot of value:

AAKK 11. KQJT 21. QQAK
AAJT 12. KKTT 22. QQAJ
AAQQ 13. KKAQ 23. AAAT
AAJJ 14. KKAJ 24. QQKJ
AATT 15. KKAT 25. QQKT
AA99 16. KKQJ 26. QQJT
AAxx 17. KKQT 27. QQJ9
JT98 18. KKJT 28. QQ99
KKQQ 19. QQJJ 29. JJTT
KKJJ 20. QQTT 30. JJT9

This table is not only based on pre-flop equity, but also playability. That's for instance the reason AAJT is ranked higher than AAQQ and JT98 higher than KKxx. These hands does not come around often, so what else is playable from early position? The simple answer is when hands are double suited and have the same structure as the top 30 hands. Examples are hands like T987ds and 8765ds. They have a lot of potential to flop huge draws, or made hands with back-up draws. For example T987ds on a 762 or 873 board. Hands with gaps such as QJ98 and T976 got less value, as it's harder to flop a wrap with them or strong draws to go with your made hand. The higher the rundowns are, the more playable they are. The lower rundowns such as 6543 can be dangerous hands, as it's a disaster to meet hand like T987 on a flop as 762. In this case you are about a 25% underdog, which is almost as bad as you get it in PLO. This illustrates well how important it is to build nut draws, especially out of position. In NLH it's a big difference between QJs and 76s, but not as huge one as between high and low rundowns in PLO. The reason is that you seldom will hit a straight over straight in NLH. It's one important exception to point out in this context. In a 3-way all-in pot pre-flop, low rundowns are usually better than the higher ones, as your opponents are likely to hold AA** and high cards:

AA** 34.79% AA** 49.02%

BBBB 27.62% BBBB 19.58%

6543ds 37.59% QJT9ds 31.40%

Single-suited hands with three connected broadway cards and a dangler, like JsQhTs5s and KdQhJs2d, might not look as pretty as double suited hands such as 3c3s4c5s or Qd9c7d6c, but they got a lot of value post-flop. They got high card value and can still flop 13 out wraps without having to worry about higher straight draws. It's very hard for the more pretty looking hands to hit the nuts while giving someone else a decent second best hand. By the same reasoning a hand like QJ96 got a lot more value than Q987, even though they got the same structure. Playing weak and marginal hands in position will nevertheless add to your win-rate. As we will get a better understanding of when we discuss post-flop play, position is huge in PLO. Position is of great importance in NLH too, but not even close to as important as in PLO. If it gets folded to us in the cut-off or on the button, we should therefor usually open anything that resembles a hand, such as a hand including a suited ace or any double suited hand.

Multi-way or heads-up?

Hands that doesn't have much nuts potential prefer to play in a heads-up pot, as the chance of your draws being dominated are smaller. If the pot is raised to you in late position, you should therefore 3-bet hands such as QJ87ds and 6543ds to isolate the raiser. If you just call and get a multi-way pot, you sure will find yourself in some rough spots. Due to the power of position these weak hands play well in 3-bet pots. Your 3-bets will rarely make anyone fold, but will put you in a nice post-flop spot. Hands like bad aces and kings (such as AsAc7h2h) and sutied aces (such as AhTc9d5h), would rather prefer multi-way action. This will give them a greater chance to set over set or flush over flush another player. Premium hands doesn't really mind if the action is head-up or multi-way, but to 3-bet them for value is usually a good idea.

Limping behind?

In PLO you should often concider limping behind. For NLH players this might feel a bit counter-intuitive, as isolating limpers with hands like 54s is routine. In PLO however wou seldom get anyone to fold, so all you acomplish by raising limpres with marginal hands is to create a bloated multi-way pot with hands that are difficult to play post-flop. Good candidates to limp behind are hands consisting of two hold'em hands, like KsJs8c8d or AdTcTd9d. It's not uncommon to limp behind with bad aces or kings either. If you are in the cut-off with an aggressive blayer on the button, you might be better of just folding the weaker hands.

In the blinds

You should play very tight from the blinds. It's tempting to defend light against a late position raise, but you will only put yourself in grose post-flop spots. Folding up against 90% of hands from the blinds is not uncommon. You should play at least as tight as from early position, including folding hands like Q965ds and 7632ds, especially against strong aggressive players. You should also play tight from the SB versus the BB, and call/3-bet a wide range of hands when in the BB versus the SB. Also raise anything semi-playable versus a limp from the SB.

plo: introduction

2009-08-31T20:26:29+02:00

I have started to play more and more PLO lately, and am going to write an article series on the subject. There are many reasons to take a closer look at PLO for NLH players. The games are softer and action packed. Because of the high variance it appeal to weaker players and gamblers. Often it take a long time before they realise they are losing. The pre-flop edges are small and you are almost never drawing dead, so if they are running hot they often get a chance to build a healthy bankroll.

There are a few reasons you might not want to play PLO too. If you feel uncomfortable with a lot of variance and are prone to tilt, it might not be the game for you. If you decide to try it out, I would start playing lower stakes than you usually do, and at least have a 50 buy-in bankroll. When it comes to software, Omaha Manager is the nuts, and propokertools.com is at the moment the PokerStove of PLO. I'm going to focus on a solid and aggressive playing style in these articles, as I feel it's the easiest way to start beating the games relatively fast. Some of the concepts may be harder to incorporate in a LAG game-plan, as you will be given less credit in a lot of spots. To start off, I would suggest you play a lot of cap games in the start, and run the equities in all-in situations ans showdowns. Omaha is a game about equities and to get a feel for these numbers is the best thing you can do to get a good start.

basic combinatorics

2009-08-29T12:13:26+02:00

Combinatorics, or counting combos, is a tool that help you dissect your opponent's range. It will give you a better understanding of the nature of other peoples ranges, how often they include draws, made hands or pure bluffs. A combo is simply one specific hand, for instance AcAs (AcAd is a different combo). Before the flop it's 6 possible combos of every pair (3+2+1), four combos of any suited hand (4x1) and 12 combos of all unsuited (and unpaired) hands (4x3).

Post-flop we can find the possible combos of a given unpaired hand by multiplying the reminding cards. If you for instance want to know how many combos there are of AK on a A82 flop, you multiply 3(aces)x4(kings)=12 combos. There are 3 suited (3x1) and 9 (3x3) unsuited combinations left. If we want to compare how often villain will have AK versus AA on this flop, we have to count the combos of AA first, which is 3 (2+1). If villains range were only AK and AA here, we would now know that he is 80% (12/15=0.8) likely to have AK and 20% (3/15=0.2) likely to have AA. By breaking our opponent's range down in this way, it's far easier to figure out the best possible line to take.

To give a few basic numbers of combos:

One pair (AQ on AK2) = 12 combos

Two pair (AK on AK2) = 9 combos

Straight (AK on QJT) = 16 combos

Full house (AK on AAK) = 6 combos

Quads (AK on KKK) = 4 combos

Set (KK on AK2) = 3 combos

Quads (KK on KK2) =1 combo

Remember to not include dead combos if you hold a relevant card in your own hand. If you have AQ on a AQ6 flop for instance, it's just one combo of AA, one combo of QQ and 8 combos of AK left. I think this covers the basics of what combinatorics in poker is about. If we have a good estimate of our opponents range and frequencies, we should be able to relatively fast (after some practice) be able to estimate how big part of it is made up of draws, different made hands and air. For more complex problems, and to get a better feel for different situations, I suggest you download Stox Combo (free). Play a little bit around with it and use it in your session analysis. It works in about the same way as P okerStove, but counts and compare combos rather than calculating equity.

Relevant posts/articles:

decision making

value and polarized ranges

decision making

2009-08-26T16:59:12+02:00

I want to talk a little bit about a thought process you should go through in every situation at the table. Poker is a dynamic game, and one of the most costly and common pitfalls is to start playing on auto pilot. If it's something you doesn't do already, you have to start asking yourself the following questions before making a decision:

1. What is my opponent's range?
2. What is my perceived range?
3. How does my actual hand do?

Being able to answer these questions well is one of the most important skills in poker, and you will be surprised how often you can find more profitable and creative lines, rather than to throw out a "standard" bet. I'm not advocating any FPS, but to actually understand why you make the moves you do. I doesn't agree with a lot of other regulars these days, who says NLH is a dying game and close to "solved". Yes, the games are tougher than a few years ago, but still the games changes and there will always be room for beating them. A lot of these regs have been used to "standard lines" that used to work out well, but because of approaching the game in a lazy way, they have problems following the trends and changes in the dynamics. To survive as a poker player you have to stay ahead of the marked and being able to think for yourself, no matter how many instructional sites that pops up. Well, let's get started:

What is my opponent's range?
To answer this question is often not as easy as it sounds. Based on your observations of your opponent(s) tendencies, you have to make an educated guess. Is he likely to have a polarized range in this situation, and in that case; how well balanced is it between bluffs and value hands? Is he betting thin for value? It's equally important to know your opponent(s) range when he call or check to you. What does this mean - is he most likely to check-raise, being trappy or weak? Most of these questions can't be answered by stats, you actually have to pay attention and take notes.

What is my perceived range?

This is all about how your opponent(s) answers the first question - what you are able to represent. This is for obvious reasons extremely important against strong players. If a good hand reader has a reason to think a big part of your range is draws and the river bricks off, you are far more likely to get called by a weak hand than if a scary card did fall. Another case is if a "scary" card fall, but it doesn't help your range too much; be prepared to be called down light by a good player! To be conscious about your perceived range is important against weak players too. The secret is that also bad players thinks, just not in same way as you. Their answer could be something as simple as "he got to have AK", "he got to have a flush", "he never has anything" or something along those lines. To be able to get into your opponent's head has always been a mantra in poker, but is not such a romantic idea as it often sounds like - it's all about being able to use sound reasoning. One of the easiest and biggest mistakes many players do, is to transfer their own way of thinking to other players. They doesn't think in the same way as you! So don't blame them when they call your third barrel bluff (on a board that crush your range) with second pair.

How does my actual hand do?

This is an important question, and something many players struggles with. Maybe your K-high actually is quite likely to win a showdown or maybe your two pair-never is good. To be able to truly think in terms of relative and not absolute hand strength, is the key to finding the best moves. The tool you use to figure out when to go for pot-control and when to consider making a made hand into a bluff. How does your hand fit into the bigger picture? This is what you should base your decision on.

Putting it together

I think that the biggest problem for most is to put all of this together. You might say "he is weak most of the time, so I will get him of his hand with a few barrels" or "I look super-strong if I check-raise here". In the first case you might not think closely enough about what you are representing, in the second one you might ignore how strong your opponent's range is. You have to take everything into consideration before making your decision.

Relevant posts/articles:

combinatorics

value and polarized ranges

practical introduction to game theory

G-Bucks

value and polarized ranges

2009-08-20T12:06:55+02:00

I assume most of you are familiar with the terms polarized and value. To give a short explanation; when you mostly bet the top of your range, you are betting for value and/or protection. The wider the range of hands you bet for value, the thinner your value range is (ref. G Bucks). When you polarize your range, you still bet the top of your range, but often not so thin. Instead you include the hands that are just a little bit too weak to check/call with, in your bet/raising range (gets a bit different on the river). The main idea of value betting thin is to protect and push your thin edges, while polarizing your range mostly is about pot-control; to not being blown of the best hand. In many ways you can say polarizing your range is a defencive idea. You will see many of the strongest players disagree in these marginal spots. A player like Brian Townsend is usually a proponent of pushing your value edges, even if you risk being blown of your hand, while Phil Galfond is more of the "pot-control" and "range balancing" school. We are of course talking about marginal situations here, but it illustrates that poker is a game far from being solved.

This post is mostly going to be about when to apply the two in general. I will just discuss the use at single streets, as it gets a lot more complicated with future streets of betting in mind. I will write about more specific situations, multiple streets and ways to misrepresent your range (range-merging) in later posts and hand analyzes. I will refer to value range and polarized range as VR and PR from here on.

Of course neither a VR nor a PR is superior to the other in principle, and you should usually mix it up according to game theory. I think there are some guidelines that direct the best course of action with your medium-strength hands in a given situation though. After all, our goal should usually be to play as exploitative as possible, not as optimal as possible (see a practical introduction to game theory). These criteria are based on how your opponent(s) is likely to think and respond. This has a lot to do with not just how the player usually responds, but also the dynamics of the table and the history between the players (the meta game).

The arguments for using a VR:
- Your opponent(s) is likely to respond loose
- Your opponent(s) is likely to respond passive
- It’s dangerous to give away free-cards
- Your opponent(s) is likely to read you for a PR
- You want to isolate a player with a made hand
- You want multi-way action with a draw
- Against a low intensity player

The arguments for using a PR:
- Your opponent(s) is likely to respond tight
- Your opponent(s) is likely to respond aggressive
- It’s not dangerous to give away free-cards
- You can easily represent a wide VR
- Your semi-bluffs got high fold-equity
- Your opponent(s) is likely to have used a thin VR with his previous bet
- Against a high intensity player

There are probably more points to add to the list, but these are the most important arguments. Maybe not all of them make sense yet, and that you see some paradoxes. It's not unusual that you have a "conflict of interest" between two arguments, and the situation dictates which is the most important. There is also something to be said about position; often I prefer a VR oop, while a PR ip, but this is a more situational concept and doesn't fit in as a general rule. I will talk in greater depth about this later. This short article is by no means comprehensive, but I hope it at least will stimulate some thoughts around the topic.

a practical introduction to game theory

2009-08-18T16:00:00+02:00

I will try to explain some game theory concepts that apply to poker in this post. It's a whole branch of mathematics, but I'm not going into much depth here. I will cover some of the mathematics later on. The important thing for now, is that you understand the concepts/terms before reading my upcoming articles. The truth is that I'm not a game theory expert, not even much of a mathematician. I only know the concepts which apply to poker. What I want you to know after reading this post is the difference between a pure and a mixed strategy, between an optimal and an exploitative strategy, and how one strategy can dominate another.

Pure strategy

A pure strategy simply mean that you use the same action every time. That you doesn't mix it up at all. Say you got AA in the big blind and one player has gone directly all-in before it's you to act. The obvious correct strategy is to call 100% of the time in this scenario. This is a pure strategy. It's no need to fold some percentage of the time to "mix it up". This is also an example of a dominant strategy. To call dominates all other options (more profitable every time), and is both the most exploitative and optimal strategy at once.

Mixed strategy

Say you got 85s on the button. All players are 100bb deep. One player raise 3xbb from the cut-off. Against a strong player it's probably not profitable to raise or call 100% of the time here, but to do so a small percentage of the time probably is. Say you fold 60% of the time, raise 30% of the time and call 10% of the time. This would be a mixed strategy, as you doesn't take the same action every time. In this case folding isn't a dominant strategy, as (you think) it's more profitable to raise or call some percentage of the time.

Optimal strategy

An optimal strategy is maybe not quite what you expect it to be. It's usually not the most profitable strategy (unless your opponent also is using an optimal strategy), but an un-exploitable strategy. In this case it's better to use an easier game as an example. In "scissor, rock, paper" the optimal strategy will be to use each option 1/3 of the time. Your opponent simply can't beat this strategy, the best he can do is to do the same. In poker an example is to bluff at an optimal frequency versus the times you value-bet on the river, to make your opponent indifferent to what action he takes (the options are equally profitable for him).

Exploitative strategy

Say in the "scissor, rock, paper" example, that your opponent only plays paper, no matter what you do. The optimal strategy is still to use each option 1/3 of the time, but it's clearly not the most profitable. It will still beat his strategy, but you will win far more often if you always play scissor. In this case you exploit the weakness in his strategy. The problem is that if he realize what you are doing, he can now exploit your strategy. In poker an example would be to bluff far more frequently in a river spot than what's optimal if you know your opponent folds too often. Sometimes you might hear a player say a play is +EV in a vacuum. What he mean is that the play will show a profit given the conditions (your opponent will fold too often for instance), but not something you should do every single time (because you can easily be "re-exploited").

Practical use of game theory in poker

In hold'em no one plays optimally. It's a far too complex a game. What we often do though, is to make "single street games" and solve them. Meaning very simplified versions of poker, where it's possible to find the optimal strategy. They still learn us a lot and can often be applied very well to real situations.

If we feel an opponent has an edge on us in one spot, it's a good idea to play with as optimal frequencies as possible. The point being to cancel out his edge and rather exploit him in other spots. A common example would be against a player who is far too loose pre-flop, but very solid post-flop. You would generally try to get as much money in pre-flop against him as possible (with a stronger range). After the flop though, it could be an idea to mix it up as close to (what you think is) optimal as possible, instead of trying to out-play and out-guess him.