Game Theory and Poker

by Cocky Fish on December 21, 2010

Thinker Game Theory and PokerPoker is getting tougher and a lot of top players are turning to game theory to help get an edge or, at least, eliminate their opponents’ edge.  You can find a lot of articles about game theory in top poker magazines like CardPlayer and on top training sites like CardRunner.  It’s great advice and it works great in tough poker games but it’s not a magic bullet.  In fact, if misapplied, it can hurt your game rather than help it.

CardPlayer is Costing You Money

And they’re not the only ones. Bluff Magazine, CardRunners, LeggoPoker, DeucesCrack, all of them are costing you money.  It’s not their fault.  They’re all great sources of information but you’re misapplying the information.

Have you noticed that you tend to lose money after your watch your favorite pro give a lecture on how to apply game theory in poker?  You balance your raises and 3-bets.  You float dry flops and you three-barrel bluff.  You do everything thing your idol tells you to do and you wind up spewing money all over the felt.  The question is – why?

Hawks and Doves

Before we go deeper into poker game theory, we need to have a better idea of how game theory works and for that we’ll use a simple game called Hawks and Doves.

Richard Dawkins talked about the Hawks and Doves game in his book The Selfish Gene but the game was originally proposed by J. Maynard Smith, a 20th century evolutionary biologist.  According to Smith, the rules of the game are as follows:

Hawks will always attack when it confronts another Hawk or Dove and will only retreat if seriously injured.

If a Hawk and Dove engage, the Hawk will attack and the Dove will fly away unharmed.

If two Hawks engage, they will fight until one is seriously injured or dead.

If two Doves engage, they will threaten each other until one tires of the contest and flies away.

A bird doesn’t know if it’s facing a Hawk or a Dove until they have a conflict.

The contestants are arbitrarily awarded 50 points for a win, 0 points for a loss, -100 points for getting seriously injured or killed and -10 points for wasting time in a long contest.

As it turns out Hawks have the advantage when there are a large number of Doves in the populations and Doves have the advantage when there are a large number of Hawks in the population.  Neither Hawks nor Doves have an advantage when exactly 5/12 of the population is Doves and 7/12 of the population is Hawks.

Hawks, Doves and Poker

So what do Hawks and Doves have to do with you spewing your chips?

When poker pros talk about line balancing and optimum bluffing frequencies, they’re talking about a game in which the strategies at the table are in equilibrium.  Here’s the theory behind it:

Let’s say 10 strong, thinking no-limit hold’em players sit down at a table and each of them has a different default strategy.  Some of these strategies will be successful and others will be unsuccessful.

Now let’s say that these players have an infinite amount of money and can never leave the table.  Being strong, thinking players; the players using an unsuccessful strategy will alter their playing style to exploit weaknesses in the superior strategies at the table.  Soon some of the previously successful players will start losing money and will have to adjust.

In time, these 10 theoretical players will reach equilibrium.  No strategy will be superior to any of the others at the table.

Now if one of these players leaves and you sit down in his place, one of two things will happen. First, you could have a superior strategy to the equilibrium and start cleaning up.  In that case, the other players will adjust their strategy and a new equilibrium will develop.  Second, you could get your ass handed to you at first until you adjust your strategy to fit the current equilibrium.  In this kind of game, the strategy suggested by your favorite pro will work just fine.

Poker Games Aren’t in Equilibrium

Poker is a lot more complicated than a game like Hawks and Doves.  There are multiple streets and multiple moves you can make on each street.  There is no single “best” poker strategy – which brings us back to why you’re losing money when you play a balanced strategy the second you sit down at a table.

Don’t Balance Your Play.  Exploit Theirs’.

Poker favors the aggressor and balancing your line for the sake of making your play unexploitable is a defensive strategy.  You should look for weaknesses in your opponents’ strategies and attack them.  Here’s an example (don’t bash the stats. They’re round numbers to make things easy):

Let’s say you sit down at a table and notice that a player continuation bets 100% of the time but gives up on the turn if he doesn’t have at least top pair.  To simplify the example we’ll say that you can only call or fold and the game ends after the turn.  The game is $1/$2 heads up no-limit hold’em.  Your opponent will always raise to $8 pre-flop and always bet the pot when he bets. Given these restrictions, you adopt the following strategy to exploit your opponent…

Call anytime the player raises pre-flop.

Call 100% of his flop bets.

If he bets the turn and you can’t beat top pair, fold.

If he bets the turn and you can beat top pair, call.

If he checks the turn, bet.

Your opponent will make top pair or better 20% of the time by the turn.  Again, for simplicity’s sake, we’ll consider the times you win the turn and the times your opponent wins the turn are equal.  Here’s how it plays out (100 games):

You call pre-flop and call flop but fold turn (18 times) – Lose $432 [($8 preflop + $16 flop) x 18 times].

You call pre-flop, call flop and lose (1 time) – lose $56 [$8 preflop + $16 flop + $32 turn]

You call pre-flop, call flop and win (1 time) – win $56 [$8 preflop + $16 flop + $32 turn]

You call pre-flop, call flop and bet turn (80 times) – win $1920 [($8 preflop + $16 flop) x 80 times]

Total: Won $1976 – lose $488 = $1488 total profit

Obviously your strategy is highly profitable – even more profitable than if you folded your poor hands and called with a balanced range of big hands, suited connectors, etc.

“But a Balanced Strategy is Unexploitable.”

True.  If you bluff with optimal frequency and balance your lines, your opponents won’t be able to read you and will make mistakes.  The trouble is that you’re not going to develop a balanced strategy after reading one article or watching one video.  Hell, a TON of pros don’t even play a balanced strategy.  It’s difficult to do.  It takes study, discipline and a total lack of emotion and…oh yeah…the perfect, unexploitable poker strategy doesn’t even exist.  At least, no one has found it yet.   You’ll make a lot more money in the long run if you can put your opponents on accurate ranges and exploit leaks in their games.

Does Game Theory Help Your Game?

I’m not saying that game theory is worthless.  Far from it.  Game theory provides a reliable framework for analyzing your lines to make sure you’re taking the most profitable line possible.  Game theory will show you where you’re missing out on money and where you’re making –EV plays (plays that lose money in the long run).  Of course, you still need to practice and learn to put your opponents on a range.

I believe that poker is too complicated to ever have a single dominating strategy.  However, you can use game theory to exploit your opponents’ weaknesses and modify your game when you encounter a strategy that dominates yours but it’s going to take more than one article  or one video to teach you how to do it.

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How Good Is Your Poker Face?

by Cocky Fish on August 4, 2010

Do you wish you could intimidate your opponents with shifty eyes like Phil Ivey?  Or have the impassive stoicism of Chris Ferguson?  Well a recent study suggests that you’re better off with the wholesome, friendly face of Jack McBrayer.

 How Good Is Your Poker Face?

BPS Research Digest Blog reports on a 2010 study that took a look at human waging behavior.  Participants in the study had to decide whether to fold or call based on an image of their “opponent.”  Here are the images the participants saw (without the labels).

Poker Face How Good Is Your Poker Face?

If the participant folded, he or she was guaranteed to lose 100 chips.  If the participant called and was beat, he or she would lose their entire 5000 chip stack.  Calling and winning would win 5000 chips.  There was no prior history available about the opponents so participants had to make a decision based on the face alone.  Now for the interesting part…

Untrustworthy and neutral expressions had no effect on the participants’ decision-making process but the trustworthy face gave the participants problems.

When confronted with the trustworthy face, participants took longer to decide and made less optimal decisions.  I can’t help but wonder if there’s a way these findings would apply to online poker as well.

Thanks to Rush Poker on Full Tilt we have the opportunity to play opponents in a vacuum.  There are times, many times, where the only information we have to work with is a screen name and maybe an ironman chip.  I’m curious – can screen names be neutral, untrustworthy or trustworthy?  Would you be more likely to fold to a raise from HoneyFlower21 than from IstackUR_azz?

What do you think?

Schlicht EJ, Shimojo S, Camerer CF, Battaglia P, & Nakayama K (2010). Human wagering behavior depends on opponents’ faces. PloS one, 5 (7) PMID: 20657772

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Decision Fatigue and Poker

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