Poker Game Theory And Math Are Actually Very Easy To Use, Here We Look At
Using Game Theory to Improve Your Online Tournament Results.
Game theory is a branch of applied math which looks at competitive situations where 2 or more people have conflicting interests. This has been applied to global politics, economics and of course to poker. David Sklansky covered poker game theory in his seminal work ‘The Theory of Poker’ and Chris ‘Jesus’ Ferguson made this famous by using poker game theory rather than experience to achieve his phenomenal success.
The key to application of poker game theory is that there are ways to vary your poker strategy depending on your opponents and the individual situation. After all, any poker strategy which does exactly the same thing each time is very easy to exploit.
So we have 2 dynamics at work – on one side a mixed vs static strategy, on the other an Unexploitable vs exploitable strategy. Unexploitable strategies are defensive in nature, they will prevent you losing chips and will win small amounts. In order to win you need to play in such a way as to exploit your opponents weakness – this of course involves deviating from Unexploitable strategy yourself and is where Poker Game Theory really starts to get interesting.
Below are 4 common ways in which poker game theory can be put to use at the table.
Poker Game Theory Application #1 – Optimal Bluffing Frequency
As made famous by David Sklansky the idea is that you should bluff with a busted hand on the river at the same frequency as the odds you are offering your opponent from the pot. Thus if the pot offers 4/1 at the river bluffing 25% of the time will mean your opponent loses the same amount whether he calls or folds, all else being equal. A great way to do this is to calculate the odds you will offer on the end of the hand when you bet and then randomize your bluffing by choosing a number of extra cards which do not make your hand. For example if you are offering 4/1 and have 8 real 'outs' to make your hand then choose 2 bust cards to bluff with.
Of course – this is the Unexploitable strategy. If you feel that your opponent either calls or folds more frequently than is correct you can adjust your bluffing frequency accordingly... adaping to expliot your opponents tendencies.
Poker Game Theory Application #2 – The Independent Chip Model (ICM)
ICM simply represents your current chip stack in terms of 'dollar equity' in the prize pool of the tournament. It is most commonly used in Sit and Go play as the numbers are easier to calculate (due to fewer paying places)but also has applications at MTT final tables. When you or your opponents have short stacks in comparison to the blinds (less than 10BB is usually quoted) then it is possible to calculate a mathematically ‘correct’ range of hands to push all-in with or call an opponents all-in bet. Playing using ICM is an Unexploitable strategy, as long as you can put opponents on correct hand ranges for calling or pushing then you will profit from ICM based decisions over time. Even if you choose not to use ICM yourself, it is worth learning about this - since many of your opponents will be basing their decisions on this math, once you understand what is driving their decision making it will be easier to put them on a range of hands.
As with any Unexploitable poker strategy there is a counter. Adjusting play based on stack sizes (especially the presence of very small stacks) or making mathematically ‘bad’ calls against regular opponents to prevent them correctly using this strategy in future are just 2 examples of poker game theory in action. For more on ICM see my SNG Strategy Articles section.
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Poker Game Theory Application #3 – Stack Sizes and The Gap Concept
The gap concept states that you need a stronger hand to call an opponent's bet than you need to raise yourself. In a no-limit Holdem tournament the ‘gap’ is usually small when stacks are shallow compared to the blinds (since implied odds are far higher) and shrinks considerably as the game approaches the bubble.
Poker Game Theory suggests that opponents understanding of the gap concept can be exploited. This happens when you strongly re-raise a player who has raised a pot ahead of you when stacks are getting shallow. If your opponent understands the gap concept he may be open-raising with a wide range of hands. The second ‘gap’ – that between the hands he will open with and those he will call a re-raise with – may be very wide. If your opponent raises with 20% of hands but will only call with 5% he will fold to your re-raise 75% of the time.
Using mathematics to exploit this concept will gain chips in many tournament situations. This is particularly true when stack sizes are balanced in such a way as to commit your opponent to the pot. The danger of using such a strategy is that yet another opponent picks up a monster hand behind you – so this is best used from late position!
More recently the 'exploitative' strategy of re-raising light is well known by regular tournament players. You might find your re-raised raised once more (4-bet) simply because your opponent knows that you will fold a good percentage of your hands (this could continue to 5-betting etc if stacks are deep enough). Remember, a novice player is unlikely to be bluffing when they make the 4th bet - since they are not considering game theory, just looking at their own cards.
Poker Game Theory Application #4 – S.A.G.E. Poker System / Nash Equilibrium
The SAGE poker system uses Nash Equilibrium math to create an unexploitable system for heads-up play at the end of a poker tournament. ICM does not work heads-up, since you are effectively playing for a single prize (the gap between the 1st and 2nd place payouts). Sage has a points system based on the number of big blinds in your stack, and tells you whether to shove all-in or call your opponents all-in with certain hands.
SAGE is best used when you are playing against an opponent who is more skilled or experienced than you are. While this system is 'unexploitable' it is not flexible enough to adjust to errors that your opponent is making. To take advantage of errors you need to step outside of the nash equilbrium 'game-theory' system, and call more or bet more depending on how you perceive the weaknesses of your opponent. For example, if your opponent folds too often (according to game theory) you can exploit this by betting more frequently.
Remember, applying Game Theory is even more effective against weak opposition – find out which is the best place to find those easy to exploit opponents in our Best Poker Tournament Sites section.