Game Theory Applied To Poker
Posted By admin On 13/04/22Game of Life in Java John Conways Game of Life in Java, either as a applet or as a stand alone program. Game theory poker A game theoretic poker player (written in 2005). Gamemasterdice Game Master Dice is (yet another) dice app, focused at the 3D20 system. Gamesim A simple social game workload simulator. Poker Game Theory Application #1 – Optimal Bluffing Frequency. As made famous by David.
Intermediate Lessons
Game Theory Simplified, And Why Fixed-Strategies Fail
This article first appeared in Card Player magazine.
Good morning. I was supposed to write this column last night. It’s 8:38 a.m. now Christene will log onto her computer at Card Player and look for it via e-mail. But, alas, it just won’t be there. Steve and Linda will be wondering where it is. They will swear aloud; I know they will. They will say that I am irresponsible. They will be right.
Shirley will phone me in desperation. Janet will be waiting to type these words into her terminal to be printed out in high resolution, just like you see it now. She’ll be mad, too. Sometimes, it’s just not pleasant being me. You’re wondering why I’m telling you this. Well, actually, I just babbling while my mind starts to focus. My cerebrum is in shock. The only times it has experienced this early stage of the morning is when it has accompanied me through a poker session carried over from the night before.
Clearly, we’re going to have to keep things very simple today as I strive to become more alert. I know. Let’s start by talking about game theory.
Exactly what is game theory?
Sure, if you’re an astute student of poker, you probably know what game theory is. If you’re schooled in higher mathematical concepts, you also know. Sort of. But the plain fact is, most poker players don’t have a clue. Don’t worry. Game theory is just a term you hear bandied about by poker nerds. Frankly, the term frightens most normal poker players, because it suggests that a few opponents know something they don’t. Something powerful. Something sinister.
Say it ain’t so, Mike. OK, it ain’t so. I haven’t seen anyone show me a purely game-theory approach to any real-life poker game that could come anywhere near the profit potential of even common-sense poker. And nobody is likely to show me one for many years.
And when someone does come up with a complete strategy for a given game, based on game theory, nobody will be able to apply it very successfully during the course of a game. You’d need a secret computer to quickly analyze which action to take when. The game that probably comes closest to being cracked by pure game-theory principles is ace-to-five lowball. But even there, a naturally skilled player armed with some basic research will fare better.
So, relax.
Anyway, I never did tell you what game theory is, did I?
Game theory explained, finally.
The legendary mathematician John von Neumann is credited with pioneered game theory about 70 years ago. Also sometimes called the theory of games, it doesn’t just apply to poker. In fact, it’s most powerful application today is not to what you and I think of games at all. It is used for military decisions (or should be), for politics, and for everyday choices..
All you need to know right now about game theory is that it tries to provide the best decision at a given moment for a poker player by taking into consideration what your opponent’s best strategies is. For instance, should you bluff for $20 at this moment, attempting to win a $300 pot? Well, if you always bluff, your opponent should always call with his semi-weak hands. And if you never bluff, your opponent should never call with his semi-weak hand.
The truth is that to perfect your strategy, you shouldn’t bluff all of the time, but you must bluff some of the time. You need to consider your opponent’s options. For instance, if he has a weak hand does this mean your bluff will succeed? What if he raises? Should you just give him the pot then, or should you re-raise? Through game theory, you can determine – if all goes well – what frequency you should bluff and what frequency you should take any other poker actions.
What’s important is that once you know the frequently you should try to bluff in a situation, you need to randomize your actions. What does that mean? It means that if the answer you came up with through game theory analysis is that you must bluff one out of 10 times in a certain situation, this does not mean that you must choose one time in 10 to bluff. If you do that, your actions theoretically will be predictable by an all-knowing opponent. He would say, 'Gee, no bluffs observed in the last eight tries. This means my opponent is going to bluff once out of the next two times, so I better call.'
Randomizing your choices.
To get around this problem, all decisions should be randomly generated. Every time that the same situation occurs, you should act as if it has never occurred before and randomly decide whether to bluff. You might go 50 times in a row or more without bluffing, or you might bluff three times in a row. Just so you choose randomly, you’re safe.
How do you choose randomly? There are several ways that are almost random. One method I sometimes use is to remember combinations of suits that I saw on the previous hand, but that’s another topic for another day. Just trying to be random in your own head may be close enough, in practice.
You need to know this about game theory. Your objective is to choose an action that leaves your opponent with no way to take advantage of it. In the case of bluffing, a perfectly randomized strategy will mean that it doesn’t matter to your opponent whether he calls or not, as long as his decision is also randomly based and he calls the correct percentage of the time in the long run. A theoretically correct game theory solution cannot lose through eternity, but it cannot win through eternity, either, when pitted against a similar strategy. The only reason such strategies win is because opponents make mistakes. That’s the same way any other poker strategy wins, by the way.
Game Theory Applied To Poker Rules
It turns out that some hands are almost always playable, and some hands are almost never playable. but many hands fall in the middle and they should be played sometimes, but not others. This is why I cannot usually answer questions that players pose about whether they should play a hand. The situation is usually borderline, thus prompting the question, and the answer is often that they should play the hand sometimes. This does not turn out to be a very satisfying answer in the minds of most players, but it is the right answer.
Why game theory fails.
Game theory fails, because poker is just too complicated. There are too many things to consider in a real game, and calculating a tactic for a given situation is seldom possible with any degree of precision. Even if you could calculate the exact answers for every situation, you wouldn’t have the time to do this while you were at the table, so you’d need to memorize all the answers. Good luck.
Another problem is that the game theory solution is apt to be aimed at opponents who respond perfectly. That’s the main challenge behind game theory. Play perfectly and let your opponent destroy himself, if he chooses. Although it may seem strange to you, if you have a perfect game-theory solution, you don’t need to adjust. No matter what your opponent does, he cannot win. The more he strays from the perfect strategy that you’re playing, the more you’ll profit from his exceptions.
But wait! What if your opponent bluffs all the time? Are you just going to let him do it? Again, you don’t need to adjust. If you stubbornly stick to your predetermined game plan (which means calling most of the time in a limit poker game), you win more when your opponent bluffs too much. However, you won’t win as much as you would if you simply said, 'To hell with this game-theory stuff. I’m going to call all the time.'
Yes, you could adjust game theory to the circumstances, but that would mean going to the poker table armed with many sets of incredibly complex strategies, and I’ve already said that I don’t think anyone could handle even the basic one.
Another problem with game theory is that, although it can more readily be applied to two-player competition, poker games among three or more players add a complicated twist, due to the possible benefits of implied cooperation among opponents. This does not need to be cheating. The complication arises, even in honest multi-way confrontations. I’m not saying this cannot be resolved through game theory. I’m just saying, show me.
Having said all that, you still should realize that game-theory investigations are going on right now in poker, and that they will yield some valuable information. We will tune strategies accordingly. But it is unlikely that you will ever personally need to understand anything other than the basic concepts of game theory, because you certainly are unlikely to use such a complex strategy in a real poker game.
Why fixed strategies fail.
Actually, you can hone in on a very decent strategy by using a computer to try out tactics. You let the first 'opponent' adjust until it is maximizing its profit. Then you let the second 'opponent' adjust, and on and on. I have seen situations in which this won’t work, because the strategies stubbornly whipsaw back and forth, rather than finding a focal point. But it’s sometimes a very powerful technique. At the end of this experimentation, you arrive at a fixed poker strategy.
The main point I want to make today is that fixed strategies fail, whether they’re game-theory strategies or strategies.. By fixed strategies, I mean ones that don’t adapt to the conditions a the table right now.
Even a perfect game-theory strategy, targeted at perfect opponents, is not the best approach in real-life games. That’s because, most likely, your opponents are not playing anything near perfect strategy. If they are, you probably don’t want to be in that game, anyway. So, the best strategies are those geared for imperfect opponents.
That is why much published hold ‘em advice, for instance, is far off the mark when speculating that hands like A-J are seldom profitable. When opponents play A-9, A-8, A-4 with regularity, A-10 is more likely to beat up on another ace than to fall victim to one. Whether you should play A-J or not depends on the exact circumstances and the nature of your opponents. An A-K often makes more money against A-J than A-J makes against A-9, so you need to consider that, too.
Here is what’s wrong with fixed strategies in poker. The problem is threefold
If you use a perfect strategy geared at holding off perfect opponents, you probably won’t maximize your profits against weaker opponents;
2. If, instead, you use a perfect strategy geared at typical weaker opponents, you may have to wait for the game to adapt to you (the wrong set of opponents can sit down and cost you money while you hope for a better group to arrive);
3. Even an apparently excellent strategy can be overcome by two or more opponents playing inconsistently with the true strength of their hands.
Anyway, I’m going back to bed now.
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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.
Planet Mark's Rec : If you are thinking about Poker Game Theory, then you are already more advanced than the majority of players. What you need to do next is stop playing against other experienced players on the big sites, and check out sites where the majority of players are amateurs, recreational poker fans or just plain fish! Your returns will be much bigger at 888 Poker - I strongly recommend you check out the tables at 888 Poker now and see just how soft their games are for yourself!
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.
Game Theory Applied To Poker
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.
Planet Mark's Rec : If you are thinking about Poker Game Theory, then you are already more advanced than the majority of players. What you need to do next is stop playing against other experienced players on the big sites, and check out sites where the majority of players are amateurs, recreational poker fans or just plain fish! Your returns will be much bigger at 888 Poker - I strongly recommend you check out the tables at 888 Poker now and see just how soft their games are for yourself!