Wednesday, October 01, 2008

Game Theory and Bet Sizing

I have been trying to use the principles of game theory to improve my game for a while now. Poker is a game of incomplete information, and game theory tells you how to maximize your advantage in these types of games and situations. A player whose game was fully developed using game theory could tell you exactly how they would play their hand in all situations, and even if you knew this, you would still not be able to beat them. I have always wanted to post my exact strategies and challenge someone to exploit them, but my game still needs a bit of work. There are a few areas where my game can be exploited and I am painfully aware of most of them. Luckily only a few players out there are capable of recognizing these weaknesses and actively exploiting them. So even though there is a hole here and there in my game, it is pretty rare someone jumps in and tries to take advantage of my specific weaknesses.

What I wanted to post about today is how you can use game theory to make your decisions easier, while still increasing your profitability. Game theory tells you to disguise your hand by playing many different ranges of hands in the exact same way. You also determine these ranges in a way that the percentages that you fold/call/raise/reraise can’t be exploited. For example if you are bluffing 20% of the time in a specific situation and everyone knows this, they still can’t exploit it because 80% of the time in the same situation you are not bluffing. Someone trying to exploit your bluff percentage will win a bit when they are right, but will lose more when they are wrong, making the overall strategy –EV for your opponent.

One way to disguise your hand is by bet sizing. Game theory tells you to not vary your bet sizing based on hidden information (your actual hand). Your bet sizing can vary based on public information like your position, your stack size, the number of active players in the hand and there positions and stack sizes, and the board cards. One of the most complicated things in NL Holdem is to determine proper bet sizes. When you can eliminate your actual hand from the equation the decision becomes much easier. This easier decision also better disguises your hand, so your game is simplified while also improving. I will give a couple of examples here. When I want to open raise preflop in MTTs I simply raise 3x the blinds, no matter what cards that I have. If there are limpers in before me (public information), I may raise a bit more based on this. As the MTT progresses and the blinds become a higher percentage of the stack sizes this is also public information. You could lower the open raise amount at that point, but because there are antes involved late, you should also raise a bit more. This actually becomes a bit of a wash, so you can just continue to raise 3x the blinds. When I start jamming preflop late, this is based on my current stack size (public information), and not on my starting cards.

Early in MTTs I play pretty tight, so when I do raise preflop from early position, you can be pretty sure that I have a big pair, or big ace most of the time. My range widens as my position improves, but is still pretty compressed even when “stealing” from the button. So hopefully my raise will get some respect and limit the amount of players seeing the flop to 2-4 total. Now the flop comes which is public information. So now I am forced with deciding to continuation bet or not. If I do C-Bet, the amount will not be based on my actual hand. I just C-Bet 2/3s of the pot in general. You can make a size adjustment based on the texture of the board and number of opponents, but not on your own hand. So if I am allowed to get a C-Bet in, I will go ahead and make it if I started with a pig pair and now hold an over pair, if I started with a big ace and hit either the Ace or my kicker, or if I completely missed and there are just one or two opponents. So when you see my C-bet, it means that a certain percentage of the time I have an over pair, a certain percentage of the time I have top pair, a certain percentage of the time I have a monster, and a certain percentage of the time I have nothing. The amount of the C-bet tells you nothing, because it is not based on my actual hand. The fact that I did C-bet does not really narrow my range either. It was pretty tight already with the preflop raise. So what happens is that my C-bets can’t really be exploited. If you reraise my C-Bet, you are asking for trouble unless you can beat an over pair or TPTK. Now there are times when I don’t C-Bet. This is typically when too many people call preflop, I am out of position, and I completely miss. To balance that out, you also need to miss a C-bet most of the time you flop a monster in EP, and occasionally when you flop an over pair or top pair. So when I C-bet my hand is disguised, and when I don’t C-bet it is still disguised.

What is the moral to this story? If you are adjusting your bet sizes in NL Holdem based on your actual hand, you are giving away information which will lower your EV, while at the same time making your bet size decision more complex. Why go to this trouble if it is hurting your game?

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