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“Life is like a game of cards. The hand that is dealt you is determinism; the way you play it is free will.”
–Jawaharlal Nehru
It’s almost that time. Time for the biggest poker tournament in the history of the game. And also time for the second gathering of the strange breed of folks called “poker bloggers”. I’m excited to participate in both.
After a long internal struggle of whether or not I wanted to put my dead money in the prize pool for the first event of this year’s WSOP, I finally gave in to the call of the bracelet, and sent in my registration. After a couple of excellent sessions in the Party $15-30, I had won enough for a semi-guilt free buy in. Although I rarely play tourneys, I have played and read enough to play a tight aggressive strategy reasonably well. I played well in the LA Poker classic, and felt like I could compete with the few pros I sat with during the tournament. In the end, I decided that one shot at a bracelet was worth the experience, even though I don’t like my chances against 2000 of the world’s best.
Even after 18 years of football experience, I always got very nervous the night before the first game of every season. The nerves went away as the season went on, but I was always on edge for the opener. 5 days away from the tourney, I’m feeling like the season opener is upon me. It’s a feeling I haven’t felt in 2 years, a feeling I miss and thought I’d never get back. I can see how people get hooked on these tourneys… Although I lack experience, I feel focused and ready to play the best game I can on Friday.
Of course, the afterparty with the bloggers on Friday will be the icing on the cake (assuming I’m not miraculously still in the hunt for a bracelet).
Game Theory
I’m not sure why, but over the past two weeks, in books and conversations I keep stumbling upon the role of Game Theory in poker. Although I never got into it as deeply as I would have liked, I did study a fair bit of game theory in my academic career. So when I come across poker related game theory, my eyes/ears perk up.
Game theory is the study of how people interact and make decisions, and usually involves a mathematical model that simplifies the real-world interaction and decision-making process among the people involved. The key assumption required for these models to “work” is that the actors in the game are Rational: people make decisions that are in their best interest, and their best interest involves the end goal of “winning” the game.
Whether or not an individual poker player is rational is a completely different topic, and I’m not going to touch that one.
My main interest in poker game theory is introducing non-optimal (in terms of odds) plays in order to confuse opponents, thereby creating greater future returns.
Assume we have a table full of bots that play tournament poker. Assume that these bots play “by the book,” and raise when the odds are in their favor, and fold otherwise. The bots never bluff, and have no knowledge of their opponent bots strategy.
This game would be extremely boring to watch– most of the hands would be decided before the flop, but for those that weren’t, they would involve primarily pair vs. pair or AK vs. pair all-ins (much like a real game).
Now imagine you sit down at the table. What is your optimal strategy? It’s pretty clear that you would just min-raise the bots to death preflop, folding when you’re called or raised. You’d be able to steal plenty of blinds, and wait for a double up when holding a big pair. Your advantage is huge since you can narrow down your opponents’ possible hands down to a very small range.
Now suppose another game theorist sits down at the table with you. Your old optimal strategy goes down the toilet, and the complexity of the game increases tremendously. Your opponent knows that you will be min-raising with trash hands, and when he has position on you, it’s very difficult for you to combat his re-raises. The game becomes a struggle between you and the game theorist for the blinds of the bots.
How best to combat the game theorist’s re-raises? If you only raise him when you are fairly certain your hands are stronger than his (your hand is much better than a random hand), you will be giving up too much money to his raises. The answer is choosing a percentage of re-raises that will allow you maximize your expectation. If your opponent continues to re-raise you, the optimal bluffing frequency in this case is probably somewhere just under 50% (you’d have to take into account the probability that the bots have a hand).
Note that this model looks something like a table full of weak-tight players with two hyperaggressive players battling it out. The point of this simplistic model is not to advocate a particular playing style, but to stress the importance of adding some randomized plays that “keep the other players honest” and keep them guessing as well.
For the most part, everyone at the table has the same knowledge of poker odds. Most players say that tells are hard to come by among expert players. This means that the difference between good players lies in their abillity to confuse and deceive their opponents. The only way to avoid pattern-izing your deception is to use randomization, so that you don’t even know what move you will make before you make it.
For example, if you never limp with big pairs, observant opponents will pick up on this and have no fear of raising your limps. One way to randomize your play is to say that 17% of the time, I’m going to limp with a pair (the “sub-optimal” play) and 83% of the time I’m going to raise. This is enough to put the fear of our opponents, so now we need a way to randomly make this play with our big pairs. The simple way is to limp when both cards are red, and raise otherwise. I’ll leave the math to the reader.
Of course, your opponents have to be paying pretty close attention to your play for any of these plays to work. But at the highest levels, you can bet they will be.
For most of the games I play, deception has little value, since most of my opponents aren’t paying close enough attention to remember I play I made 20 minutes ago. But it’s fun to think about anyway.
Thanks for reading, and I’ll see you at the World Series.