The Game
Be warned, this upcoming post contains some horribly applied economics theories to poker. Not that they don’t apply, they do somehow, but I’m not smart enough to articulate perfectly how they do. But we’ll try anyways.
Ok so if you’re a student of poker, and have read and watched a lot of poker material, then you will have stumbled across players who claim they play poker based on something called “Game Theory”. Now, while I call bullshit on most of these pseudo-intellectuals, game theory does have its applications.
Quick lesson on game theory:
Basically it’s usually a 2 party (firm) model where you examine the various options to each party and their respective outcomes. So for example, 2 firms who compete in the same market (lets say 2 pig farmers) have to decide what price to charge for their product. And in this example they are the only 2 in their market. So there are basically 4 total combinations of prices.
A) They charge the same high price that maximizes their joint profits ($100/pig each)
B) Firm A undercuts Firm B (Firm A: $100/pig, Firm B: $60/pig)
C) Firm B undercuts Firm A (Firm A: $60/pig, Firm B: $100/pig)
D) They both end up charging the “undercut” price. ($60/pig each)
This happens all the time in the business world, especially when the firms can sell their product for “secret” prices. Now the theory goes, that if they both just chose option A, where they set a price that maximizes both their profits, they would both be better off in the long run. But what happens, is that there is strong incentive to cheat, and undercut each other. Because they are the only 2 in the market, if one undercuts, they will have 100% of the market share. The theory continues, that they will almost always end up at $60/pig each because the incentive is too great not to cheat, and a collusive agreement to stay at $100/pig never works out.
Ok, that’s pretty clear. But how the fuck does it apply to poker? Well, I’ll tell you it took me a while to see it. It truly only applies when you are playing against opponents who are skilled, think critically and have lots of experience. So don’t worry about this at the $5 buy-in’s. I’ll try to construct a poker example where this works.
It’s late in a tournament and blind stealing is very important. You are on the button at a 5 handed table and it’s folded to you. The player in the BB is smart, critical, experienced etc. Because it’s 5 handed, your opponent can just as easily raise your blinds as you can his. Now, what hands should you be raising here?
A) Any 2 cards
B) Any decent hand like A2 or J8
C) Top 20% hands, which is something like 55+, A8+, KTs+
Putting this into a game theory model, lets say you are firm A and the opponent in the BB is firm B. Lets assume that the frequency of your raises will be directly correlated to how often B reraises and calls you. What is the optimal raising scenario? Well, that answer is simple; the one in which best jointly maximizes both your profits (chips). Think about it, if you and your friend were playing in a tournament and decided to soft play each other, how would you maximize chips in this scenario? You would most likely only raise their blinds with stronger hands and when one friend picks up a big hand they would reraise them to let them know that this time they can’t fold. And that’s basically the optimal solution. There is no use raising the blinds with any 2 cards because eventually you will receive playback, and have to end up folding. So what you want to achieve is a non-communicative collusive agreement with your opponent in the BB. You want to let him know that you will only be raising with hands that warrant it and that he should do the same. This way you both maximize your chips saving lost chips that would have been uselessly thrown away by fighting each other with reraises. And you achieve this by only raising when you are likely to have the best hand. There’s nothing unethical about raising when you probably have the best hand, but many people feel that it is unethical to raise when you don’t. Of course this is a whole other debate because poker is poker and you can do whatever you want. Ultimately, at this stage of the game, stealing the blinds is usually all you want, unless you have a monster, and by making sure he knows that you are raising with strong enough hands and to only playback with even stronger hands.
But there is always incentive to cheat, just like in the pig farm example. If you start raising with junk from the button, for a bit, he won’t notice it. But eventually he of course will, and start reraising you with junk. And what happens is you both lose more chips to each other because you’ve started a little “pricing” war because the value of your hands has dropped.
But maybe you want that. Maybe you enjoy playing these games, or maybe you enjoy gambling with shit hands. I personally don’t. I usually will just raise with a playable hand and take it from there. Of course assuming your opponent is decent is a heroic assumption online, so there’s always that danger.
After reading this over I don’t love the example I came up with and there are certainly many more I could think of. Basically it just comes down to when you and your smart opponent are heads up against each other, and you both know the options to each player, you put them on a range of hands and play accordingly. It’s only when people start playing out of line that the “collusion” breaks down. And isn’t that always the case with any collusion? My advice is to stay in line and play the game. But a lot of people don’t get excited folding to their opponent 4 times in a row, so they make plays, and that’s what ends up driving poker.
This post sounded so much better in my mind, but I hope it was interesting.
Ok so if you’re a student of poker, and have read and watched a lot of poker material, then you will have stumbled across players who claim they play poker based on something called “Game Theory”. Now, while I call bullshit on most of these pseudo-intellectuals, game theory does have its applications.
Quick lesson on game theory:
Basically it’s usually a 2 party (firm) model where you examine the various options to each party and their respective outcomes. So for example, 2 firms who compete in the same market (lets say 2 pig farmers) have to decide what price to charge for their product. And in this example they are the only 2 in their market. So there are basically 4 total combinations of prices.
A) They charge the same high price that maximizes their joint profits ($100/pig each)
B) Firm A undercuts Firm B (Firm A: $100/pig, Firm B: $60/pig)
C) Firm B undercuts Firm A (Firm A: $60/pig, Firm B: $100/pig)
D) They both end up charging the “undercut” price. ($60/pig each)
This happens all the time in the business world, especially when the firms can sell their product for “secret” prices. Now the theory goes, that if they both just chose option A, where they set a price that maximizes both their profits, they would both be better off in the long run. But what happens, is that there is strong incentive to cheat, and undercut each other. Because they are the only 2 in the market, if one undercuts, they will have 100% of the market share. The theory continues, that they will almost always end up at $60/pig each because the incentive is too great not to cheat, and a collusive agreement to stay at $100/pig never works out.
Ok, that’s pretty clear. But how the fuck does it apply to poker? Well, I’ll tell you it took me a while to see it. It truly only applies when you are playing against opponents who are skilled, think critically and have lots of experience. So don’t worry about this at the $5 buy-in’s. I’ll try to construct a poker example where this works.
It’s late in a tournament and blind stealing is very important. You are on the button at a 5 handed table and it’s folded to you. The player in the BB is smart, critical, experienced etc. Because it’s 5 handed, your opponent can just as easily raise your blinds as you can his. Now, what hands should you be raising here?
A) Any 2 cards
B) Any decent hand like A2 or J8
C) Top 20% hands, which is something like 55+, A8+, KTs+
Putting this into a game theory model, lets say you are firm A and the opponent in the BB is firm B. Lets assume that the frequency of your raises will be directly correlated to how often B reraises and calls you. What is the optimal raising scenario? Well, that answer is simple; the one in which best jointly maximizes both your profits (chips). Think about it, if you and your friend were playing in a tournament and decided to soft play each other, how would you maximize chips in this scenario? You would most likely only raise their blinds with stronger hands and when one friend picks up a big hand they would reraise them to let them know that this time they can’t fold. And that’s basically the optimal solution. There is no use raising the blinds with any 2 cards because eventually you will receive playback, and have to end up folding. So what you want to achieve is a non-communicative collusive agreement with your opponent in the BB. You want to let him know that you will only be raising with hands that warrant it and that he should do the same. This way you both maximize your chips saving lost chips that would have been uselessly thrown away by fighting each other with reraises. And you achieve this by only raising when you are likely to have the best hand. There’s nothing unethical about raising when you probably have the best hand, but many people feel that it is unethical to raise when you don’t. Of course this is a whole other debate because poker is poker and you can do whatever you want. Ultimately, at this stage of the game, stealing the blinds is usually all you want, unless you have a monster, and by making sure he knows that you are raising with strong enough hands and to only playback with even stronger hands.
But there is always incentive to cheat, just like in the pig farm example. If you start raising with junk from the button, for a bit, he won’t notice it. But eventually he of course will, and start reraising you with junk. And what happens is you both lose more chips to each other because you’ve started a little “pricing” war because the value of your hands has dropped.
But maybe you want that. Maybe you enjoy playing these games, or maybe you enjoy gambling with shit hands. I personally don’t. I usually will just raise with a playable hand and take it from there. Of course assuming your opponent is decent is a heroic assumption online, so there’s always that danger.
After reading this over I don’t love the example I came up with and there are certainly many more I could think of. Basically it just comes down to when you and your smart opponent are heads up against each other, and you both know the options to each player, you put them on a range of hands and play accordingly. It’s only when people start playing out of line that the “collusion” breaks down. And isn’t that always the case with any collusion? My advice is to stay in line and play the game. But a lot of people don’t get excited folding to their opponent 4 times in a row, so they make plays, and that’s what ends up driving poker.
This post sounded so much better in my mind, but I hope it was interesting.
posted by RikkiDee at 2:20 PM
1 Comments:
Hmm. Interesting post very INTERESTING! I first heard about Game Theory in the form of “mutually assured destruction”, it’s the idea that the full scale use of nuclear weapons by one of two opposing sides would result in the destruction of both the attacker and the defender, in a discussion about the cold war in class of course. Also I learned about it in the form of “The Prisoners Dilemma”, an idea in which each player pursuing their own self-interest leads to both players to being worse off than had they not pursued their own self-interests. Although I have never considered it since, thinking about it now it could almost be applied to a crap load of topics including poker.
I’m not going to lie to you RikkiDee I Googled it, and get this the first record of Game Theory is in a letter in 1713, about a strategy to a two-person version of the card game called le Her (I don’t know what the game is or how to play it). I soon came across something called a “Nash Equilibrium” which is a kind of optimal collective strategy in a game involving two or more players, where no player has anything to gain by changing only his or her own strategy. If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium. This took me awhile to understand and yes I did read a number of times before I somewhat grasped the idea.
Here is an example I found, consider the following two-player game: both players simultaneously choose a whole number from 0 to 10. Both players then win the minimum of the two numbers in dollars. In addition, if one player chooses a larger number than the other, then s/he has to pay $2 to the other. This game has a unique Nash equilibrium: both players choosing 0. Any other choice of strategies can be improved if one of the players lowers his number to one less than the other player's number. If the game is modified so that the two players win the named amount if they both choose the same number and otherwise win nothing, then there are 11 Nash equilibria.
You see that the equilibrium is trying to keep your opponents profits to a minimum and speaks nothing about trying to maximize your gains. So, in a heads up match, which is a zero-sum game (you gain only what your opponent loses) you could take this idea in to consideration, i.e. you play optimal hands only, therefore minimizing the risk of losing money and decreasing your opponents gains, which is exactly what you said Rikkidee.
On a side note, a game that does not have a Nash Equilibrium is rock paper scissors, although psychology is a huge factor in it there is a strategy to it. The optimal strategy is to play completely random, play like a computer program would; this in turn is supposed to eliminate psychology from the equation. There is a catch you have to be playing an optimal opponent, and by optimal I mean a person that is incapable of being defended more then expected by chance. In fact, if the opponent is human or a non-random program, it is almost certain that he plays suboptimally and that a modified strategy can exploit that weakness. You’re probably asking yourself what the hell does this have to do with poker, well Phil Hellmuth enters in to a little tournament called the world championships of Rock Paper Scissors every year, yea that’s right.
On a side note to that side note one high-profile strategic opinion came in 2005 from Alice Maclean, age 11. When rival auction houses Christie's and Sotheby's agreed to play rock-paper-scissors to determine the rights to a highly valuable art collection, Maclean's father Nicholas, a Christie's employee, asked her for advice. As later told to reporters, her strategy was summed up thus: "Everybody knows you always start with scissors. Rock is way too obvious, and scissors beats paper." (Christie's won, with scissors).
Shit sorry this is so long…
WP
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