Fundamental, schmundamental
Possibly the most over-hyped theoretical principle in poker is Sklansky's "Fundamental Theorem". All it really says is: "Poker is a zero sum game". What makes it worse is that it says it in a way that makes it easy to misinterpret. Now that's not directly Sklansky's fault (except inasmuch as he maintains the incredibly arrogant position that clear expression is less important than good ideas) but it does mean that it's not uncommon to run across howlers like the following from Barry Tanenbaum:
from which he then infers that the raise was incorrect.
That's just so wrong. It can be correct both for you to raise, and for your opponent to call. Here's a simple example. There's a $10 bill on the table. We're going to draw one card from a shuffled deck. If it's an Ace through seven I win, if not, you win. Obviously I have a 7/13 chance to win. The catch is that I can raise the stakes, putting an extra $20 into the pot. You either have to match this or fold.
Am I correct to bet? Certainly. If I don't bet, my expectation is 70/13. If I do bet and you fold, I win $10 and am better off. If I do bet and you call, I still win that $10 seven times in 13, and I win our $20 sidebet seven times in 13 at even money.
Are you correct to call? Let's start you out with a $20 bill in your wallet. If you fold it's still there. If you call, then seven times in 13 your wallet is empty, and six times in 13 it contains $50. Since 300/13 > 20, you're better off calling (unless that $20 is very very important to you!)
Sure this is a simplified situation, as opposed to the one Barry is considering (what to do on the button preflop if one or both of the blinds never fold to a preflop raise). His conclusion, that it may be correct to limp with some hands, is certainly defensible (if nothing else, it lends authority to subsequent continuation bets on hands that begin with a raise), but it has nothing to do with the fundamental theorem of poker.
...if you raise with a hand what your opponents are correct to call, and they do call, you lose ...
from which he then infers that the raise was incorrect.
That's just so wrong. It can be correct both for you to raise, and for your opponent to call. Here's a simple example. There's a $10 bill on the table. We're going to draw one card from a shuffled deck. If it's an Ace through seven I win, if not, you win. Obviously I have a 7/13 chance to win. The catch is that I can raise the stakes, putting an extra $20 into the pot. You either have to match this or fold.
Am I correct to bet? Certainly. If I don't bet, my expectation is 70/13. If I do bet and you fold, I win $10 and am better off. If I do bet and you call, I still win that $10 seven times in 13, and I win our $20 sidebet seven times in 13 at even money.
Are you correct to call? Let's start you out with a $20 bill in your wallet. If you fold it's still there. If you call, then seven times in 13 your wallet is empty, and six times in 13 it contains $50. Since 300/13 > 20, you're better off calling (unless that $20 is very very important to you!)
Sure this is a simplified situation, as opposed to the one Barry is considering (what to do on the button preflop if one or both of the blinds never fold to a preflop raise). His conclusion, that it may be correct to limp with some hands, is certainly defensible (if nothing else, it lends authority to subsequent continuation bets on hands that begin with a raise), but it has nothing to do with the fundamental theorem of poker.
Labels: math
posted by Michael Albert at 8:43 am
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