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In Getting Started In Hold'Em Ed Miller discusses a "very common debate" about a hypothetical situation in tournament poker where everyone at your table goes all-in and you look down at your cards and find AA. In my copy it's on page 158.

I'm going to show why his analysis (not necessarily the conclusion) of the situation is wrong.

He analyzes the situation in terms of pot odds and pot equity. Saying you have 30% chance of winning so the "opportunity is worth well over $20,000 to you". He concludes that you should go all-in even if it's the first hand of a long tournament and that anyone who would argue otherwise is simply letting their emotions get in the way of proper play -- not wanting to get eliminated before they get a chance to play.

But he misses an important detail. The $20,000 gain is in tournament chips. It has absolutely <font color="red">*NO*</font> intrinsic value.

The <font color="red">only</font> value those chips have at all is in the increased chance of winning the tournament that they give you. How much of an increased chance of winning a tournament does having 10x everyone's else's stack on the second hand? It sure ain't gonna be 10x their chance.

So, hypothetically, let's say you had a 1% chance of winning the tournament when you entered and with 10x the normal stack you've tripled your chances to 3%. Now going all in with AA looks weak. You win 30% of the time but you're only getting 3:1 odds.

Unfortunately it's very hard to estimate the degree to which having a 10x stack would help your odds of winning the tournament (and just doubling or tripling up would be even harder). In a tournament with a flat prize distribution it might give you a near lock on a smaller prize.

This also explains why playing conservatively when you're on the bubble isn't entirely irrational. If you know your own playing strength and know you have very little chance at the top few prizes that play well then your entire upside is limited to an increased chance at some slightly larger prizes. It can be hard or impossible to get odds that justify going all-in if you don't think you really have a shot at the prizes that are more than 2-3x the prize you already have a lock on if you just fold.

So people's emotions aren't necessarily leading them astray here. Their instincts are on the right track. You have to consider what those chips really are worth to you and before you risk going all-in for a chance to double-up ask yourself whether you're really doubling your expected tournament winnings even if you double-up.

In the actual scenario described I suspect having a 10x stack on the first hand of a tournament does in fact increase your expected winnings by more than 3.3x so calling with AA would be a +EV play in real dollars, not just tournament chips.


Actually, this would be an interesting question to analyze using empirical data. It's doesn't require any non-public information about people's hands either, just stack sizes of the field. Plot people's eventual winnings versus stack size after some hands, say, just before the first blind increase. Then look for a curve fit. Hm. To do it properly you would have to look at the same players across multiple tournaments to eliminate the effect that larger stacks will tend to indicate better players. But it could be done and it would give some hard numbers for how much you should expect doubling-up in early stages to increase your real dollar winnings.