Playing $1-$2 no-limit hold'em at Mandalay Bay this afternoon, I saw a move that makes perfect emotional sense, but is completely insane from a profit-maximizing perspective.
On my left was a retiree, obviously local and well known to all of the dealers and floor personnel. His name is Sammy. He is a stereotypical--maybe even archetypal--local "rock." On the hand in question, a middle-position player raised to $10 after a couple of limpers. Nobody called behind him. Sammy was in the small blind. He put in a curiously large reraise, to about $55. The big blind and limpers folded.
The original raiser was the only one left with a decision, and he looked unsure what to do. As he was contemplating his options, Sammy deliberately turned face up his two red aces, and said, "Does that make your decision any easier?" His lone remaining opponent smirked, then said, "I suppose I could go in with a 9% chance of winning," but then folded. (I'm guessing from this comment and the fact that he apparently had a genuinely difficult decision that he most likely had A-K, which is indeed in the ballpark of a 10:1 dog to pocket aces.) As Sammy was scooping up the itty-bitty pot, he said, "Good. The last thing I need is you drawing out on me."
As I said, on an emotional level I can understand perfectly what was going on there. Sammy has played poker for a long time and has seen his aces cracked by inferior hands too many times. The sting of those memories weighs heavily on him, and he has devised a strategy to reduce the chance that he will have to feel that hurt again: He bets so big that nobody will call. And if it looks like that didn't do the trick by itself, and somebody might call anyway, he shows them the aces to dissuade them. He collects the small pot, quite content with the outcome, because he didn't lose.
It's obvious that that last phrase is the key to the whole thing. Never losing with aces has become his primary focus.
But it's a completely irrational way to play the hand if your goal is to maximize your lifetime profit from all of the times you are dealt pocket aces. In order to do that, you somehow have to get opponents to put as much money as possible into the pot when they are 4:1 or even 10:1 underdogs to win. If maximizing long-term profit were Sammy's goal, he should bet an amount that he thinks is the most that will be called by a player with A-K. (Exactly what that amount might be will vary with the opponent, relative table position, chip stacks, etc.) The question he should be silently asking himself is, "What is the most that this guy will be willing to call?" Sammy, contrarily, is asking himself, "How much will it take to make this guy fold?"
Given that that is his goal, one might wonder why he doesn't just move all in. My guess is that the psychological pain of possibly losing his entire stack if he fails to chase somebody away (e.g., somebody sitting on K-K, or a player who is drunk or otherwise entirely carefree, or one who is stuck badly and willing to gamble it up) and his aces get cracked is just too much to bear. So he instead has evolved this one-two punch of a big over-raise, followed by showing his cards, if necessary, to complete the effect without putting his entire stack at risk.
Most players, though, understand that being a winning player means getting maximum value from the rare occasion of being delivered a prize such as A-A. That, in turn, means coaxing opponents into the pot with more money. Yeah, it also means that you'll occasionally lose--and the amount may well be large, even one's entire stack. But the math doesn't lie: over the long run you really will make a lot more than you lose if you somehow manage to get opponents to put as many chips as possible into the pot when they have only a 10% or 20% chance of winning it.
I'll take A-A over A-K for as much money as I have in front of me, if my opponent is willing, and eagerly step up to do it again and again and again, as many times as possible. I know that this means losing that stake one out of ten times or so. I also know that I don't get to choose when the loaded chamber on that ten-round revolver pointed at my head will be the one under the firing pin. In a lifetime, it will sometimes happen three or four times in a row, and I'll feel like I got run over by a truck, and may start whining like Phil Hellmuth or Mike Matusow about how the universe is stacked against me. (See here for my personally most painful story of aces cracked for large pots nearly back-to-back.) But I understand that that is the price one necessarily must pay in order to reap the most long-term profit. It is not optional. It is literally impossible to get the greater reward without taking the risk.
There is a theorem in economics and game theory about something called "minimax" strategy. It involves picking a strategy that minimizes one's maximum possible loss. This isn't quite that, because Sammy could still lose everything on the hand (unless he secretly has a third component to his strategy, which is to fold if he gets reraised--I kind of doubt that he would, but with a set of values so distorted, it's hard to say for sure). Instead, he is trying to minimize the probability of losing anything at all. If there's a specific name for that in game theory, I don't know what it is.
But regardless of the label we might put on it, Sammy's strategy is essentially the equivalent of accepting a virtual certainty of walking away with the tiny slice of pie in the illustration above, rather than go for the whole pie, because he's unwilling to take the chance of losing everything, even when he is, at minimum, a 3:1 favorite. (Statistically, the best hand to put up against A-A is something like 7-8 of a suit not held by Mr. Aces. You're only about a 3:1 underdog in that scenario.)
It's not necessarily irrational, if one values avoiding the pain of a loss more than one values maximizing long-term profit. But I have to admit that that is an ordering of values and priorities that is utterly foreign to me.
Matt Lessinger, who I think is one of the finest columnists in Card Player magazine's stable, wrote an enlightening and clear-headed piece on the Sammy mindset a couple of years ago. I recommend reading (or re-reading) the whole thing here. I'll leave you with the excellent mini-lecture embodied in just one of his paragraphs:
I don't care if you are a rank novice or a world champion. It doesn't
matter whether you are in a tournament or a cash game. You could be playing for
pennies or Porsches. It's all the same. If you can get all of your money in as a
4-1 favorite, do it. And if you lose, live with it. It happens. Wait
for the next opportunity to arise, and then do it again. If you are
able to consistently create that scenario, you will be a successful player--end
of story.
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