Aces cracked

Image from: http://pokerchaos.blogspot.com/2006/04/cracked-aces.html


Yesterday was, I think, the first time I have played poker during an aces-cracked promotion since moving to Vegas--and I did it twice, first at Flamingo, then again at Harrah's. Yesterday was definitely the first time I have ever been dealt pocket aces during an aces-cracked promotion, and thus had to decide how to play them. I went for the standard approach with a raise and a continuation bet. A short stack shoved and I called. I won, though less than the $100 bonus I would have earned by losing the hand.

I first encountered an aces-cracked promotion back when I was living in Minnesota and playing at an Indian casino in Wisconsin. I quickly tired of the inevitable stupid arguments that would break out over whether one should play to win the hand or play to lose it and pick up the jackpot. I maintain that avoiding having to listen to such arguments endlessly repeated is an excellent reason to stay away from poker rooms during aces-cracked promotions. They make me want to stick an ice pick in my eardrums.

The argument should be purely mathematical, though precious few of those engaging it seem to understand how to evaluate it.

The first part of the analysis is straightfoward, thanks to marvelous tools such as PokerStove: What is the probability of losing when you have pocket aces? Here's the answer, given the number of opponents (assuming that they all stay in the hand to the river):

1--14%
2--27%
3--36%
4--44%
5--51%
6--57%
7--61%
8--65%
9--69%

As you can see, you have to drag five people all the way to the river to have even as much as a 50% chance of having your aces cracked. Even in loose-passive games, that does not happen very often.

But the math gets murky after that point. If you're playing to lose--i.e., limping and check-calling--you can't control how much your opponents like their hands, and therefore how much they'll charge you to stay to the river. Furthermore, your attempts to minimize the pot will often--usually, in fact--backfire when you end up winning in spite of yourself, and raking in a much smaller pot than you might otherwise have won.

Knowing the statistically predictable frequency of loss is easy. But determining the optimal strategy also depends on knowing how much equity you'll sacrifice by having minimized the pot when you win, and how much you'll have to put into the pot on calls when you lose. Those numbers are not at all obvious, and they will vary tremendously with the style of play of your opponents at any given table. They are effectively unknowable, and at best can only be guesstimated.

If the jackpot were, say, a million dollars, the conclusion would be obvious: try to lose. Conversely, if the jackpot were one dollar, the conclusion would be obvious: ignore it and try to win the hand as usual. The problem is that the jackpot--typically $50 or $100--is in a range such that one's assumptions about the costs of trying to lose make all the difference in the world about one's conclusion as to the optimal strategy.

And that is why the table arguments about how to play aces are so pointless: nobody knows what is actually best because the answer is completely contingent on unmeasureable and constantly changing input variables.

Because of that, I had decided long ago that if I found myself in such a situation, I would play as usual, try to win, and take the jackpot as a consolation prize if I lost. That may or may not be optimal for any specific mix of opponents, but, in its defense, (1) it is not clearly wrong or suboptimal for typical conditions in a $1-2 NLHE game, and (2) it saves me having to try to run complex math at the table.

Given that aces-cracked promotions are relatively common, you might wonder how it is that I can say that I think yesterday was the first time in 4+ years I've encountered one. First, they typically run during hours that poker rooms are slow; management is trying to get games going when the room would otherwise be idle. I am usually not playing during those hours. Second, I usually try to avoid rooms running such promotions, because I seriously dislike how they distort the game. Yesterday I was seated at both the Flamingo and Harrah's before I knew that the promotions were in effect.

Since leaving the Midwest, I have therefore had a blissful respite from hearing nits criticize somebody who plays his aces aggressively, or stupid laments from a nit who is so "unlucky" as to win with his aces, or endless speculation about what would have happened if an aces hand had been played differently from however it was actually played--a respite which came crashing to a halt yesterday. These are among the most pointless and annoying, yet seemingly inevitable, conversations that will ever afflict a poker table, ranking right up there with jackpot discussions when a bad-beat bonus has become unusually rich.

Spare me. I hope it's another four years before I have to listen in on another round of it.