Practical Probability — Part VII

I recently did a “pro chat” on Full Tilt Poker, asking players what questions or problems they had in the areas of probability, statistics, and mathematics in relation to poker. I was somewhat surprised that a lot of players still have questions about calculating and using pot odds, outs, and related concepts. It seemed to me that so much has already been written about these ideas that there is no excuse for not being up to speed on them. One other subject created a lot of interest, and as you can see from the subtitle of this column, that topic is folding aces before the flop. Everyone wanted to know if I had ever folded aces before the flop, and if it could ever be right to do so. Answer both of the following questions before you proceed to read the rest of this column.

Have you ever folded aces before the flop? First let me inform you that the most successful tournament no-limit hold’em player of the last 20 years has probably folded aces preflop more often than anyone else. I also have done it a fair number of times, in exactly the same situation. The typical tournament procedure is to deal in all of the stacks at the table. If a player isn’t in his seat when the last card is dealt, he is automatically folded. Some of those times, he has aces. Since Phil Hellmuth has made late arrival at tournaments his standard policy, he has probably folded aces more than anyone else. (I guess that if you wanted to be really technical, you could say that the dealer folded them for him.) Many players who play online, especially those of us who multitable, are occasionally timed out, when focusing on another table or due to disconnection. As is the case with missed hands, this sometimes results in aces being folded.

Is it ever right to fold aces before the flop? Yes, there are at least three situations in which it is clearly correct. The first occurs in supersatellites. A supersatellite is a tournament that rewards winners with seats into a big tournament. If 20 seats are going to be awarded, finishing first is exactly equivalent to finishing 20th. Let’s suppose that this is the case, and that there are 21 players left. The blinds are 500-1,000. The chip leader has 60,000 and is on the button. You are in second place with 59,000 and are in the small blind. There are several players with short stacks, between 800 and 2,000. Everyone folds to the button, and he moves in. You have aces. Should you call? No. In fact, you should just fold blind. The only realistic way for you not to win a seat is to call and lose. I’d estimate that by calling, you will get your seat 85 percent to 90 percent of the time, but by folding, about 99 percent of the time. Folding is clear.

The second situation also relates to the bubble, but it occurs in regular tournaments when you are one of several players with very short stacks, and it is especially common in tournaments with huge fields. The tournament is now played hand for hand. (The next hand is dealt when the current hand is completed at all tables. This continues until someone is knocked out.) You are on the button, and can guarantee surviving seven hands by folding every time, but if you call the blind, you will be all in. Several of the other short stacks will be forced to go all in before you if you don’t call. Let’s look at the math for a recent online tournament. There were 8,000 entrants. Finishing 568th to 1,170th got you $320. Finishing slightly better than that, 451st to 567th, got you $480. If you made it all the way to 250th, you’d gain about $1,000 more than just getting into the money. With 1,171 players left, the strategy of folding every hand would make you certain to finish in the money, for $320. If you are unfortunate enough to get aces and go all in, I’d estimate that your equity is less than $300. For example, let’s estimate that you have an 84 percent chance to get the same $320, a 1 percent chance to do better, averaging out to $2,000, and a 15 percent chance to get nothing. This amounts to $288 (.84 x $320 plus .01 x $2,000). You do 10 percent worse if you play your aces, so, mathematically, it is clearly right to fold.

How accurate are those estimates. I have assumed that folding every time guarantees you a place in the money every time. This is reasonable, although maybe only 99.5 percent is correct. On the other hand, I have assumed that folding every hand until you’re in the money can result in only a last-place finish. Obviously, there are some times when you’d be in the money after one or two hands, and then go on to survive long enough to increase your payday. Aces win approximately 85 percent of the time against a random hand, but do slightly worse against hands that players elect to play. For example, aces win less than 80 percent of the time against suited connectors. In reality, you will very seldom beat even the 600 players you need to beat to get an extra $160. Remember, they all have significantly more chips than you would have, even after winning the hand. So, both the 1 percent and the $2,000 are generous. There is, however, some chance that you would share bubble elimination, and get half of $320. If we upgrade the numbers very generously to show that you are never eliminated alone, we go from 15 percent of $0 to 15 percent of $160, or $24. Even this added equity still leaves you $8 short of $320.

There is one last situation in which it is correct to fold aces before the flop. It is so rare that I hesitate mentioning it in a column with the word “Practical” in the title. The situation arises when you are three-handed at a final table, and the payouts of the remaining money are 60 percent for first, 30 percent for second, and 10 percent for third. You have slightly less in chips than the other two players. They both go all in ahead of you, and you somehow know that one of them has the 8 7 and the other has the A A. You have the A A. Should you call? If you fold, you will have slightly less than one-third of the chips heads up. You will finish first 33 percent of the time, and second 67 percent of the time. Your equity is almost 40 percent of the prize pool. If you call, you will finish third 25 percent of the time, and first and second 37.5 percent of the time each. Your equity by calling is around 34 percent of the prize pool. Obviously, it is better to fold.

Don’t worry too much about all of this. If the worst mistake you make is not folding aces before the flop when it is correct to do so, you will eventually be a huge winner. What you should do is develop a feel for what your equity is and how your decisions change it. I’ll say more about equity in my next column.

Steve “Zee” Zolotow, aka The Bald Eagle, is a successful games player. He currently devotes most of his time to poker. He can be found at many major tournaments and playing on Full Tilt, as one of its pros. When escaping from poker, he hangs out in his bars on Avenue A — Nice Guy Eddie’s at Houston and Doc Holliday’s at 9th Street — in New York City.