Ranking Hold'em Hands

In my last column, "A One-Question Quiz," we established that there are 169 possible starting-hand types, which result in 1,326 combinations. For example, A-K suited is one hand type, but it can occur in four different combinations. Now our chore is to rank the 169 hands from best to worst, and find their percentile position among the 1,326 combinations. The top of the list is clear: A-A is the best. It is followed by K-K and then Q-Q. After that, it is far from clear.

The first sensible ranking of starting hold'em hands appeared in David Sklansky's book Hold'em Poker. These rankings were updated by Sklansky and Mason Malmuth in Hold'em Poker for Advanced Players, 21st Century Edition. They are designed for limit hold'em, and put playable hands into groups. The hands within each group can "be played roughly the same before the flop in many, but not all, situations." They go on to say that hands can move up or down in rank, depending on the situation. Clearly, when we add no-limit hold'em situations into our calculations, hand rankings can change fairly radically. To illustrate this fact, let's examine three reasonable starting hands: A Q, 10 9, and 5 5.

One obvious way to examine a starting hand is to see how it does against a random hand if played to the river. Against one random hand, the A Q wins 64.4 percent of the time, more than a 1.8-1 favorite; the 5 5 wins 60.2 percent of the time, about a 3-2 favorite; and the 10 9 wins 54.1 percent of the time, about a 6-5 favorite. But what if these hands are matched against more than one random hand? Against four random hands -- that is, fivehanded -- the average hand wins 20 percent of the time. All of our three hands are better than average; the A Q wins 30.4 percent, the 10 9 wins 25.8 percent, and the 5 5 is barely better than average, winning 22.4 percent. Notice that the 10-9 suited now performs better than the small pair, while heads up, the small pair performs better against the random hand.

This type of analysis is obviously flawed. First of all, our opponents don't play random hands, although we wish they did. Second, all hands are not played to the river. Third, even in those situations in which hands do arrive at the river, some will win bigger pots than others. So, next let's examine how these hands fare against each other. The A Q beats the 10 9 59 percent of the time. The 5 5 beats the A Q 54 percent of the time. Strangely enough, even though 5-5 is favored over A-Q offsuit, and A-Q offsuit is favored over 10-9 suited, 10-9 suited is favored over 5-5, winning 52 percent of the time. What if all three hands play a pot together? Amazingly enough, now the 10 9 does best, winning 35.6 percent of the time, followed closely by the A Q, which wins 34.6 percent, and bringing up the rear is the 5 5, which wins only 29.5 percent of the time (there is a tie 0.3 percent of the time).

Thus, we see that any of these hands can be better than the other two, depending on how they are compared. Now let's complicate the situation even more. Let's see how they do in no-limit hold'em. We'll look at three common situations: pushing all in, calling a push, and playing for a normal raise in deep-stack poker. The book Kill Everyone gives a very detailed discussion of pushing and calling a push for different, relatively short stack sizes in tournaments when you are far from the money. I can add that their conclusions also can be applied to similar short-stack situations in cash games. In each case, your opponent's range of hands drastically changes what you should do. In a heads-up confrontation with an overly tight opponent and a short stack, you profitably can push with any two cards.

In short-stack situations, the A Q is an excellent hand with which to push all in or call a push. In these situations, it is better than about 93 percent or 94 percent of hands. As stacks become deeper, A-Q offsuit loses a lot of value. It is considered a "trouble hand." That is, A-Q offsuit will win some small pots but lose some large ones. If a sound player raises from early position, your choices are to fold or call. Don't reraise. If either an ace or a queen comes on the flop, you should try to play a small or medium-sized pot, but avoid getting your whole stack involved unless you believe very strongly that you have the best hand.

In short-stack situations, the 5 5 is a reasonable hand with which to push all in or call a push. In these situations, it is better than about 90 percent of hands. As stacks become deeper, a pair of fives gains value. You have great implied odds - as you frequently win a huge pot when you flop a set. Unfortunately, you only will flop a set around 12 percent of the time. Therefore, your strategy is to keep the pot small before the flop; call, but don't reraise. After the flop, try to play a huge pot with a set. Without a set, just fold quietly if your opponent shows any strength at all.

In short-stack situations, the 10 9 is a reasonable hand when you are going all in. In this situation, it is approximately equal to a pair of fives. It is better than almost 90 percent of hands. It does much worse when calling a push. As a calling hand, it is better than only 75 percent of hands. Why is there such a big drop-off? A typical opponent will push with an assortment of high cards or pairs. As we already have seen, 10-9 suited is a big dog to A-Q offsuit or any two bigger cards. It is dominated by hands such as A-10 or even J-10. Against pairs, it is a modest favorite against small pairs, but a big underdog against higher pairs. Therefore, feel relatively comfortable moving in with 10-9 suited, but avoid calling someone else's move-in, unless you think he is really desperate. As stacks become deeper, 10-9 suited starts to pick up value. As with a pair of fives, your strategy is to keep the pot small before the flop; call, but don't reraise. After the flop, try to play a huge pot with a straight or flush. Be willing to gamble with a big draw (to a flush and straight, or to a pair with a straight or flush draw). If you make a pair, even top pair, with no draw, proceed cautiously. Keep the pot small and consider folding if your opponent shows any strength at all.

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 on Houston and Doc Holliday's on 9th Street -- in New York City.