Poker players need to be acquainted with math. Most of the time, they are concerned with the odds on making whatever hand they are drawing to, making sure the pot odds and/or implied odds are sufficientBob Ciaffone is one of America’s best-known poker players, writers, and teachers. He has numerous poker tournament wins and placings, the most prominent being third place in the 1987 World Championship. He has been a poker teacher since 1995, with his students having earned well over a million dollars in tournament play. Bob's website is www.pokercoach.us to stay in. But there are other odds that also are relevant to poker situations. For no-limit hold'em, especially tournament play with its high frequency of players going all in preflop, it is important to know the approximate chances for each hand on the more frequent matchups. Let's discuss the odds in various types of situations when we get all in before the flop. (Note: Odds given are approximate.)
One of the worst situations you can be in is when someone has an overpair to both of your cards. Whether you have a pocket pair or not, you are really hurting. Two aces are a big favorite against two kings. If the aces are of the same suits as the kings, they are a 4.75-to-1 favorite. It is slightly better for the kings if they can make nut flushes, but the aces are still a 4.4-to-1 favorite against two kings of differing suits from the aces. Smaller pairs actually have a better chance than kings of drawing out, because of improved straight possibilities, but 7-7 is still a 4-to-1 underdog to the aces.
Non-pair hands can be either better or worse than an underpair is against an overpair. For example, K-Q offsuit is a 6.5-to-1 underdog to the bullets. Being suited of course helps, but K-Q suited is still a 4.6-to-1 dog versus the aces. Midsize connectors have the best chance; a 7-6 suited is about a 3.5-to-1 underdog. That is better than any pair would have, but still, obviously, no bargain.
An important concept to understand is that of domination, meaning the superior hand has one or two cards that are of the same rank as a card in an inferior hand. If one hand dominates another, it has that hand in serious trouble. It will be difficult for the weaker hand to draw out, whether the hands are all in against each other before the flop or both hit the flop with the card that is common to both hands.
Domination, of course, occurs more often in practice between two good hands than between a good hand and a bad hand. For example, if one is all in against an A-K, a hand that contains an ace is in worse shape than a clunker like 8-7 offsuit.
One hand can be dominated by another in several ways:
1. Bigger kicker. The classical matchup here is A-K against A-Q. The actual odds vary a meaningful amount according to whether the hands are suited or unsuited. The weaker hand finds that being suited is significantly beneficial in trying to draw out. Against an A-K offsuit, an A-Q offsuit is a 2.8-to-1 dog if the queen has no cards of its suit in the opposing hand, and 2.95-to-1 if the opponent's ace or king is of the queen's suit. With the A-Q being suited, the odds drop to 2.3-to-1 in favor of the A-K, which is quite an improvement for the underdog's chances. Whether the A-K is suited is not as important, but it still matters. With an A-K suited, those odds against A-Q suited are 3.1-to-1, and against A-Q suited, 2.5-to-1. Note that if a hand is dominated, the gap between the kickers of each hand is of little importance. For example, with the superior hand being A-K, it hardly matters whether the weaker hand is A-Q, A-J, or A-10, because the method of drawing out is the same. The weaker hand needs to hit its kicker, and have the stronger hand not hit its kicker. Having a midsize kicker (for straights) is of only tiny help to the underdog. For example, the A K is a 2.75-to-1 favorite over the A 10. (If the 10 were instead the Q, the odds would be 2.8-to-1.)
2. Pair matches the lower card. An example would be A-Q against two queens. If your lower-ranking card is tied up, you are in approximately the same amount of trouble as the previous situation; you need to hit your kicker. Actually, it is measurably easier for the dominated hand to fight against the pair than against the higher kicker, since the boss hand has only the case card of a rank to lock you out of winning, rather than three cards that do it. With A-Q offsuit, you are a 2.35-to-1 underdog to a pair of queens. With A-Q suited, you are a 1.9-to-1 underdog to a pair of queens. The odds show about the same ratios for A-K against K-K.
3. Pair matches the higher card. If your higher-ranking card is tied up, as when A-Q runs into two aces, the weaker hand is obviously in dire straits. It takes some sort of parlay in hitting the flop for the underdog to draw out, rather than simply making a pair for a card in your hand. Two aces are an 11.65-to-1 favorite against A-Q offsuit and a 6.95-to-1 favorite against A-Q suited. Even though the underdog is still buried when suited, the improvement in chances is noteworthy.
What conclusions can be drawn from the statistics of all-in situations that we have been looking at so far? First, it is desirable to avoid these traps of running into an overpair or dominating hand. Of course, this is easier said than done. You cannot see your opponent's hand. But such a situation is easier to avoid if you are the bettor instead of the caller. An all-in bettor has a chance to win without a fight, whereas an all-in caller is certainly risking all of his chips. Second, the benefit of being suited is apparent in all of these matchups. If you run into an unexpectedly good hand and are dominated, the chance to win with a flush significantly changes the odds against you. This suited factor is especially important when you are thinking about going all in with an ace-rag.
I think it is highly worthwhile to look at how various hands do against each other when no hand is dominated by another. The most common example here is A-K against two queens. Two red queens against a black A-K offsuit is a 57-to-43 favorite. (I think one gets a better feel for these closer matchups when we use percentages to give the winning ratios.) The relative percentages are virtually the same if the queens are of the same suits as the A-K. It is harder for the A-K to make a flush, but the queens can never win by making a flush.
If the A-K is suited, this is of meaningful help to it. The queens are favored by 54-to-46, whether one of the queens is of big slick's suit or not.
If the A-K runs into a significantly smaller pair than queens, it has another way to win the pot. The A-K wins when there are two pair on the board that are both higher than the opponent's pair. This is impossible when facing two jacks, and highly unlikely when facing two tens. But as we approach the tiny pairs, it is meaningful. It is also helpful to the A-K if the pair is lower than tens, because it greatly increases big slick's straight-making chances. A-K suited is a 52-48 underdog against two red nines, and a 51.5-to-48.5 underdog against two red fours.It is easy to see why A-K is the workhorse of tournament play all-in bets, especially if suited. It dominates any other ace. If all in against two queens or a smaller pair, the blinds money is usually sufficient to more than make up for the slight underdog status and give odds that justify playing. Of course, if it runs into two kings, it is roughly a 2-to-1 dog, and if it runs into aces, it is in dire straits. But when holding an ace and a king in your hand, the chances of running into A-A or K-K are cut about in half, compared to a hand with no ace or king in it. This does not mean that it is OK to play back at a hand that reraises you, but it almost always means you are OK in moving all in on a hand that raises you if your reraise will be no bigger than the pot size.
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