Hold'em Posers

Here are a few situational questions about hold'em hands. The answers appear after the last question. If you want to try to figure these out for yourself and can't keep your eyes from straying to the answers, grab another magazine or a piece of paper and cover up that portion of the column.

1. Here's an easy one. Can you flop a full house against one opponent and have no chance of winning or splitting?

2. What is the worst possible hand you can have on the river and have the nuts? Specify all five cards.

3. The following question was posed and discussed on the BARGE mailing list. (BARGE is the Big August rec.gambling Excursion. An annual convention held in Las Vegas by members of rec.gambling.poker, that is, on-line poker players, featuring a no-limit tournament, other less-organized events, and much hilarity, including "must-toke" games such as Chowaha.) What is the minimum number of hands such that at least one of them has no pot equity? That is, such that at least one cannot win or tie (including board ties). Specify the hands. Related to that question, what is the maximum number among that group that can have no pot equity?

4. And now let me leave you with a question that also was posed on the BARGE mailing list. You hold pocket aces. What is the minimum number of opponents needed to give you zero equity on the pot, and what would be their hands? I'll discuss this in another column.

A good place to test your answers is with the poker odds calculator at Twodimes.net. For most hand comparisons, it generates all possible boards. It does not work on a Monte Carlo simulation, that is, a dealing out of millions of randomly generated hands, as do many poker odds calculators.

Answers

1. If you have pocket deuces, your opponent has either 3-3 or 2-3 and the flop comes 3-3-2, you can't win. In fact, if you have any pair smaller than aces and the flop gives you a full house by bringing the third of your pair plus a higher pair and your opponent has either the remaining member of your rank and one card to match the higher pair or a pocket pair of the rank of the flopped pair, you're drawing completely dead. So, for example, your pocket kings with a flop of A-A-K against either A-K or K-K also has you dead in the water.

2. The worst possible hand you can have on the river and still have the nuts is Q-Q-Q-8-7, and the board must be Q-8-7-3-2 rainbow. No worse hand than a set of queens works, because you can't then specify a board that wouldn't permit someone to have a straight or better. If you had J-J with a jack on board, for example, the four non-jacks could not include a card higher than a jack, because that would give anyone with that pocket pair a higher set, thus the other four cards must all be smaller than a jack. And that necessitates some three-card combination that could give someone with the right holecards a straight or better.

3. The minimum number of hands such that at least one of them has no pot equity is eight. One set of possibilities uses all the aces, tens, sixes, and fives, as, for example, A A, A A, 10 10, 10 10, 6 6, 6 6, 5 5, and 5 5. Here all the hands are pairs, and they preclude the possibility of any tie involving five board cards that constitute a straight (because such cannot be made). The only possible straights, those with four cards on board, give winners to either the aces or tens. Any flush or four-flush on board gives a winner to one of the ace hands. Any four of a kind or full house does the same, as do three of a kind, two pair, and one pair. This gives all four lowest pocket pair hands zero equity. So the answer to what is the maximum number of hands among that group that can have no pot equity is four. You can change that to just two hands having zero equity, by exchanging cards such that there are two 6-5 hands, as A A, A A, 10 10, 10 10, 6 6, 6 5,6 5 , and 5 5. Or you can guarantee that only one hand has zero equity by also changing two hands to A-10, as A A, A 10, 10 A, 10 10, 6 6, 6 5, 6 5, and 5 5.More possibilities exist. The eight hands must consist of all the aces and tens and either the sixes or fives, plus four more cards of the same rank. Thus, A A, A A, 10 10, 10 10, 5 5, 5 5, 2 2, and 2 2 is one of another set of possibilities.Tiltboy Perry Friedman had a good alternative response: "I can do it in two hands: K K vs. A. In that situation, A has zero equity." However, if we're going to quibble that a foul (due to too few cards) hand has no equity in a pot, I would counter that if the mistake were seen in time, the hand with only one card would either get another card or there would be a misdeal. But I guess if we're going to split hairs, we can also say that a one-card hand would never have any claim on a pot.

Michael Wiesenberg's The Ultimate Casino Guide, published by Sourcebooks, is available at fine bookstores and at Amazon.com and other online book purveyors. Send riddles, rebuttals, and ribaldries to queue@CardPlayer.com.