Poker Quirks

So far in my short Card Player writing career, I've done columns related only to poker strategy. Even I get tired of strategy. I play poker almost every day, and believe it or not, "check-raising stupid tourists and taking huge pots off them," as Mike and Worm do in Rounders, can eventually lose its allure. When that happens, I like to remember some of the fun facts about poker, and I thought I might share some of those in this column. Don't worry, strategy junkies, some useful stuff sneaks in here, as well.



1. Any straight must have either a 5 or a 10 in it – but if you're dealt 10-5 in hold'em, there is one straight you can't make.



Think of all the straights you can make in poker. The lowest one is the wheel – A-2-3-4-5. The biggest one is Broadway – A-K-Q-J-10. You can list all the ones in between and you'll see that there is a 5 or a 10 in every single one of them. So, that would mean if you get 10-5 offsuit in hold'em, you could make every possible straight, right?



The key to this puzzle is to think about how Texas hold'em works. By rule, you must make the best possible five-card hand out of the two cards in your hand and the five cards on the board. You are not allowed to pick and choose which hands to play, out of all the hands you could conceivably make with your seven cards. You have to use the best one. Has this hint helped? Read the next paragraph when you're ready to see the answer.



The one straight you can't make with 10-5 in Texas hold'em is a 9-high straight. The only way you can make any straight with 10-5 is to use four cards from the board and one from your hand. So, to make a 9-high straight, the cards 9-8-7-6 would have to be on the board. But with those four cards on board, you always have at least a 10-high straight!



2. In Omaha, if you're dealt the 9 3 3 3, you can still make three different hands that are the nuts on the river.



It's a terrible hand, unplayable from any position except the unraised big blind in any form of Omaha. But if you're stuck playing the old 9-3-3-3, how might you make the nuts?



The first, and most obvious, way is for there to be three nines on board, without a pair on board higher than nines, and with no straight flush possible. In that case, you have quad nines, and they are unbeatable. So, four of a kind is one hand you can make with 9-3-3-3 that will give you the nuts.



The next two solutions are both pretty tricky, and when I tell people this puzzle, it varies as to which solution proves the most difficult. Here's one hint: In each of the last two solutions, there is only one possible board that works. Here's one more hint: In each of the last two solutions, the board would make a better hand than yours, if you were allowed to play the board. Read the next paragraph when you're ready for the answer.



The last two solutions use the following two boards: A K Q J 10, and 3-2-2-2-2. With the royal flush on board, you have a 9-high flush – and it is the nuts. No one can have a higher flush, and no one can have a straight flush, because you're holding the 9. With the quad deuces on board, you have threes full – and it is the nuts. Omaha requires using two cards from your hand, so no one can have four of a kind or a better full house than yours. Doesn't it stink that you can't play the board in Omaha?!



3. If you and I each get to choose one hold'em hand among the 4 4, the J 10, and the A K to be all in with before the flop, I will let you choose first every time.



Just so that we're clear, we're not going to play poker with these hands; we're just going to run the cards hot and cold. You get to pick one of the three hands above, and then after you pick, I'll pick. We'll then deal out a flop, turn, and river, and whoever has the best hand wins. I'll have the advantage every time.



At first glance of this game, you might think it's correct to pick the two fours, and that I won't have an advantage over you, because two fours is a pair. Any pair is a favorite over any two overcards, right? Actually, it's not. In fact, the J 10 is a 53-47 favorite over black fours. The fours, however, are a 54-46 favorite over the A-K that repeats its suits, so you can't pick the A-K, either. But then the A K crushes the J 10, 59-41.



The situation is analogous to a game of rock-paper-scissors, when I already know your selection. If you pick the fours, I pick J-10 suited. You pick J-10 suited, and I pick A-K. You pick A-K, and I pick the fours. I'll always have an edge. Try this bet with your friends! Incidentally, if you were to play this game with three people, you should always pick the J 10. Even though it's the "worst" hand of the three, the J-10 suited wins most often (36.25 percent of the time) when the pot is contested between all three hands. The fours, the "best" hand, win the least often. If you've got two friends who will take the fours and the A-K, you can try the threehanded bet, as well.



4. If we were never dealt A-A, K-K, or Q-Q in limit hold'em, almost all of us would be losing players.

Go ahead, check your PokerTracker (or whatever software you use to keep track of your limit hold'em results). My combined profit with aces, kings, and queens is greater than my overall profit in limit hold'em. And I suspect this is true for almost all players who have a reasonable sample size. Now, we have to play a lot of other hands in limit hold'em to make up for the money we're losing in the blinds, but the big pairs are the breadwinners – and that's worth remembering.



5. John von Neumann was the pioneer of game theory in poker.



I include this one mostly because I received an e-mail chastening me for claiming in an earlier column that Chris Ferguson was the pioneer of applying game theory to poker. While Chris is certainly the modern-day version of von Neumann, von Neumann was the one who started it all. With co-author Oskar Morgenstern, von Neumann wrote the classic text Theory of Games and Economic Behaviour, which was published in 1944. Von Neumann invented game theory, and his inspiration for developing it was to help explain decision-making in poker. No one other than von Neumann deserves to be called the pioneer of applying game theory to our little pastime. I'm happy to give credit where credit is due, and to print this correction.



There, I've reminded myself that poker is fun, and interesting, and worthy of an enormous investment of time and energy. Now, back to deciding what to do with my A-K when I miss the flop and get check-raised.

Matt Matros is the author of The Making of a Poker Player, which is available at www.CardPlayer.com.