Poker Lesson 12

Your starting hands will perform better against fewer opponents

Before I move on to discuss starting hands in Texas hold'em in greater detail, it is time to instill an insight just as important as the one you received in the previous lesson. And this insight is the following one: Starting hands, even mediocre ones, go up in value the fewer opponents you face. The reason for this lies in pure mathematics. (And I take the opportunity to pass on this bit of wisdom too: Winning poker is heavily built on mathematical foundations. In the words of the gambling expert Darwin Ortiz: "Respect the odds, and they will respect you.") If you play on the Internet and want to buy into a cash game, you can usually choose between either a "full" table with 10 seats, or a "shorthanded" table with only 5 or 6 seats. (And not all of these seats may be taken by other players: opponents come and go, so even at a table with room for 10 players there may be only 7 or 6 or even 5 others, for example.) However, different numbers of opponents change the mathematical conditions in Texas hold'em, and especially so before the flop. (After the flop the circumstances are usually more similar, where for example you face one or two remaining players.) Do you want it in figures? Let me then assume a typical "marginal" hand like A-7 suited, meaning that both cards are of the same suit. (A marginal hand is one that is better than practically worthless hands like 7-2 or J-5, but at the same time a clear underdog against a good number of other possible hands, such as A-Q, 8-8 and so on.) Let us also assume that you are the first to act in the first betting round, right after all players have received their two starting cards; this is called being "under the gun" in poker English. In an earlier lesson, I told you that there are 1326 different possible starting hands in Texas hold'em. Exactly how many of these starting hands are better that A-7 suited? (Remember, once you have a particular hand, your opponent or opponents will have hands made up from the remaining 1225 possible combinations.) In the first place, you are an underdog against all pairs 7-7 and higher, and against all hands A-K and on down to A-8. There are altogether 114 such different possible starting hands, when an Ace and a Seven are missing from the deck since you have them in your hand. But let us be on the safe side and also include the pairs 6-6 and on down to 2-2, since they are also actually slightly favoured against your A-7 suited; now there are 144 possible and much or slightly better starting hands you have to watch out for, among the 1225 which are left since you are holding the A-7. Against a single opponent, the chances are 88% that your A-7 is the best hand right then, according to the above calculations. Against four opponents the chances are only 61% that your hand is still the best starting hand at the table; against five, 54%; and at a full table, against nine opponents, the chances are only 32% that your A-7 is still the best starting hand right then. Think about it. Already against five opponents it is even money that someone else is holding a better starting hand than you do; and against nine opponents, you may safely assume that not one, but possible even two other players have better starting hands. The more opponents you are facing, thus the greater the risk that someone else has a better starting hand than yours. It is as if you had thrown a 5 on a regular die: the more players throwing the die after you, the greater the risk that one of them will roll a 6 to beat you. Keep it in mind.

DAN GLIMNE