Odds: Part VI

This series of columns has been devoted to odds. An understanding of odds is essential for anyone interested in poker, sports betting or many other types of games and gambling. In one of the earlier columns, we looked at converting percentages to odds. The chance that something will happen divided by the chance that it won’t. If an event will occur 80 percent of the time, then divide 80 percent by 20 percent. The odds in favor of it happening are 4 to 1. In another of the earlier columns, we looked at the odds of various hold’em hands beating other hands. These calculations of winning chances preflop are best done using a computer program like the Card Player Calculator. In live games, you will frequently face decisions on the flop and the turn. In these cases, there are more cards to come, and the odds of winning can be figured by comparing winning cards to losing cards. The cards that will make the worse hand into a winner are called outs.

A flush draw typically has nine outs. (There are 13 cards in a suit. Four of them are used to make the four-flush. This leaves nine cards that will complete the flush.) If there are 45 cards out, then 36 cards aren’t outs. Thus the odds of completing this flush are 36 divided by 9 or 4 to 1.

The Rule of 2 and 4: There is a very simple formula for estimating your winning chance (in percentage) based on the number of outs you have. If you are on the turn, with one card to come, multiply your outs by two. With the flush draw discussed above, nine outs times two yields 18 percent. This approximates your winning percentage. On the flop, when there are two cards to come, multiply by four. In this case nine times four yields 36 percent. To convert this to odds, first find the chance of missing, which is 100 – 36 = 64. Now 64 divided by 36 gives you the odds against making a flush, which turn out to be a little less than 2 to 1.

I’m sure that some of you are new to this type of calculation. Think about various situations and practice calculating the odds. More sophisticated readers may be bored by this review. Even when you become very familiar with this procedure, it is still not easy to know how many outs you have. Even more difficult is comparing your true odds (the chance of you actually winning) with your money odds (what you will get when you win.) Pot odds measure what is in the pot compared to the amount you must call. Implied odds are what you think you will win after you hit your hand.

Continuing with the example of a four-flush. Let’s say you have A 10 and the flop is 9 5 2. How many outs do you really have? There are nine hearts. Are these all really outs? The 2 pairs the board, and may give one of your opponents a full house. Even the 8, 7, and 6 could make a straight flush for someone. How about the three aces and three tens, are these outs? I’d expect to win some of the time one of these cards comes on the turn, but it may be hard to judge when aces with a ten kicker will be the winning hand. A rough approximation might be to assume 10 or 11 outs. With two cards to come, multiply by four, and you have at least a 40 percent chance of winning. If my only options were folding or calling, I’d call. I consider this an automatic call in limit hold’em and a relatively easy call of a pot-sized bet in no-limit. (POP QUIZ: what odds are you getting when your opponent makes a pot sized bet? Answer will appear later.)

Folding is wrong. Calling can’t be bad, but there is another option. You could raise. Is this better or worse than calling? This is one of the those standard poker situations for which there is no definitive answer, just, “It depends.” What does it depend on? Is the game limit or no-limit? If no-limit what are the effective stack sizes? What is your position? What is your table image? Who is your opponent, and how will he react to a raise? In no-limit, you must also decide what is the best amount to raise. If you call, and hit the flush, what are your implied odds (how much more will your opponent lose?)? If you raise in position, get called and miss, you will have another decision after your opponent checks to you on the turn. You can take your free card or you can continue betting with your semibluff. Note that you could also call on the flop, and then try to bluff on the turn, after a miss. As an author I hate stating that, “It depends!” I feel like I am letting my readers down, abandoning them when I should be letting them know what to do. As a player, when I face this type of situation, I wish I always knew what to do. My decision is often more instinctive (based on table feel) than it is mathematical. At least I can definitely answer the pop quiz. You are getting 2 to 1 odds when faced with a pot-sized bet. ♠

Steve ‘Zee’ Zolotow, aka The Bald Eagle, is a successful gamesplayer. He has been a full-time gambler for over 35 years. With two WSOP bracelets and few million in tournament cashes, he is easing into retirement. He currently devotes most of his time to poker. He can be found at some major tournaments and playing in cash games in Vegas. When escaping from poker, he hangs out in his bars on Avenue A in New York City -The Library near Houston and Doc Holliday’s on 9th St. are his favorites.