Chances Are: Part II

Practice and repetition are essential for learning or building a skill. I will begin this column with a brief review of some basics. Calculating chances can range from simple to virtually impossible. The basic rule is that chances can be calculated by dividing the outcomes you are interested in by the total number of outcomes. The result can be expressed as a fraction, a decimal, or a percent. For example, the chance of picking the A from a deck of 52 cards is 1/52, or .0192 or 1.92 percent. While the chance of picking any of the four aces is 4/52 or .0769 or 7.69 percent. Odds are determined by dividing the chance that some event occurs by the chance that it does not occur. Usually it is expressed as some number to one. Using the above examples, the odds of picking the ace of spades are 51-to-1. The odds of picking any ace are 12-to-1.

Notice how easy it is to calculate the real odds when you know exactly how often something will happen and how often it won’t happen. Odds are also used to describe the payout you will get when something happens. For example, if there is $400 in the pot, and your opponent goes all-in for $200. There is now $600 in the pot and it costs $200 to call. If you call, you are getting 3-to-1 odds on your money. If you think you will win the hand more than 25 percent of the time, you have a very profitable call. Understanding the difference between the odds you are being offered and the real odds is one of the most important elements in being a successful gambler. If you can consistently take odds greater than the true odds, you will be a winner. If you consistently take odds worse than the true odds, you will be a loser. In this case it was easy to calculate that you were getting 3-to-1 odds. The hard part is to develop the ability to accurately estimate what your real chance of winning is.

Let’s look at two cases. Both times you are getting 3-to-1 odds. In the first case, the board is Q-9-4-2 rainbow, and you hold J-10. You are sure your opponent has at least a pair of queens. You know six cards (the two in your hand and the four on the board). There are 46 cards you haven’t seen. Eight of them give you a straight (four kings and four eights). What are the true odds? Thirty-eight cards are bad and eight are good. You are a 38-to-8 underdog. You are a 4.75-to-1 underdog to win, but you are only getting 3-to-1. Since your opponent is all-in, you can’t win any more after you make your straight (these are known as implied odds and I will discuss them at great length in a future column). Calling would be a mistake.

Case two is very similar. The action, your hand and the board are all the same. Now your opponent is very aggressive. You feel he is trying to force you out with a hand like A-K or A-9. If your read is right, how many good cards do you have now? Not only the eight cards that make a straight, but also the remaining three jacks and three tens will give you a pair. Against A-9, you have 14 winners. Against A-K you only have 13 outs since one of the kings is gone. To be conservative you estimate 13 winners out of the 44 cards. Why 44 instead of 46? Now you are assuming you know eight cards, your two, his two and the four on the board. The odds against winning are now 31-to-13 or around 2.4-to-1. Notice that this is less than 3-to-1. You are getting greater odds than your chance of winning, so calling is now correct.

In the first case you had eight sure winners. The second case is much more difficult because of the fact that you can’t really “know” what you opponent has. So nearly half of your winners are based on your read. Notice that you must both read your opponents accurately and be able to do the appropriate calculations of the odds. Players who master these two skills know when it is right to call and when it is right to fold in these types of situations. The best live players are incredibly accurate in making these judgments. If your reads are more accurate than your opponents, you will have a better idea what you chances of winning really are. This will enable you to make fewer and less costly mistakes than your opponents. You will beat them. ♠

Steve ‘Zee’ Zolotow, aka The Bald Eagle, is a successful gamesplayer. He has been a full-time gambler for over 35 years. With 2 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.