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Chances Are: Part IV

by Steve Zolotow |  Published: Oct 16, 2013

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Steve ZolotowIf you know exactly what you opponent has, it is usually easy to figure out his chance of winning. The hard part, obviously, is knowing what he has. Frequently, small differences in his holdings may make a big difference in his chance of winning. In my last column, I left with a quiz. Let’s see what the questions were and what the answers are. This is the situation: With one card left to come, the board has two spades. You have none, but your opponent has two. You know he will win with a spade, but not necessarily just every spade. He may have other outs as well.

What is his chance of winning and what are the odds against his winning?

You both have stacks of 500 and the pot is 500. How much should you bet to insure that he is making a mistake by calling?

Your Hand Board His Hand
AHeart Suit KDiamond Suit ASpade Suit KHeart Suit 8Spade Suit 4Club Suit QSpade Suit 9Spade Suit
AHeart Suit QDiamond Suit ASpade Suit KHeart Suit 8Spade Suit 4Club Suit QSpade Suit JSpade Suit
AHeart Suit KDiamond Suit ASpade Suit KHeart Suit 8Spade Suit 4Club Suit QSpade Suit JSpade Suit

The first question should be easy for you to answer.

Remember that the chance of something occurring is expressed as a fraction, a decimal or a percent. There are eight cards gone so there are 44 cards left. Nine of these are spades. Three are tens that aren’t spades. To find the odds against his victory, compute losing cases divided by winning cases.

He has eight winners. The KSpade Suit makes his flush and your boat. His chance of winning is 8/44 or 18 percent. The odds against his winning are 36/8 or about 4.5-to-1.

In this case he has 12 winners (nine spades and three tens.) His chance of winning is 12/44 or 27 percent. The odds against his winning are 32/12 or 2.7-to-1.

In the final case, he has only 11 winners. The 12 we counted above, but now the KSpade Suit loses. His chance of winning is 11/44 or 25 percent. The odds against his winning are 33/11 or 3-to-1.

So how much should you bet in these three cases? This is not as simple as it might seem. Let’s assume you know exactly what he has, and therefore you will never lose any money on the river. In this case, you must bet enough so that he isn’t getting the appropriate odds to call. Let’s see what this implies for these three cases.

Case 1: A bet of 150 or more insures he is not getting the 4.5-to-1 odds he needs to call (after your bet the post is 650. It costs him 150 to call. He is getting 650-to-150, or about 4.3-to-1). In reality, you probably should bet more for reasons to be explained shortly.

Case 2: In this case, you must bet over 300. If you decide to bet 320, the pot is now 820 and a cost of 320 to call, his odds are 820-to-320, or 2.5-to-1.

Case 3: Here the 300 bet works well. The pot odds are now 800-to-300, or about 2.7-to-1, which is less the 3-to-1 he needs to make a call correct.

In reality, there are two reasons why you should probably bet more than the minimum amounts suggested above. The first is that you are unlikely to know exactly what your opponent has. Imagine that you think Case 1 is in effect and bet 150. If it is really Case 3, you are giving him more than 4-to-1 on a 3-to-1 shot. This is a sure recipe for going broke. To avoid giving him the appropriate odds in the worst case, bet 300.

The other reason for betting more involves the concept of implied odds. The concept of implied odds is both important and complicated. By way of an introduction, implied odds arise when there is more money left to be bet. If you can win more money, you are getting positive implied odds. If you can’t win any more, but you might lose more, then you are getting negative implied odds (sometimes called reverse implied odds). In all three of the cases above, you have negative implied odds. You won’t win more money (if no spade comes, he’ll fold), but you might lose more (he hits one of his outs and you call a river bet). In the next column, we will examine implied odds in more detail. ♠

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.