Odds: Part II

This article on odds will continue the discussion of those concepts introduced in the first part. In particular, it will focus on converting from percentages (or fractions) into odds and vice-versa. In Part I, a distinction was made between true odds and money odds. True odds reflect the chance of something really happening. Money odds relate to the amount you can offer or take that it happens. Generally, you want to offer less than the true odds or take more than them.

As I write this column, just before the Super Bowl, the New England Patriots and the Seattle Seahawks are considered to be evenly matched. This is reflected by odds of pick or pick’em. It implies that the true odds are even money. If you and a friend bet $100, the winner wins $100 and the loser loses it. If, however, you wander into a casino and bet $100 at Pick, the situation is different. You must risk $110 to win $100. The extra $10 that you must wager is often referred to as the Vig, the Vigorish, or the Juice. It means that the money odds you get are less than the true odds, and you have the worst of the bet.

The following comes from something I previously wrote, but I want to emphasize the importance of these concepts for making decisions in poker playing, gambling, and many other areas of your life. A simple, not too rigorous, way to approach probability is to think of something that has a number of possible outcomes. Each outcome is equally likely. Then specify a specific outcome or group of outcomes. The probability of the specified group is its’ number of outcomes divided by the total number of outcomes. For example, a deck has 52 cards. There are 13 spades in the deck. The probability of drawing a spade is 13 divided by 52. This can be written as a fraction, ¼, a decimal, .25, or a percentage 25 percent.

Odds are often the easiest way for a gambler to apply probability to making betting decisions. The odds compare the outcomes that aren’t in the specified group to those in it. Thus there are 39 non-spades. If we divide this by 13 spades, we come up with 3 to 1. (As an item of trivia for rock music buffs, the Doors miscalculate the odds in one song. “The odds are five to one, yes one in five, that no one here gets out alive.” If the odds are 5 to 1, then there is one chance in six.)

This trivial musical mistake illustrates how easy it is to go wrong when using odds or probabilities. Look at the idea of counting outcomes. Suppose we want to know the odds against flipping heads twice in a row. How many outcomes are there? A frequent mistake is to say that there are 3 – two heads, two tails, or one of each. This would lead you to think that two heads occur one-third of the time and that the true odds against two heads should be 2 to 1. There are really four outcomes, which are HH, HT, TH and TT. Two heads occur only ¼ of the time and the odds should be 3 to 1.

Here is a brief quiz to test your knowledge of this material:

1. Something will happen 80 percent of the time. What are the true odds of it happening?
2. Someone offers you money odds of 10 to 1 on an event you think will happen 10 percent of the time. Is this bet good, bad, or neutral for you?
3. How many ways (suit combinations) can you have two aces?
4. If you have two aces, then what fraction of the time will you have:
• A) two red aces
• B) exactly one red ace
• C) the ace of hearts
5. Convert these three fractions to odds.

Answers:

1. 4 to 1 This is calculated by chance it happens 80 divided by chance it doesn’t 20.
2. Take the bet it is good for you. The true odds are 9 to 1 (90 percent divided by 10 percent) and you are being offered money odds that are greater than 9 to 1.
3. 6 (Spade-Heart, Spade Diamond, Spade-Club, Heart-Diamond, Heart-Club, and Diamond-Club)
4. A) 1/6 B) 4/6 or 2/3 C)1/2
5. A) 5 to 1 against two red aces, B) 2 to 1 in favor of exactly one red ace, C) 1 to 1 on having the ace of hearts.

Future columns will cover calculating odds of more than one event occurring and the important concept of implied odds. ♠

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.