Odds: Part I - Introduction

Everyone who does any kind of wagering, betting, or investing should become familiar with odds, probabilities, and many related concepts. This column will introduce some of the basics of odds, and discuss the poker-related ideas of pot odds and card odds.

Odds are a method of comparing one group of outcomes to another group of outcomes. True odds reflect the real chance of something happening. If you roll one die, there are six possible outcomes. What are the odds of rolling a one? There are five numbers that aren’t one, and only a single one. The odds against rolling a one are 5 to 1. This simple statement compares the two groups of outcomes, but it conceals several important ideas.

First, if something will happen less than half the time, it is ’against’ the odds. These events are often referred to as underdogs or dogs. If something happens more than half the time, the odds are shown in favor of it occurring. It is the favorite. Odds are most frequently stated as some number to one, although a few other sets of odds are often used for simplicity. For example, 3 to 2 is often used in place of 1.5 to 1. Both refer to something that happens 60% of the time. When both cases are equally likely, they are 1 to 1, and referred to as even money. It is extremely useful to be able to convert odds into percentages and vice-versa. This topic will be covered in detail in a subsequent column.

Here is one more simple example of figuring odds: what are the odds of picking a card that isn’t a spade from a full deck? There are 39 cards that aren’t spades and 13 spades. The odds are 39 to 13, which can be stated more simply as 3 to 1 in favor of picking a non-spade. This could also be stated as 3 to 1 against picking a spade. Anyone who plays poker or any other card game must become fluent in this type of calculation, both with a full deck and when some cards are already out. Let me emphasize that this is a calculation of the true odds or card odds.

Money odds reflect risk and reward. If I risk $300 to win $100, I am laying odds of 3 to 1. Note that betting on the favorite is called laying the odds, while betting on the underdog is called taking or getting the odds. When we refer to pot odds in poker, we are comparing to the amount we will win if we win (the reward) to the amount we can lose (the risk). At the end of a hand, there is 300 in the pot and then my opponent goes all-in for 100. There is now 400 in the pot and it costs me 100 to call. I am getting pot odds of 400 to 100 or 4 to 1. Remember pot odds relate only to what you can win and lose. They have no relation to the true odds, which reflect the actual chance of something happening. Note that I picked an example in which there is no more betting. When more betting can occur and/or there are more cards to come, this becomes more complicated, and I will return to those situations in subsequent columns.

First, let’s clarify how odds can be simplified to a number to one. If the pot had 450 and then my opponent bet 225, half the size of the pot, what would my pot odds be? After his bet, the pot is 450 plus 225, which equals 675. It costs me 225 to call. The pot odds are 675 to 225, an awkward number. To simplify it, I’d like to express this as something to 1. To do this, I divide by 225, and get 3 to 1. In most practical situations, approximations will be sufficient for decision-making purposes. If there were now 700, instead of 625, I’d think a little more than 3 to 1.

If both the true odds and the money odds are known, it is easy to determine if one should take the odds. If the true odds are 3 to 1, you should take anything more than 3 to 1. This is known as having a positive expectation, but it simply means that you are getting the best of it. Of course, you should avoid taking less than 3 to 1. That would give you a negative expectation or you’d be taking the worst of it. You could also lay less than 3 to 1. Remember, you want to take money odds that are greater than true odds, and to lay money odds that are less than the true odds.

I am going to end this introduction to odds with a brief, simple quiz:

What are the odds against picking an ace from a deck of cards?

What are the odds against picking a picture card (king, queen, or jack)?

Someone offers to lay 10 to 1 that you can’t pick an ace. Should you take the bet?

Someone offers to lay 4 to 1 that you can’t pick a picture card. Should take the bet?

Answers:

12 to 1

10 to 3 or 3 1/3 to 1

No. They are offering money odds that are less than the true odds.

Yes. They are offering money odds that are greater than the true odd. ♠

Steve ‘Zee’ Zolotow, aka The Bald Eagle, is a successful games player. 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.