## Gambling Wisdom: Odds

### Gambling (general), Strategy

July 30, 2007

In this series I discuss topics that are well known within the gambling community, but that may be new to players who come to the game of poker from a non-gambling background.

Gamblers have a funny way of talking about how likely it is that something will occur. Instead of citing the percentage chance that some event will occur, they cite the “odds” that it will occur. Odds notation works as follows: the odds that something will happen is the ratio between how many times it will happen and how many times it won’t. The bigger side of the ratio is always stated first, so you have to specify whether the odds are “in favor of” or “against” the event occurring. For example, if you have a race with 6 horses, and each is equally likely to win the race, then you could say the odds are 5:1 against horse #3 winning the race. On the other hand, if you had a race with 6 horses, and 4 of them were black, and all had an equal chance of winning, you could say the odds were 4:2 in favor of a black horse winning.

This brings us to a key point: all the mathematical manipulations that can be performed on ratios can be performed on odds. So in the black horse example, instead of saying the odds were 4:2 in favor, we could divide both sides by 2 and say the odds were 2:1 in favor of the black horses.

Now, odds notation serves the same role that percentages do for non-gamblers. But for gambling purposes, there are several reasons that it’s advantagous to think in odds rather than percentages.

1. Odds facilitate comparisons with other ratios. For example, say you believe the odds are 2:1 against your horse winning, but you can lay 3 dollars to win 7 betting on your horse. By comparing 7:3 to 2:1, you can determine that you’re being laid an attractive price on the wager. This form of comparison is the basis for “pot odds” and related concepts in poker, which we’ll get to in a future article.
2. Odds are directly compatible with thinking about cards. Say you’re drawing to a flush on 5th street in holdem. There are 46 unseen cards in the deck, and 9 of them make your flush. You can immediately say the odds are 37:9 against you making your flush. However, it would take a bit of mathematics to figure out that’s equivalent to 19.5%. So in many cases odds are far easier to compute.
3. Odds facilitate estimation. When faces with a daunting, un-reducible number like odds of 37:9 against, you can fudge each number slightly in the same direction to make it easier. Just call it basically 40:10, or 4:1, which is the same as 20%. That’s awfully close to the 19.5% we got for 37.9. You lose almost no accuracy by doing this if you’re careful not to fudge too far.
4. Odds facilitate Bayesian reasoning. If you don’t know what that is, that’s OK. I’ll explain in a future article, but believe me it’s worth it.

The only real disadvantage of thinking in terms of odds is the confusion about “odds in favor of” something vs. “odds against.” But that’s more of a language thing than a numeric one: in written form, I suggest you always put the number of times something won’t happen first, and the number of time it will second. I’ll try to always follow that convention. This means that odds in favor of something simply need to be reversed, and that’s not too hard.

So, I suggest you start trying to do all your poker thinking in terms of odds. Some of the payoff will be delayed, because I haven’t explained all the useful things you can do with odds. But I think you’ll find once you break the years of conditioning in favor of percentages that you received in school that odds are actually simpler and more useful for poker. You just have to develop the mental facilities to think about them quickly.