Poker Odds and Expectations

Mathematical analysis in poker is a topic that you could fill a book or two with. Actually, a shelf full of books. Well, on reflection, more like a library of books. The good news is that many of these books have already been written.

For our purposes here, a brief introduction to the subject will suffice. But if you're serious about pursuing knowledge on the pure game of poker, you will definitely want to expand your reading.

As a beginning player, one of the most basic and useful mathematical concepts to have under your belt is the idea of pot
odds. Simply put, the term pot odds refers to the ratio of the amount of money currently in the pot to the amount of money it will cost you to call a bet.

Let's look at a quick example. You're deciding whether to call a bet of $5 after the flop in limit Texas Holdem. There is currently $25 in the pot. That gives you pot odds of $25:$5, or 5:1.

This becomes useful when compared to ratios you can generate for your chance of winning the hand. Another simple example: In Holdem, suppose you have a spade flush draw (four to a flush) after the flop with two cards to come. The odds of making your flush can be determined mathematically. Out of 47 unseen cards (52 cards minus the five cards you're looking at), the nine remaining spades will make your flush, while the remaining 38 will not. Therefore you have odds of 38:9, which reduces to 4.22:1.

Because your chance of making the flush (4.22:1) is better than the current pot odds (5:1), it makes sense to call this bet.
Doing so will not necessarily win this particular pot for you, of course, but in the long haul the math works out to favor making a call in this situation.

To get more specific would require another 20 or so articles, so we're going to leave it at that. Generally speaking, the greater the pot odds, the more likely you should be to call a bet.

If you really dig into this topic, you'll add many arcane and delightful new terms for your vocabulary, such as effective odds, implied pot odds, and reverse implied pot odds. For now, though, a basic grasp on the concept of pot odds and positive
expectation will provide another brick of solid foundation for your game.