The Simple Math of Hold'em Odds

By its very nature, poker is a game of math. Every hand, every bet, every moment involves making some sort of calculation. And, in Texas Hold’em, those calculations—whether you intuit them or think them through—are referred to as “odds.”

Really, any halfway decent Texas Hold’em player can learn to calculate and play the game’s odds to the best of his advantage. After all, knowing the odds of any game allows players to know when to bet, call or fold, and even if you only understand the theory behind the game’s odds, you’ll be light years ahead of most other players.

With that in mind, is giving you all that—yeah, and a bag of chips—so that, the next time you sit down to a round of Texas Hold’em, you’ll know for a fact that the odds are all on you.

Types of Hold'em Odds

Outs: Similar to baseball in a way, the “outs” refers to the number of cards left in the deck that will improve your hand (i.e., the number of chances you have left to win a round). For example, if you have four spades on the Turn, you have nine outs left to finish a flush.

Pot Odds: These odds are determined when you analyze the size of the current pot versus you next call. For example, if the pot has $200.00 in it, and there is only a $10.00 bet coming your way, you have good pot odds if you hit the flush mentioned in the example above.

Bet Odds: These are the odds that you get from analyzing the number of callers to a raise. For example, if you have a 1/5 chance of picking up the flush, and you know all six players are going to call your bet, your bet odds are good.

Implied Odds: Like the name suggests, these are the odds you get after the assumed (or implied) result of betting for the rest of the hand. For example, if you think the other players are going to call on the Turn and on the river, your implied odds are pretty good.

Calculating Odds

When you play Texas Hold‘em, you will most likely use outs and pot odds the most—especially if you are just learning to play the game. Assuming that you are a beginner, then, here are some time-honored tricks of the trade that will help you calculate your odds without needing a calculator:

Outs: Figuring “outs” is relatively easy. In fact, outs odds are nothing more than simple division. It breaks down like this: the numerator (or top number of the fraction) is the number of outs you have. The denominator (or bottom number of the fraction) is the number of cards that you haven’t seen (meaning both your opponents’ hole cards and those left in the deck). To calculate the outs odds, all you have to do is divide the numerator by the denominator. This will tell you the chance you have of making one of those outs. If you haven’t done much math lately, it may take some getting used to. But, in the end, determining outs odds is pretty easy, and once you get the hang of it, you’ll find you have a deeper understanding of how the hand is unfolding—putting you in a good position to make chip leader.

Pot Odds: Figuring out “pot” odds is as simple as determining outs odds. All you have to do is compare your outs (or your chance to winning) to the size of the pot. To figure out your bet-to-pot ration, simply put the amount you’ll have to bet if you see your opponent over the total amount that would be in the pot after the betting round ends. If your odds of winning are better than the ratio of the pot size to the bet, you have good pot odds; if it’s lower, you have poor pot odds.

For example: let’s say you’re in a $5/$10 Texas Hold’em game, have a jack and a ten and are facing one opponent on the Turn. The board shows 3, 6, 9 and Q, so you have a chance of making a straight draw. However, you only have the river card. Knowing poker, you understand that any eight or king will complete the straight for you, and there are four eights and four kings left in the deck, plus 46 unseen cards. Using outs odds, then, you have a 1/6 probability of making the straight (i.e., eight outs over 46 cards breaks down to about a 1/6 probability). What’s more, you know that your opponent has bet $10.00 and that, if you take his $10.00 bet, you could win $200.00. Again, using simple math, you know that you’d stand to make 20 times more than your bet if you call. Since 1/6 is higher than 1/20, your pot odds are telling you that calling your opponent’s bet would be a damn good idea!

Bet Odds/Implied Odds: Determining these odds is a little more complicated because you have to predict the other players’ reactions. With bet odds, you try to determine how many people are going to call a raise. With implied odds, you try to anticipate reactions for the rest of the game. Here’s how it all works out:

Okay, so you’re in another $5/$10 Texas Hold’em game and have a four flush on the flop. One of your opponents bets, but everyone else folds, making the total pot $50.00.

First off, your out odds tell you that you’ve got about a 20-percent chance of hitting the flush on the Turn (about 1/5). Your opponent makes a $5.00 bet, which using pot odds means you should call because you stand to win 10 times what the bet is. Also, your out odds are pretty good, so calling makes sense according to the numbers.

No doubt, everything sounds perfect so far, but before you make your move, you also have to consider your bet odds and implied odds. Assuming, then, that your opponent is going to bet on the Turn and the River as well, you’ll have to see the original $5.00 bet, plus two more $10.00 bets. Now, using bet odds, you know you are looking at putting in $25.00 until the end of the hand, and you have to consider your chance of hitting the flush on the Turn or on the River. The chance of hitting the flush is a bit better than 1/3 now, but your pot odds are 1/4. Those two figures are pretty close (i.e., the hand is starting to “tighten up”), and here is where knowing all the odds works to your advantage. For example, if you don’t hit the flush on the Turn, your outs odds of scoring the flush on the River will be a little less than 1/5, while your pot odds will also shrink to 1/5. Obviously, then, with the odds now even, they can only get worse if you don’t hit the flush. That means it’s time to get out of the game and position yourself for a win on the next hand.

Finally, knowing all the odds in any poker game is naturally going to help you out tremendously. But instead of trying to cram them in all at once, first learn the outs and pot odds. Once you’ve mastered those, you can move onto bet and implied odds pretty easily because they’re just extensions of the first two. Take some time to figure these out, and when you do, you’ll see how much more developed your game is. After a while, you’ll even find you can calculate the odds without any thought at all.

-Jim Abrahamsson