How to Calculate Texas Holdem Odds

Holdem Odds: The Good and the Bad News

Let’s start with the bad news: Calculating the odds for each Holdem scenario is not the easiest of tasks. Unfortunately, it involves some (simple) arithmetic. But if you’ve decided to play, you might as well give it your best shot. Without knowing your odds, after all, you’re basically betting in the dark: You don’t know what your chances of winning are, nor what the payout is if you do win.

Now for the good news: Once you've learned to calculate poker odds, you'll stand a better chance of winning consistently at every kind of card game. Yes, it may hurt a little bit at first, getting all that tough math into your noggin. But, in the end, you'll be able to do some more likeable math - like counting all that money you just won in a huge pot.

How do pot and out odds work? Well, the golden rule of poker odds is "If your pot odds are greater than your out odds, you should make the bet." This is because, over time, you are expected to see a profit. But to understand why this works, let’s start by calculating pot odds...

Pot Odds

Pot odds are very similar to payouts at casinos. They are normally expressed in ratios representing the amount you stand to win per bet. The ratio itself is pretty simple. It's just the money in the pot divided by the money it costs to call the bet.

For example, if there's $50 in the pot and calling the bet costs $5, then the pot odds are 50:5, or 10:1. This basically means that the payout for this specific bet is 10 units for every one unit you bet – and you therefore stand to make $50 by betting $5, which is $10 for every $1 you put in.

Armed with this knowledge, it's easy to understand its application if you replay the last few hands you lost in your head. Did you bet, for instance, when the pot odds were in your favor? Or did you, like a complete doof, bet $50 to win $5? If your answer is the latter, you may want to jump back a few paragraphs and reread the info above. Otherwise, it's now time to learn out odds and how these two concepts fit together.

Out Odds

Out odds are simply your chances of hitting a good hand in poker. This information is very important because, after you know your pot odds, you can compare the two to see if betting makes sense. For example, if your pot odds are 10:1, and you have 4:1 chance of making your hand, then you would be calling a good bet. (Remember: If your pot odds are greater than your hand odds, the bet is good). Over time, you will win one out of every five times you call an odds-favored bet. And, when you win, you will make 10 times the bet, which is more than double the amount you put in (you paid for five bets, assuming that all the bets were for the same amount).

But how do you calculate your chance to make a hand? The basic formula is: the number of "outs" (or the cards left in the deck that would give you your desired hand) over the total number of cards remaining in the deck. This will tell you how likely it is that you'll make your hand, expressed as a fraction.

Outs

"Outs" are the cards you need to appear on the table in order to make the hand you’re drawing for. For example: if you’re holding two diamonds, and the flop shows two diamonds, then you need one more diamond to hit your flush. There are a total of 13 diamonds in a deck of cards, four of which are already out (the two you’re holding plus the two on the table). So there are nine more cards that will complete the flush and "make" your hand. This means you have nine outs.

Now, assuming you are playing at a table with three other players, we can safely say that your total out odds are 9/39 - assuming, of course, that no other diamonds have gone out of the deck. How did we get this figure? Well, for one thing, there are three other players plus you, for a total of four, and each of you have been dealt two cards at the start of the game. As we hope you know, two times four is eight, so we can be sure eight cards are out of the deck. Also, the dealer has already burned a card, dealt three community cards and will burn another, bringing the total number of cards out of the deck before the turn to 13. Considering then that there were 52 cards in the original deck, by the time the turn comes, there must be 39 (i.e., 52 - 13 = 39). So your total out odds - or chance of getting another diamond on the turn - are 9/39, or 23 percent. Not so shabby of course, but also not so marvelous.

Why "not so marvelous"? Well, because out odds become more complicated when you consider that you're not the only player at the table - and, needless to say, one, two, even three or more opponents may be holding diamonds too. The way to figure for this, then, is to use your reading skills to try and determine what's in their holes and if your cards are even still in the deck. Because many players will at least pay to see the flop - especially if they've got a suited hole - you can be sure the guy who seems just as excited as you feel on a flop where the only other possible hands are pairs, trips or quads... That guy is more than likely holding two of your diamonds, bringing your out odds down to 7/39.

Now, let's imagine too that you're sitting at a table with nine other players and all of them pay to see the flop. What do we know? Well, for one thing, there are 18 cards out of 52 somewhere around the table. Also, people could be holding a suited hole or bluffing or playing any number of different ways. Because you can't see what they're holding, you just can't be sure.

This is where out odds seem to break down, but in reality, they don't. The logical person, after all, knows that there is a greater probability of several other diamonds going into his opponents' hands than that the fourth and final card he needs for his flush will arrive on the turn or river. This brings us to the second rule of poker odds: You don't talk about... Hehheh, just kidding - The second rule is, you never stay in on a draw if you're playing at a long-hand table and didn't flop the necessary outs to make your hand.

Remaining Cards

As we said before, there are 52 cards in a deck, you’ve been dealt two, and let’s suppose, there are four open cards on the table. You have no information about all the rest – your opponents may be holding diamonds or they may not, but either way, two cards have definitely come out of the deck for each opponent who was dealt in. The number of remaining cards before the river in a three-handed game, therefore, is 52 – 3 (the burns) - 2 - 2 - 2 – 4 = 37.

Meanwhile, unless your opponents are giving off strong tells, you can't be sure whether or not they have any diamonds. The logical thing to do, then, is assume they don't, but here's where poker and logic part ways. To be on the safe side, you should always assume your remaining opponents are holding your other outs if they're in. This may not be so, but it may be. And, if it is, whoever is cocky enough to be staring down two or three flush draws with a measly pair is going to be very happy when you and your drawing opponents lose.

All-tolled, then, your realistic (or should we say pessimistic?) out odds after the turn in a three-hand game are 5/37, or about 14 percent. Those ARE pretty crap odds, and conventional wisdom says you should fold and wait for the next hand – unless, of course, your pot odds are 1000:1 (Hey, what the heck, right?).