Calculating Probability On The Flop In Texas Hold'em Poker

If you want to become a master poker player, you’re going to have to brush up on your math skills. It’s the unfortunate beast that comes with the beauty that is texas hold’em poker. While it’s impossible to calculate every hand’s possible odds, unless you’re the Rainman of course, it’s a good idea to get a feel for how to calculate odds on the fly in order to better educate yourself on what hands to play and when to play them.

In order to calculate probabilities in texas hold’em poker, you’ll need to understand how that is applied to the deck of cards in play. In texas hold’em poker, there are 52 cards to randomly choose from before the cards are dealt. You receive two cards out of that deck of 52 cards. The odds of receiving any card out of the deck on your first card are 1 in 52. This leaves 51 cards in the deck. Now, the odds of receiving any remaining card in the deck on your second card are 1 in 51. Therefore, if you take 52x51 and divide it by the two cards you’ve received, you’ll come up with 52 x 51 divided by 2 = 1326. All this means is that there are 1326 possible starting hand combinations that you can draw from that initial deal. Out of that 1326 possible cards you might draw, there are 169 unique possible pocket pair combinations that you can end up with on the initial deal. This means that out of every pocket pair combination from 2-2 to A-A, there are 169 possible pairs you can make. For those interested in the math: (13 pocket pairs + 78 suited cards + 78 unsuited cards = 169).

That’s the easy part. Now, the hard part comes when trying to decide whether or not your two pocket cards have better or worse odds to win in comparison to your opponents’ cards, without knowing what cards they might hold. Aye, there’s the rub. So, the first thing you want to consider is what two pocket card combinations hold the greatest chances for success before the flop. As always, in texas hold’em poker there are multiple factors to consider when choosing to play a hand, but just knowing what cards hold the greatest odds to win is a good place to start.

Your pocket cards actually lose their power depending on how many players there are at the table. For example, holding an A-A has about an 85% chance of winning if you are only playing against one other player, but the odds dramatically fall to about a 31% chance of winning if you are playing against nine other players. While they’re still the strongest pocket cards to start with, your odds of making the best hand decreases simply because more cards have already been dealt from the hand and are no longer available for you to use. Having said that, there are certain starting hands that, if you hold them, should probably be played through to the flop due to their high-win potential. The following percentages are based on play against only one other player, yet their weight holds up the same no matter how many players are at the table. The best starting hands based on their high probability of winning are, AA (85%), KK (82%), QQ (80%), JJ (78%), TT (75%), 99 (72%), 88 (69%), AK (66%), AQ (65%), AJ (64%), AT (63%), and KQ (62%). This is not to say that you will win the pot every single time with these pocket cards, but it’s definitely the best way to go into the flop strong.

Now, let’s talk about calculating probability on the flop. There is a quick and simple way to calculate the odds of your hand catching a higher value on the flop. First you need to determine the number of outs you have to make a better hand. Outs are simply the number of cards possibly available in the remaining deck that could make the best hand possible. To calculate the outs you need to add up the number of possible cards left that would increase the value of your hand. For example, let’s say your pocket cards are a Ks-6h. The flop comes down as Qs-8h-6c. You have a pair. If you wanted to calculate the odds of getting a three-of-a-kind, you would need to draw one of the two sixes. This means you have two outs available to make your hand. There are two more cards that are going to be dealt, so you would take your two outs, multiply that by two, and then multiply that by two again (or just multiply by four to keep it simple). So, your two outs multiplied by four equals eight (2x4=8). This means you have an 8% chance of drawing one of those sixes in order to make a three-of-a-kind. Not good odds.

Let’s say you have the same pocket cards Ks-6h, but the flop shows Kc-8h-6c. You now have two pair and want to shoot for the full house. You would need to draw one of the two sixes or one of the two kings left in the deck. This means you have four outs available. So, you would take your four outs and multiply that by four (4x4=16). This means you have a 16% chance of making the full-house. Not good, but better.

Now, again with the pocket cards Ks-6h, but the flop shows 10s-8s-2s. You hold nothing, but are shooting for the flush. So, there are thirteen possible spades available in every hand, four of them are already shown, that leaves nine outs available. Take your nine outs and multiply that by four (9x4=36). This means you have a 36% chance of catching another spade to make the flush. Pretty good odds, but since the other players might be holding a spade as well, it’s probably not the greatest hand to play.

Finally, with pocket cards Ks-6h and the flop shows Kh-9h-4h. You’re obviously going to shoot for the flush, so you would need one of the nine remaining hearts (9x4=36) giving you a 36% chance of hitting the hand. However, you could also shoot for the three-of-a-kind, which means the two remaining kings would give you an additional two outs. Adding the two possible hands together would give you eleven possible outs (11x4=44). So, this means you would actually have a 44% chance of increasing your hand strength. Now, those are odds you can win some pots with. See, math isn’t so hard, is it?

Remember, these are just general odds of how many times a specific card might show up next from the deck. Probability is just that, probability, not a guarantee, so don’t take these calculations at their face. You still need to take into consideration how many players are still in the game, your position at the table, and the value of the pot. But, that’s another lesson.