Texas Holdem Hand Odds

Texas Holdem is a game of outs, odds and probabilities. In a previous article, we detailed the Starting Hand Probabilities in Texas Holdem. This time we're going to delve much further into mathematics as we define Texas Holdem Hand Odds on the Flop, Turn and River.

A good example would be holding a Flush Draw that needs to catch a Heart on the River. The chart below will describe your exact odds of catching an Out - in this case, a Heart.

Calculating Outs

For easy reference, an Out is any card that will improve your hand. In the example scenario above, any Heart would be an Out. If drawing to an Open Ended Straight, there would be two card values that could help you. For example, 6-7-8-9 would need either a 5 or 10 to complete. Since there are four 5s and 4 Tens in the deck, you have 8 Outs.

Unseen Cards

In order to determine your Hand Odds, you'll also need to know how many unseen cards remain. Unseen cards are not just the number left in the deck, but all cards you are not privy to. No matter how many opponents you are up against, the Unseen Cards are every card you cannot see. So, you have 2 Hole Cards, plus all visible Community Cards. If the Flop comes down, that's 2 + 3 = 5 cards seen. There are 52 cards in a standard deck, so 52 - 5 = 47 Unseen Cards.

For easy Reference, Unseen Cards in respect to the progress of the game are...

Pre-Flop: 50 Unseen Cards

Flop: 47 Unseen Cards

Turn: 46 Unseen Cards

River: 45 Unseen Cards

Calculating Hand Odds

It's a relatively simple mathematical process to calculate your Texas Holdem Hand Odds at any given time. It does not take a savant to pull this off, just a basic knowledge of division.

The equation for calculating hand odds is...

Outs ÷ Unseen Cards = Hand Odds

Let's try an example of a Flush Draw on the Turn. There are 13 of each suit, and you have 4 of them. That leaves 9 Outs with 47 Unseen Cards.

9 ÷ 47 = 19.1% Hand Odds

Let's say you missed it on the Turn - what are your Hand Odds on the River? The 9 Outs remain the same, but there are now 46 Unseen Cards.

9 ÷ 46 = 19.6% Hand Odds

Okay, so maybe it's not quite so simple to calculate these numbers in your head, but there's a pretty easy way around it that will get you very close to the actual Hand Odds. In the last example, we were looking for 9 Outs in 46 Unseen Cards. Simple math tells us that 9 does not go into 46 evenly, but if know our ‘Times Tables' (think back to grade school everyone!), we should know that 9 does go into 45. So, to make it easier, we'll use 45 and reverse the equation from 9 ÷ 45 to 45 ÷ 9...

45 ÷ 9 = 5

Now, to get the percentage, how many times does 5 go into 100?

100 ÷ 5 = 20

We can safely assume that your Hand Odds are "about" 20%... which is actually very close to the 19.6% we'd get with a calculator :)

Hand Odds Charts

Below we've provided you with two charts, one depicting the amount of Outs specific hands have, and other displaying the Hand Odds in relation to the number of Outs. Memorize this chart and you'll never have to worry about calculating your Hand Odds.

Number Of Outs That Will Improve Your Hand

Hand Odds - Probability of Catching Outs