Poker Probability
Knowing the odds of certain events happening in poker is one of the single most critical skills that you need to have if you want to have any chance of success in the game.
Thankfully, there are a number of shortcuts that you can use to do these calculations so that you don't need to be some kind of math wizard who uses advanced equations at the table to be able to use odds to your advantage.
Five-Card Draw and the Concept of Outs
Five card draw is a good game to explain how probability works with five card poker hands because everyone is familiar with how the rules work.
Let's suppose that you have A♦ Q♦ 7♦ 4♦ 2♠ before the draw, and you decide to discard the 2♠ to go for a flush. All of the cards that can help you to improve your hand are called outs, and you can use the number of outs to find your chances of hitting your flush. In this example, there are nine other diamonds left that could make your hand, so you have nine outs. You also know that there are 47 other cards that you could be dealt. Your chances of hitting your flush can be expressed as odds or a percentage:
- To find the percentage, you would divide 9 by 47 to get 0.191, and multiply that by 100 to get 19.1 percent.
- If you want to know your odds, you divide the other way to get 47 / 9 = 5.2, but then you'll need to subtract one from that to get your odds of 4.2:1.
The concept of outs can also be applied to other forms of poker, but the calculations are always of the same nature.
Texas Holdem Starting Hand Probabilities
Before we give you a poker probability chart showing the chances of getting different hands pre-flop, we want to show you how these values are found. There are 1,326 different possible combinations of hands that you can be dealt before the flop in Texas holdem. If you figure out how many combinations there are available for a specific hand, then you can divide that by 1,326 to find your chances of hitting that hand.
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For example, there are 16 ways to be dealt AK before the flop, so you could divide 16 by 1,326 to get 1.2 percent. To find the odds, you would divide 1,326 by 16 and subtract one to get 81.875:1. To save you the trouble of doing all of these calculations on your own, we have a chart here that will give you a lot of common values.
Hand Being Dealt | Combinations | Chance of Being Dealt | Odds of Being Dealt |
Specific Pocket Pair | 6 | 0.45% | 220:1 |
Specific Offsuit Hand | 12 | 0.90% | 110:1 |
Specific Suited Hand | 4 | 0.30% | 331:1 |
Any Pocket Pair | 78 | 5.88% | 16:1 |
AA-QQ | 18 | 1.36% | 73:1 |
JJ-88 | 24 | 1.81% | 54:1 |
77-22 | 36 | 2.71% | 36:1 |
AKs - AJs | 12 | 0.90% | 110:1 |
Broadway Hands* | 160 | 12.07% | 7:1 |
Two Cards Ten or Higher | 190 | 14.33% | 6:1 |
Ace-Any (Other than AA) | 192 | 14.48% | 6:1 |
Suited Connectors (AKs-32s) | 48 | 3.62% | 27:1 |
Connectors(AK-32) | 192 | 14.48% | 6:1 |
* Broadway hands are any two cards ten or higher that are not paired.
Post-flop Odds in Seven Card Games
Earlier we discussed the concept of outs and how it applies to figuring out your chances of hitting a draw. This is an idea that you have to use a lot after the flop in Texas holdem and other games with several streets of cards turned face-up like seven card stud and Omaha. Because Texas Holdem is the most popular form of poker, that's what we're going to use for our examples, but the basic concepts hold true for any form of poker.
The Critical Numbers: Outs and Cards in the Deck
There are two critical numbers that you must know when doing any post-flop calculation for a draw. You must know your number of outs, and you have to know how many cards are left in the deck. There are two main calculations that you can perform with these numbers regarding the very next card to be dealt:
- To calculate your percentage chance of hitting, divide the number of outs by the number of cards left in the deck and multiply by 100.
- To find the odds of completing your draw on the next card, you will divide the number of cards left in the deck by your number of outs and subtract one.
All post-flop calculations require these two numbers, and you must be able to do these basic calculations before you can go on to more advanced ones.
Common Post-flop Scenarios in Texas Holdem
Because the same types of scenarios come up over and over again in Texas holdem, it can be convenient to memorize some of the more common values. We have a poker probability chart here of everything you would need to know about any number of outs for this game.
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Number of Outs | Two Cards to Come | One Card to Come | Other Notes |
1 | 4.4% | 2.2% | Set under set |
2 | 8.4% | 4.3% | Pocket pair under pocket pair |
3 | 12.5% | 6.5% | Paired the board with lower kicker |
4 | 16.5% | 8.7% | Gutshot straight draw |
5 | 20.3% | 10.9% | |
6 | 24.1% | 13.0% | Overcards |
7 | 27.8% | 15.2% | |
8 | 31.5% | 17.4% | Open-ended straight draw |
9 | 35.0% | 19.6% | Flush draw |
10 | 38.4% | 21.7% | |
11 | 41.7% | 23.9% | Straight draw with overcard |
12 | 45.0% | 26.1% | Flush draw with gutshot straight draw |
13 | 48.1% | 28.3% | |
14 | 51.2% | 30.4% | |
15 | 54.1% | 32.6% | Straight draw with flush draw |
16 | 57.0% | 34.8% | |
17 | 59.8% | 37.0% |
Having this chart available for reference isn't a bad idea, but there is a shortcut that you can use to approximate your chance of hitting your draw with different numbers of outs.
The Rule of Two and Four
If you want to know the chance of hitting a draw on the very next card, then you can multiply your number of outs by two to get a very close approximation. For example, a flush draw has nine outs, and this rule would tell you that your chance of hitting with one card to come is about 18 percent. The actual value is 19.6 percent, but this is a close enough approximation for practical purposes.
Multiply your number of outs by the number of cards left to come and multiply that product by two to get your approximate chance of making your draw.
Along similar lines, if you want to know the chance of hitting a draw with two cards left to come, you can multiply your number of outs by four to get a good estimate. Suppose you go all-in on the flop with an open-ended straight draw and get called. You have eight outs, so multiply that by four to get 32 percent. The actual chance for hitting your draw is 31.5 percent, so you can see how close this is getting you.
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