Poker Mathematics: How to Calculate Outs and Pot Odds
Every successful poker player understands the concepts of outs and pot odds. These are crucial tools in their arsenal: professional decisions are always based on mathematical calculations, enabling them to win consistently over time. For those unfamiliar with poker mathematics, it may appear daunting, but in reality, it's simpler than it seems. In this article, we will demonstrate how to calculate pot odds in a few seconds and introduce you to the basic principles of poker mathematics.
What Are Pot Odds?
Pot odds are the ratio of the current size of the pot to the bet you need to make to stay in the hand. They help determine whether it's beneficial to continue in the game or to fold your hand. Let’s break this down with a simple example:
You're on the flop. The pot contains 1000 chips, and your opponent bets 500 chips. Now the total pot is 1500 chips, and you need to pay 500 chips to remain in the hand.
In this case, the pot odds are 500 / (1000 + 500) = 1/4, or 25%. This means, over time, a call will be profitable if you win at least one hand out of four.
Why Calculate Pot Odds?
Pot odds are often compared to the probability of improving your hand when you don't yet have a strong combination. Let's examine an example:
You have A♠️K♠️. The flop shows 2♠️7♠️J♦️. To make a flush, you need one of the remaining 9 spades. Additionally, your hand will improve if an Ace or King appears: 3 Aces + 3 Kings. This gives you a total of 15 outs to improve.
The pot is 1000 chips, and your opponent bets 300. To stay in the hand, you need to pay 300 chips. Pot odds: 300 / (1000 + 300 + 300) ≈ 19%. Therefore, a call is profitable if your odds of improving are 19% or higher.
How to calculate the odds of improving?
To do this quickly at the tables, multiply the number of outs by 4 if there are two betting rounds ahead, and by 2 if there's only one. We have 15 outs with two rounds left - that's 15 x 4 = 60%
Your improvement chances exceed the pot odds, meaning the call is justified.
Suppose you called and the turn revealed Q♥️. Now the board shows: 2♠️7♠️J♦️Q♥️. The pot is 1600 chips, and your opponent bets 1600. Pot odds: 1600 / (1600 + 1600 + 1600) = 33%.
Your outs now include:
9 remaining spades (for a flush)
3 Aces + 3 Kings (top pair)
3 tens (for a straight)
A total of 18 outs. The probability of improving by the river: 18 x 2 = 36%. The call is still profitable, as your improvement chances exceed the pot odds.
If you only had 10 outs, for instance, the probability of improvement would be around 20%, which is less than the pot odds, so folding would be the correct decision.
How to Quickly Perform Calculations?
The example above might be daunting with the number of calculations, but with practice, it becomes quick. To avoid having to compute improvement odds altogether, you can memorise this table:
Outs | Turn (1 card) | River (1 card) | Turn and River (2 cards) |
1 | 2.13% | 2.17% | 4.26% |
2 | 4.26% | 4.35% | 8.42% |
3 | 6.38% | 6.52% | 12.49% |
4 | 8.51% | 8.70% | 16.47% |
5 | 10.64% | 10.87% | 20.35% |
6 | 12.77% | 13.04% | 24.14% |
7 | 14.89% | 15.22% | 27.84% |
8 | 17.02% | 17.39% | 31.45% |
9 | 19.15% | 19.57% | 34.97% |
10 | 21.23% | 21.47% | 38.39% |
11 | 23.40% | 23.91% | 41.72% |
12 | 25.53% | 26.09% | 44.95% |
13 | 27.66% | 28.26% | 48.10% |
14 | 29.79% | 30.43% | 51.16% |
15 | 31.91% | 32.61% | 54.12% |
16 | 34.04% | 34.76% | 56.98% |
17 | 36.17% | 36.96% | 59.74% |
18 | 38.30% | 39.13% | 62.44% |
19 | 40.43% | 41.30% | 65.03% |
20 | 42.55% | 43.48% | 67.53% |
21 | 44.68% | 45.65% | 69.94% |
There is also a simpler way to quickly estimate improvement odds with one street to go, based on your number of outs:
Up to 3 outs: probability ≈ number of outs × 2.
From 3 to 11 outs: probability ≈ number of outs × 2 + 1. For instance, if you have 5 outs, the improvement probability will be 5×2+1 = 11%, which matches the table.
11 outs and more: probability ≈ number of outs × 2 + 2. For example, for 15 outs the probability of improvement will be 15×2+2 = 32%.
This method allows for a quick estimate without complex calculations.
Conclusion
Now you understand what pot odds are and how to use them in your game. Grasping these calculations aids in making informed decisions and increasing profit over the long term.
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FAQ
In what situations is it important to calculate pot odds?
At the beginning of your poker journey, it's crucial to calculate pot odds in every hand. While you’re playing a small number of tables simultaneously, do it consistently, so over time you intuitively understand the pot odds in each hand by looking at the bet and pot size. It’s especially important to calculate pot odds in situations where you don’t have a made hand, or the opponent’s bet has made you think and you’re hesitant about your decision.
What are implied odds?
These are the future chips you might win if you hit your out. For instance, sometimes it makes sense to call a big bet with a nut flush draw if you are completely sure that hitting the flush will allow you to win the opponent’s entire stack.
What should you do if pot odds and odds of improvement are almost equal?
In such scenarios, implied odds are used. If you are certain that improving your hand will win you additional chips, call. If you’re unsure, the call might not be profitable over the long term and is likely unnecessary.
Can you fully trust the rule "multiply by 2 or by 4"?
This is an approximate formula. It works well for quick decisions but is not accurate. In complex situations, calculate more precisely: divide the number of outs by the number of remaining cards in the deck to determine your chances of improving on one street. Multiply by two to get an approximate chance of improving over two streets.