Calculating odds and probabilities for Texas Hold’em is easy to learn. Once you understand the terminology, you can quickly figure out the pot odds without relying on a chart or calculator. We’ve broken down the poker math into four easy steps.
Make sure you go through these four steps every time you make a bet.
- Step One: Determine the number of cards that can improve your hand. Cards that can improve your hand into a winning hand are call "outs." Make sure you do not count outs that will help your opponent make an even better hand.
- Step Two: Calculate the odds of hitting your outs.
- Step Three: Calculate the pot odds and implied pot odds. Pot odds compare the cost of calling a bet against the amount of money already in the pot. Implied pot odds compare the cost of calling a bet against the amount of money you expect to win from the final pot.
- Step Four: Compare the implied pot odds and the odds of improving your hand. If the implied pot odds is 10 to 1 (i.e. it only cost you $1 to stay in a $10 pot) and the odds of you improving your hand is 5 to 1, you should definitely call the bet.
- Advanced Concepts: Once this process becomes second nature, you can make adjustments to your odds. Consider your opponent, what’s on board and your image when calculating odds.
Step One: Determine the Number of Outs
Outs are unseen cards that will improve or complete your cards to give you the winning hand. For example, if you hold :
and the flop is
You have at least nine outs because there are nine hearts left in the deck that can help you make your flush.
Classic Situations Where You Should Discount Outs
Here are some common situations where you should not give your outs full value:
- If your outs would give your opponent a higher straight than yours.
- If the flop has two same-suited cards and you do not have that suit, you should reduce your outs by half.
- If your outs would give you the top pair, but you have a low kicker, you should reduce your outs by half if you are playing against more than two players. If there are more than three players still left in the game, you should discount those outs completely.
- If you are on a flush draw and you do not have a card higher than a Queen, you should discount half of your outs.
- If your outs would only give you the second highest two pair, you should discount one of your outs.
Certain outs can improve your hand, but at the same time, give your opponent an even better hand. For example, you hold
and the flop is
You have an open ended straight draw. Since either a 5 or a 10 can help you make a straight, you have 8 outs. However, if another player is holding a Jack, if a 10 hits he will have a higher straight than you.
With the possibility of a higher straight, you must discount some of your 10s as outs. In other words, you can still count the 10 as your out, but you must lower the 10′s value to compensate for the possibility that one of your opponents can use the same 10 to beat you.
If you are only facing one opponent, you can still count at least three of the 10s as outs, since the chances of your lone opponent holding a Jack is slim. However, if there are two opponents left, you should only count two of the 10s as outs.
If there are more than two opponents left, you should not count any 10s as outs, since there is a good chance that at least one of your opponents is holding a Jack.
Step Two: Calculate the Odds of Hitting Your Outs
After identifying your outs, the next step is to figure out the odds of you getting that card.
The following chart shows you the probability and odds of improving your hand based on your number of outs. If you play online, you should post this handy chart next to your computer.
|
Number of Outs
|
After Flop |
After Turn |
||
|
Percentage
|
Odds to 1 against
|
Percentage
|
Odds to 1 against
|
|
|
1
|
4.3
|
22.4
|
2.2
|
44.5
|
|
2
|
8.4
|
10.9
|
4.3
|
22.3
|
|
3
|
12.5
|
7
|
6.5
|
14.4
|
|
4
|
16.5
|
5.1
|
8.7
|
10.5
|
|
5
|
20.3
|
3.9
|
10.9
|
8.2
|
|
6
|
24.1
|
3.1
|
13
|
6.7
|
|
7
|
27.8
|
2.6
|
15.2
|
5.6
|
|
8
|
31.5
|
2.2
|
17.4
|
4.7
|
|
9
|
35
|
1.9
|
19.6
|
4.1
|
|
10
|
38.4
|
1.6
|
21.7
|
3.6
|
|
11
|
41.7
|
1.4
|
24
|
3.2
|
|
12
|
45
|
1.2
|
26.1
|
2.8
|
|
13
|
48.1
|
1.1
|
28.3
|
2.5
|
|
14
|
51.2
|
0.95
|
30.4
|
2.3
|
|
15
|
54.1
|
0.85
|
32.6
|
2.1
|
|
16
|
57
|
0.75
|
34.3
|
1.9
|
|
17
|
59.8
|
0.67
|
37
|
1.7
|
|
18
|
62.4
|
0.6
|
39.1
|
1.6
|
|
19
|
65
|
0.54
|
41.3
|
1.4
|
|
20
|
67.5
|
0.48
|
43.5
|
1.3
|
The difference between odds and probabilities
Odds and probabilities help us describe how likely an event will or will not happen.
Probability describes how likely an event will happen. For example, the probability of getting dealt a pocket pair is 5.88%, or roughly once every 17 times. (1/17 = 0.0588).
Odds describe how many times something will not happen. For example, the odds against you getting a pocket pair is 16 to 1 (16:1). This means out of 17 hands, you will not get dealt a pocket pair in 16 times.
The Four-Two Ballpark Rule
You won’t be able to carry your chart to a live poker game. When you cannot use the chart, you can use the Four-Two Ballpark Rule to do some quick and dirty odds calculations:
1. After the flop, with two more cards to come: multiply your number of outs by FOUR to get the probability of hitting that out.
2. After the turn, with one more card to come: multiply the number of outs by TWO.
For example, if you are on a four-card flush draw after the flop, you have nine outs. With two more cards to come, you multiply nine by four, which gives you 36%. If you go back to the chart, you can see the estimate is only 1% off the actual number 35%.
If you are on a four-card flush draw after the turn, there is one more card to come. You multiply nine by two to get 18%, which is only 1.5% off from the actual number of 19.6%.
(Note that the greater the number of outs, the less accurate the Four-Two Rule becomes. We do not recommend using this rule if you have more than 16 outs. At 17 outs, 17 x 4 = 68. 68% is eight points off from the correct percentage, 59.8%.)
Basic Probabilities You Should Memorize
There are three basic probabilities every poker player must memorize:
1. Nine outs: Probability of completing your flush draw with two cards to come is 35%, with one card to come the probability is 19.6%
2. Eight outs: Probability of completing your open-ended straight draw with two cards to come is 31.5%, with one card to come the probability is 17.4%.
3. Six outs: with two over cards in your pocket, probability pairing up with two cards to come is 24.1%, with one card to come the probability is 13%.
Step Three: Calculate Pot Odds and Implied Pot Odds
Pot odds compare the cost of calling a bet against the amount of money already in the pot.
For example, if the pot is $10 and you must bet $1 to stay in the hand, the pot odds are 10 to 1 (10:1). This means you can expect a $10 return on your $1 investment if you end up winning the pot.
Implied pot odds compare the cost of calling a bet against the amount of money you expect to win from the final pot.
To estimate the size of the final pot, you must consider how many times and how much the other players will bet in this hand.
For example, you are playing in a three-way $1-$2 game. The pot is $10 and the first player bets $2 on the turn.
You are next to act, and there is a one more player behind you. Right now, the pot odds are 10 to 2 (or 5 to 1).
However, if you believe the third player will call the $2 bet as well, then you can add the third players $2 to your calculation, making the implied pot odds 12 to 2 (6:1).
Moreover, if you expect both of your opponents to each bet another $2 on the river, you can expect to win $16 from the final pot; therefore, your implied odds become 16 to 2 (8:1).
Step Four: Comparing Implied Pot Odds and the Odds of Improving Your Hand
The last step is to compare the odd of making your winning hand against the pot odds or implied pot odds. If the odds of making your hand is greater than the pot or implied pot odds, then you should bet or even raise.
For example, in a $5-10 game, you hold:
The flop comes:
There is $15 in the pot. There are two other players left in the hand, you are in the middle betting position. You all check.
The turn comes:
The first player bets $10. What do you do?
First, calculate your outs. You have nine outs to make a flush. According to the odds chart above, the odds of making a flush with only one card to come is 4 to 1 (refer to chart above).
There is now $25 in the pot, therefore the pot odds is 25 to 10, or 2.5 to 1. Since the odds of improving your hand are worse than the pot odds, you should probably fold.
However, the answer may be different if you applied the more sophisticated implied odds analysis.
There is still a third player behind you. You know the third player loves to play suited connectors. It is possible that he is on the same flush draw. You believe he will probably call the $10 bet, and probably call another bet on the river if you make the flush.
Moreover, you also know the first player is a stubborn person who does not like to fold. You believe he will also call an additional bet on the river even if you make your flush.
Therefore, you have reason to believe that the final pot will be at least $55. Therefore, the implied pot odds is $55 to 10, or 5.5 to 1.
Pot Odds vs. Implied Pot Odds
You might wonder why we discuss pot odds at all, when implied pot odds seem to give us so much more information. When you are confident in your ability to read players and situations, you should always rely on implied pot odds. However, if you are unfamiliar with the players at your table, you will have a hard time making educated guesses regarding the other player’s expected reactions. In this case, it would be smarter to stick with pot odds until you learn more about your opponents.
Advanced Concepts
Factors to Consider When Calculating Implied Pot Odds
Here are some things a good player considers while calculating implied pot odds.
- Aggressive opponents increase your implied pot odds: the more aggressive your opponents are, the more likely they will pay you off. Conversely, cautious opponents decrease your pot odds because they are less likely to call your big bets.
- Hidden hands increase your implied pot odds: if you are going for an inside straight or backdoor flush draw, your opponents will probably misread your hand.
- The size of the pot increase your implied pot odds: the bigger the pot is the more likely your opponents are willing to call every bet you make.
- Your aggressive table image increase your implied pot odds: if your opponents know you recently took down a pot by bluffing, they are more likely to call your bets.
Playing Against the Odds
Poker pro David Sklansky cautions that you cannot always use pot odds as your guide. If you always fold when the pot odds are against you, your opponents will label you as a "folder." Once in a while you have to make a call that is not justified by the odds just to keep your opponents guessing.
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