How to Calculate Odds In Poker

Poker players who can calculate the odds will consistently make correct choices on whether to call or fold and as a result, will be more profitable over time.

If you don’t learn, comprehend, and use the mathematical parameters of poker, it will be difficult to consistently win in the long run. For example, if you are playing Texas Hold’em and flop an open ended straight draw, but don’t know the odds against completing your hand, how will you make the correct choice when its your turn to act? How will you know whether calling, betting, raising, or folding, is a move with positive expectation? Consistently making moves with positive expectation, or odds in your favor, is the key to winning poker in the long haul. Its simply recognizing situations that will show profit when played over and over.

How to Calculate Poker Odds

Players use odds to determine their actions. The chances of finishing a flush or a straight, the probability of getting an overcard, the percentage of times you’re going to flop a set to match your pocket pair, are all important factors to consider when choosing whether to play or not. Knowledge of these probabilities go hand in hand with success. In online games particularly where there are very few tells, or ways to read your opponent, knowing probability is the key factor when choosing whether to bet, call, or fold.

Pot Odds

Probably the most common, fundamental form of calculating odds are pot odds. This is simply comparing the actual odds of making your hand to the amount of money you will get if you win. Comparing with pot odds allows your wins to outweigh your losses over time as you play according to a positive expected value as a result only finishing hands with favorable pot odds.

Calculating Pot Odds

Try not to be too anxious about your ability to calculate odds as calculating odds is done with simple division. The numerator is the number of outs you have or cards left in the deck that will improve your hand. The denominator is the number of cards left that you haven’t seen. Dividing the outs by the number of cards you haven’t seen will result in the percentage of chance to make one of those outs. Pre-flop the largest amount of math will be dividing small numbers by 50, 47 after the flop and 46 after the turn.

Pot odds are as easy as figuring outs. You compare your outs or your chance of winning to the size of the pot. If your chance of winning is significantly better than the ratio of the pot size to a bet, then you have a positive expected value. If it’s lower, then you have a negative expected value. Over time, finishing hands with a negative expected value will cause you chip stack or bankroll to shrink.

Calculating Pot odds while playing:

  • You are in a $10/$20 Texas Hold’em game with 10-9 facing one opponent on the turn. You have an open-ended straight draw with a board of 4-2-8-J, and only the river card left to make your hand. Any 7 or any Queen will finish this straight which gives you eight outs. Those eight outs are four 7s and four Queens. There are 46 unseen cards left. 8/46 is about a 1 in 6 chance of making your straight. Your opponent, the only one left, bets $20. You if you take a $10 bet you could win a $400 pot. $400/$20 is 40. If you call you could make 20 times more than the bet.. 1/6 higher than 1/20, which means that the chances of making your straight is higher than the ratio of the bet to the pot. You are getting good odds to call which results in a positive expected value or a profitable call over time. Pot odds tell you the correct move here would be to call.

Texas Hold’em Odds Chart

This chart will help you see the odds in correlation with how many outs you have:

 

After Flop
Two cards to come

After Turn
One card to come

Number of outs

Probability of making hand

Odds against making hand

Probability of making hand

Odds against making hand

1

4.3%

22.4:1

2.2%

44.5:1

2

8.4%

10.9:1

4.3%

22.3:1

3

12.5%

7:1

6.5%

14.4:1

4

16.5%

5.1:1

8.7%

10.5:1

5

20.3%

3.9:1

10.9%

8.2:1

6

24.1%

3.1:1

13%

6.7:1

7

27.8%

2.6:1

15.2%

5.6:1

8

31.5%

2.2:1

17.4%

4.7:1

9

35%

1.9:1

19.6%

4.1:1

10

38.4%

1.6:1

21.7%

3.6:1

11

41.7%

1.4:1

24%

3.2:1

12

45%

1.2:1

26.1%

2.8:1

13

48.1%

1.1:1

28.3%

2.5:1

14

51.2%

0.95:1

30.4%

2.3:1

15

54.1%

0.85:1

32.6%

2.1:1

16

57%

0.75:1

34.3%

1.9:1

17

59.8%

0.67:1

37%

1.7:1

18

62.4%

0.6:1

39.1%

1.6:1

19

65%

0.54:1

41.3

1.4:1

20

67.5%

0.48:1

43.5

1.3:1

 

Common Draws you might chase and want to calculate

Outs

Hands

15

Open ended straight flush, flush draw with two over cards

14

Straight draw with two over cards

12

Inside straight draw, flush draw with one over card

9

Four flush ( 4 suited cards, looking for 5)

8

Open ended straight, double gut shot straight

5

Pair( drawing two pair or three of a kind)

4

Gut shot or two pair ( drawing to full house)

Knowing how many outs you have and the odds to make your hand as shown in tables like these will help you understand your probability of winning. The next step is to figure out if that percentage is worth the size of the pot. This is how poker players maximize there profits.

Implied Odds

Implied pot odds, apply in situations where future betting may occur. A player’s implied pot is the current pot plus the value of future bets expected from opponents that may be won, excluding the player’s own bets. When figuring the implied pot, a player must estimate the bets expected from opponents in the event the player wins the pot.

Texas Holdem example, drawing to certain winner

  • With one card to come, Lacey holds a nut outside straight draw and faces a $10 call to win a $35 pot. If Lacey makes her nut straight, she expects her opponent to contribute another $10 in the final round. Lacey’s implied pot is $45 ($35 current pot + $10 future bets by her opponent).
  • Lacey’s implied pot odds are 4.5-to-1 ($45/$10) or 18% (1/(4.5+1)).
  • A call by Lacey has a borderline positive expectation because the probability of making her straight (17% with one card to come) is about the same as her implied pot odds (18%).
  • When drawing to a hand that is only a probable winner (e.g., drawing to the 2nd nut flush), the mathematics of implied odds is typically expressed in terms of expected value (EV):

Texas Holdem example, drawing to probable winner

  • With one card to come, Lacey holds a non-nut flush draw and faces a $5 call to win a $20 pot. If Lacey makes a winning flush, she expects her opponent to contribute another $50 on the final betting round (implied pot = $50). If Lacey makes a losing flush, she expects she will lose an additional $100 on the final betting round.
  • She estimates that the probability of making her flush with one card to come is 19% if her opponent is not drawing to a higher flush. If her opponent is drawing to a higher flush, the probability of hitting her flush decreases to 15% (because she only has 7 outs to hit her flush instead of 9). Lacey estimates the probability of losing if she makes her flush at 20%.
  • EV of $5 call = 19% * 80% * $50 - 15% * 20% * $100 = $4.6
  • Because the expected value of the $5 call is only $4.6, The correct move for Lacey would be to fold.

Implied odds calculations are further complicated when there is more than one card to come, because expected betting patterns (and therefore implied pots) may differ if a hand is improved on the turn or river.

If you are looking for Omaha Odds, visit our Omaha Odds Chart page.

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