Module 3 · Lesson 13 of 39 · Free
Poker odds and percentages: how to convert odds against
A 4-to-1 shot wins 20% of the time, not 25%. Odds against put the misses before the hits: 4 to 1 means 4 misses for every hit, so 1 hit in every 5 tries. Players use both forms, and reading one as the other is a costly slip.
The hand
The turn. You hold A♥ 7♥ and the board is K♥ 9♥ 4♣ 2♠: four hearts, one short of a flush. Of the 46 cards you have not seen, 9 are hearts.
Predict first
Nine of the 46 cards give you the flush on the river. As odds against, that is about:
- 5 to 1: 46 cards against 9 hearts
- 9 to 37: the hearts against the rest
- 4 to 1: 37 misses against 9 hearts
Show the answer
Answer: 4 to 1: 37 misses against 9 hearts
Odds against count the misses first: 46 − 9 = 37 cards miss and 9 hit, 37 to 9, and 37 ÷ 9 ≈ 4.1, so about 4 to 1. As a share of the 46 cards, 9 ÷ 46 = 19.6%, close to 1 in 5.
Working it out
To turn odds into a chance, add the two sides to get the number of tries. 4 to 1 is 1 hit in 4 + 1 = 5 tries: 1 ÷ 5 = 20%. The flush draw, 37 to 9, is 9 hits in 37 + 9 = 46 tries: 9 ÷ 46 = 19.6%. To go the other way, divide the misses by the hits: a chance of 25% misses 75% of the time, and 75 ÷ 25 = 3, so it is 3 to 1 against. In the same way 50% is 1 to 1, often called even money, 33.3% is 2 to 1 and 10% is 9 to 1. Above 50% the odds are on rather than against: 75% is 3 to 1 on.
Each form answers its own question. Odds line up with the money: when the pot odds are 4 to 1, the pot holds 4 times your call, and a hand that is 4 to 1 against breaks even on the call. Percentages are easy to compare at a glance: 19.6% is plainly less than 25%. Learn a few pairs by heart: 1 to 1 is 50%, 2 to 1 is 33.3%, 3 to 1 is 25%, 4 to 1 is 20% and 9 to 1 is 10%.
Formula
a to b against = b ÷ (a + b): 4 to 1 = 1 ÷ 5 = 20%. Odds against = misses ÷ hits: 25% misses 75%, 75 ÷ 25 = 3 to 1
Check your understanding
A hand is 3 to 2 against. How often does it win, in %?
Show the answer
Answer: 40%
3 losses for every 2 wins is 2 wins in 3 + 2 = 5 tries: 2 ÷ 5 = 40%.
A draw comes in 12.5% of the time. What are the odds against it, as x to 1?
Show the answer
Answer: 7
It misses 87.5% of the time: 87.5 ÷ 12.5 = 7, so 7 to 1 against.
Which comes in more often: a draw that is 5 to 1 against, or a draw that comes in 15% of the time?
- The draw that is 5 to 1 against
- The draw that comes in 15% of the time
- Both come in equally often
Show the answer
Answer: The draw that is 5 to 1 against
5 to 1 against is 1 hit in 5 + 1 = 6 tries: 1 ÷ 6 = 16.7%, more than 15%.