Odds of hitting a flush draw in Texas Holdem
I recently won a bet about the odds of getting a flush, on a flush draw. I bet $20 that the chances were better than 16%; and indeed, it actually turns out to be closer to 20%.
The simple statistical calculation is as follows. A total of 6 cards have been displayed (4 on table, 2 in players hand). 4 of the cards are a suited, leaving 9 remaining cards from that suit in a deck which could contain 46 different cards. 9/46 = 19.6%
Actual Scenario:
Billy's Odds
At this point Billy is hoping the River will hit another club. As we found above, the chance of this from Billy's point of view is 19.6%. Plus having an Ace gives him high flush and nearly 52% for a win. Since Akram bluffs a lot, a high card or pair might actually be enough.
Akrams Odds
Akram, has a different point of view; he already has the flush. A player in his position has about 95% of winning.
Actual Odds
Akram didn't hessitate and goes all in and Billy promptly calls it. Both players made the right decision, but Akrams is clearly in the lead since he has more information. The actual chance that Billy could have pulled it off was 15.9%. Just below my 16% assesment.
Clarifying Odds
This is why its important to clarify odds. There are player perceived odds and actual odds. I analysed the individual player percieved odds for Billy and Akram indepenently above, then the actual odds considers what both players have at the same time.
Whereas Akram believed he had a lock on a 95% win, it was actually 84%. Billy however felt a warm 52% chance when infact it was 16%. When you watch TV poker they show actual odds which accounts for all the cards the camera sees from all players; even the ones which folded. This gives the most accurate likelihood estimation.
In this bet, I made sure to clarify that it was a greater than 16% chance of winning from Billys perspective.... so I expect to collect soon!
Oh, the outcome.. A non-club came on the River and Akram won. Billy shouted for the 20th time that tournament, "I can't believe it, you're so lucky", for the 20th time... something which we all should have predicted!
The simple statistical calculation is as follows. A total of 6 cards have been displayed (4 on table, 2 in players hand). 4 of the cards are a suited, leaving 9 remaining cards from that suit in a deck which could contain 46 different cards. 9/46 = 19.6%
Actual Scenario:
- Billy pocket cards: Ac, 7h
- Akram pocket cards: 2c, 9c
- Flop: 4c, 6c, Jh
- Turn: 10c
Billy's Odds
At this point Billy is hoping the River will hit another club. As we found above, the chance of this from Billy's point of view is 19.6%. Plus having an Ace gives him high flush and nearly 52% for a win. Since Akram bluffs a lot, a high card or pair might actually be enough.
Akrams Odds
Akram, has a different point of view; he already has the flush. A player in his position has about 95% of winning.
Actual Odds
Akram didn't hessitate and goes all in and Billy promptly calls it. Both players made the right decision, but Akrams is clearly in the lead since he has more information. The actual chance that Billy could have pulled it off was 15.9%. Just below my 16% assesment.
Clarifying Odds
This is why its important to clarify odds. There are player perceived odds and actual odds. I analysed the individual player percieved odds for Billy and Akram indepenently above, then the actual odds considers what both players have at the same time.
| Player Perceived | Actual | |
| Akram | 95% | 84% |
| Billy | 52% | 16% |
Whereas Akram believed he had a lock on a 95% win, it was actually 84%. Billy however felt a warm 52% chance when infact it was 16%. When you watch TV poker they show actual odds which accounts for all the cards the camera sees from all players; even the ones which folded. This gives the most accurate likelihood estimation.
In this bet, I made sure to clarify that it was a greater than 16% chance of winning from Billys perspective.... so I expect to collect soon!
Oh, the outcome.. A non-club came on the River and Akram won. Billy shouted for the 20th time that tournament, "I can't believe it, you're so lucky", for the 20th time... something which we all should have predicted!
posted by David Rodecker at 2:21 AM
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