| Posted by: maltz at September 28, 2007, 2:13 am | | Topic: (Odds) Flush vs. Overflush Forum: Card Chat |
This is my true story not ery long ago.
My hole cards were Kd 4d in SB. By turn, there were three diamonds on board. Happy with my K-high flush, I raised 1/2 pot and some other guy reraised all in all of a sudden. I called to see his Ad Qd... DOH! (Good it is not real money.)
Case K-High: King-high flush runs into Ace-high flush
There are at least 3 suited cards on the board. Maybe 4, maybe 5.
We have to list them all.
- 3 suited cards on board (no Ace):
You hold 2. There are 7 non-Ace cards left.
Therefore, there are 7 kinds of A-high flush out there.
Total possibility of hole cards = 1225
In a field of 9 opponent, none of them has A-high flush: (1-7/1225)^9 = 0.9497
Therefore, chance of bumping into A-high flush = 1-0.9497 = 0.0503 (1 in 20)
To summarize: (3/4/5 flush cards on board)
9 opponents: 1 in 20/23/28
7 opponents: 1 in 25/30/35 <-- This is what happened to me!
5 opponents: 1 in 35/41/49
3 opponents: 1 in 59/68/82
1 opponent: 1 in 175/204/245
Case Q-High: Queen-high flush runs into King-high flush or above
- 3 suited cards on board (no Ace or King, if there is any then go back to above example)
You hold 2. There are 7 A-high flush, 6 K-high flush:
1-((1-13/1225)^9 = 0.0916 (1 in 11)
To summarize: (3/4/5 flush cards on board)
9 opponents: 1 in 11/13/16
7 opponents: 1 in 14/16/20
5 opponents: 1 in 19/23/28
3 opponents: 1 in 32/37/46
1 opponent: 1 in 94/111/136
Case J-High: Jack-high flush runs into Queen-high flush or above
- 3 suited cards on board (no Ace, King or Queen. If there is any go back to above example)
You hold 2. There are 7 A-high flush, 6 K-high flush, 5 Q-high flush:
1-((1-18/1225)^9 = 0.124 (1 in 8.0)
To summarize: (3/4/5 flush cards on board)
9 opponents: 1 in 8.0/9.5/12
7 opponents: 1 in 10/12/15
5 opponents: 1 in 14/17/21
3 opponents: 1 in 23/28/34
1 opponent: 1 in 68/82/102
Case T-high: Ten-high flush runs into Jack-high flush or above
Note: Still, if there is one of A,K,Q or J on board, go back to the previous case. If there are two, go back two levels, etc.
To summarize: (assume 3 flush cards on board)
9 opponents: 1 in 6.6
7 opponents: 1 in 8.4
5 opponents: 1 in 12
3 opponents: 1 in 19
1 opponent: 1 in 56
Case 9-high: 9-high flush runs into Ten-high flush or above
To summarize: (assume 3 flush cards on board)
9 opponents: 1 in 5.9
7 opponents: 1 in 7.4
5 opponents: 1 in 10
3 opponents: 1 in 17
1 opponent: 1 in 49
As you can see, your chance of being a flush underdog becomes quite significant when your own flush isn't ery good, while against a large table. If you have an 8-high flush, chances are that about 1 in 8 times you are entitled to lose all your chips.
A few days earlier, in one of our 4-player home games, a guy had 56 flush. There were 2 over-cards on board (so he has an equivalent 8-high flush). His chance of doom was 1-((1-27/1225)^3, about 1 in 15. Indeed, he ran into an K-high flush and lost his third buy-in!
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