Odds of a flush holder

[pwills]

If you're at a full table...you and 9 others..and the flop comes say. with two spades. What are the odds that someone else has a pair of spades also?

Pete...thanks

[Bugsbunny]

Assuming that everyone at the table will play any 2 suited then the chances that at least 1 person has 2 of the suit in hand:

1) If you have no spades in your hand it's just about 39.5%
2) if you have 1 spade in hand it's about 33.4%
3) If you have 2 spades in hand it's just about 27.5%


If one other spade falls by the river (making 3 spades on board + 2 non-spades) then the chances that at least 1 person has a flush are:

1) If you have no spades in your hand it's just about 36%
2) if you have 1 spade in hand it's about 29.8%
3) If you have 2 spades in hand it's just about 24.2%

Note that the 1st set is going to be more accurate (those are exact to the nearest .1%) then the 2nd set. The 2nd set assumes that all players stay until the river, and this obviously won't be the case. For example let's say that 2 people fold on the flop and we know that they would have stayed with any spades in hand. That means that they folded 4 non-spades between them. That changes things as follows:

1) No spades in hand: 42.3%
2) 1 spade in hand: 35.2%
3) 2 spades in hand: 28.8%

So as more people fold it becomes more likely that the remaining people have spades in hand. Now some of the people folding can have 1 spade in hand rather than 2 (especially if it's a low spade) etc so you can't just assume that everyone folding has no spades, but it does effect the bottom line. Just as not everyone will play any 2 suited.

The above actually shows the dangers of playing any 2 suited - especially for multiple bets preflop. If you do get a baby flush with the powerhouse of 32s (for example) you're still going to lose a fairly decent amount of the time - and we haven't even looked at redraws with 4 of the suit hitting the board.


Just one more comparison here. Let's look at how the number of players preflop changes things. We'll just look at the first set (on the flop with 2 spades on board)

No spades in hand:

8 opponents: 35.8%
7 opponents: 31.9%
6 opponents: 27.8%
5 opponents: 23.6%
4 opponents: 19.3%
3 opponents: 14.7%
2 opponents: 10.0%
1 opponents: 5.1%

Two spades in hand:

8 opponents: 24.7%
7 opponents: 21.9%
6 opponents: 18.9%
5 opponents: 16.0%
4 opponents: 12.9%
3 opponents: 9.8%
2 opponents: 6.6%
1 opponents: 3.3%

So both the number of opponents as well as the spades in hand can make a large difference.

[calgaryfan]

[pwills]

Thanks Bugs....appreciate all the work you put into this answer.

thanks again,

Pete