Odds question

[ngericl]

What're the odds of you and another player holding cards both of the same suit, given a full table. In other words, I'm holding 2 spades and another is also holding a couple spades.

[Greedo017]

depends, if i have two of a suit with a king high, the odds of someone else holding two of my suit are way way too high. if i have two of a suit with an ace high, the odds of someone else holding two of my suit are way way too low.

[sinky]

I'll take a stab at it.

You have 2 spades, so there are 11 left out of 50 cards. Chance of any given player having 2 spades is 11/50 * 10/49 = 0.045

Now to work out if anyone at the table has 2 spades you have to calculate 1 - the odds of all of them missing. Odds of each player missing is 0.955 so we get ...

1 - (0.955*0.955*0.955*0.955*0.955*0.955*0.955*0.955*0 .955) = 0.34 -> 34%

More importantly if there are 2 spades on the flop then the odds change. Each player has 9/47*8/46 = 0.033 chance of hitting 2 spades. This gives us 1 - (0.966*0.966*0.966*0.966*0.966*0.966*0.966*0.966*0 .966) = 0.26 -> 26%

Similarly if you flop a flush there is a 21% chance that someone else has done the same. Obviously you have to consider that weak suited cards may have been folded preflrop.