When the board shows 4 cards of the same suit

[Stormwolf]

Lets say on the turn he board is KdTd4d2d, I heard when its HU there is ~50% of chance the guy holds one of that suit so I use that as guideline(is that number correct?)But what about when its 3 players?How much does it increases as the number of players increases?

[LetYouDown]

Assuming 4 suited on board...and you don't hold either of the suit, shouldn't it be 1 - C(37,2)/C(46,2) or about 36% that he holds one? With two opponents, I'd say it's 1 - C(37,4)/C(46,4) that of their four cards, at least one is a diamond. Or roughly ~60%.

I could easily be wrong here...but 50% intuitively seems too high for one opponent.

[Siegmund]

36% for a random hand, yes. Do remember that villain's possible holdings on the turn are no longer random - he's chosen an action on 3 rounds of betting, and will tend to stay in with hands with flush draw possibilities and fold the ones that doesn't.

I doubt a more exact answer than "about 50%" can be given unless we dig very deeply into villain's playing strategy. (I would have guessed closer to 60, actually, myself.) If you've found "about 50" to be a useful rule heads up, then try "about 75" for 2 villains and "about 90" for 3 villains. No, they aren't independent; but in each case they will be higher than for 1, 2, and 3 random hands.