if you have 4,5 in your hand and the board is 6,7,A, what is the chance of hitting your run? i thought with 8 cards to hit and 2 chances to hit them that would mean 47/16 but im told this is wrong...
I guess I was confused (thinking Omaha )Originally Posted by mrconfused
You'll end up with a straight if one of the following two possibilities occur:
1. The turn card or the river card is a 8. This results in 4 5 6 7 8.
2. The turn card or the river card is a 3. This results in 3 4 5 6 7.
You could also see a 2 and a 3, allowing the straight A 2 3 4 5, but you wouldn't do this, since the 3 4 5 6 7 straight is higher in this case.
Altogether, there are 47 possibilities for the turn card and 46 for the river card, since you have already seen five cards. This gives 47*46 ways in which these two cards can be dealt. Since the order in which they are dealt doesn't matter for the end result, there are 47*46/2 = 1081 possibilities.
So now let's find the number of ways in which you might lose, i.e. no 3 and no 8 among turn or river card. There are 39 cards you don't want to see, and 39*38/2 = 741 ways to deal only these. All 340 other cases include at least one 8 or one 3. Therefore the probability is 340/1081, about 31.5%.