Quote:
Originally Posted by NewOldGuy
The chance of at least one ace on a five card board is 33%. If some player holds an ace and you don't then it's 28% he gets one on the board.
But if exactly 1 player out of 9 holds an ace it's 37% he hits one on the board.
I actually understated these doing it too hastily. Should be 34%, 29%, and 39%.
Quote:
Originally Posted by NewOldGuy
The calculation of five cards are: 3/48= 6,25%, 3/47=6,4%, 3/46=6,52%, 3/45=6,67%, 3/44=6,81%. Total there is a 32,65% chance that in a HU showdown your opponent or you will hit an ace.
Your method only counted the chance of exactly 1 Ace, which isn't what you need here. For the chance at least one Ace comes on the board HU when one person holds an Ace and the other doesn't, it's:
1 - (31/34 * 30/33 * 29/32 * 28/31 * 27/30) = 34.1%
And if you want the chance an Ace comes on the board HU when neither holds an Ace, it's:
1 - (44/48 * 43/47 * 42/46 * 41/45 * 40/44) = 36.6%
That's how to do it using your method, but it's easier to do using combinations. The first one would be:
1 - C(48,5) / C(52,5)
In both methods, we're showing the chance an Ace does NOT hit, and subtracting that from 1.
Last edited by NewOldGuy; 12-21-2013 at 11:37 AM.