Razz - Working out the percentages - seventh street

[Mathew82]

Instead of using a simulator, I thought I would learn how to do this manually.

Unfortunately I do not come up with the exact same answer as the simulator.

I created this hand

Player 1 - KT9832
Player 2 - QJ872A

So right now player 1 has the best hand...

If player 2 makes an 8 then player 1 can't win and since there are 4 sixes, 4 fives, 4 fours and 3 threes left in the deck totaling 15 of the forty remaining cards. Therefore 15/40 x 100 = 37.5% of the time player 2 wins.

I then took the chance of hitting a nine or a ten with the remaining three tens and three nines making 6 outs in the 40 remaining cards. Now I had to work out what the chance player 1 would have of missing making his 9 to win. To hit his nine, he would have to hit one of the 3 sevens, 4 sixes, 4 fives, 4 fours, or 3 Aces equaling 18 out of the 39 remaining cards therefore the chances of him missing is 18-38= 21/39

So therefore 6/40 x 21/39 x 100 = 8.077%

So adding these percentages together, 37.5 + 8.077 = 45.577%

So the chances of player 2 winning is 45.577%

Except when I run a simulation I get 46.15%


Edited title to reflect that we're talking about razz.