who has the advantage on this one?

[bleu329]

I've got KhKd
he has 8c4c
the flop comes 3c8dJc

after him going all in, me calling, and him catching a 4, we got in a futile argument on who had the advantage to win the hand after that flop. I'm not a math whiz, but by my calculations I think I'm at least a 55% to win...

can anyone do the math for me?

by the way this guy finished in the top 30 of the wsop this year..

[Robk]

http://www.twodimes.net/poker/

<font class="small">Code:</font><hr /><pre>
pokenum -h 8c 4c - kd kh -- 3c 8h jc
Holdem Hi: 990 enumerated boards containing Jc 3c 8h
cards win %win lose %lose tie %tie EV
8c 4c 493 49.80 497 50.20 0 0.00 0.498
Kd Kh 497 50.20 493 49.80 0 0.00 0.502 </pre><hr />

edit: first sim was wrong i guess

[Robk]

P(Kings win) =

(8/45 * 0) + (2/45 * 2/44) + (3/45 * 7/44) + (1/45 * 9/44) + (24/45 * 30/44) + (6/45 * 34/44) + (1/45 * 36/44) = (4 + 21 + 9 + 720 + 204 + 36)/(45*44)

= 994/1980 = .502

The long sum is a weighted average of the kings chances of winning, depending on the next card. In each term, in the first fraction, ie x/45, there are x possible turn cards that give the kings a y/44 chance of winning the hand. For example the 8 cards that have the kings drawing dead are the 8 clubs that don't pair the board. The two cards that give the kings two outs are the remaining eights, etc. I may have made a mistake or two, but it seems to match the sim data.