figuring odds when both parties can improve

[timex]

So there are 45 cards left in the deck, you will not hit a diamond (36/45) * ( 35/44) times =0.636, so he will win 36.4% of the time with the flush. Of the remaining times, he will hit a jack 1- (42/45) * (41/44) = 13.0%, of the times he hits a jack, you will hit a king (3/44) times, so he wins 13.0% * 41/44 + 36.4% = 48.5%, less the times when you hit the full house should make it about 47%

[mw999]

What about the two good kings? re:8% for me? isn't that deducted from his 13% chance to hit a jack? giving him about 36% plus 5% or 41% chance.

[mw999]

oops, meant to write that I have 2/44 for the two good kings, or about 4.5%, to be deducted from his 13%,