I wrote a poker simulator for seven card texas hold 'em, and I found a counter-intuitive result:
If player A starts with a pair of aces against player B who has a random hand, I get a different %win if they share five cards on the board (as it works in Texas hold'em) than if they each have separately drawn hands of seven cards. In the standard Texas Hold'em procedure player A has an 85% chance of winning, but if I draw two seven card hands separately (instead of sharing five cards) then player A has a 77% chance of winning.
In both scenarios the cards are drawn from a deck of 50 cards (ie a normal deck excluding the two Ace's I've given player A at the beginning).
Between the two scenarios the probabilities I measure of player A and player B having a high card, a pair, two pairs etc are unchanged .. but somehow player A wins more often in one scenario than the other.
I've tested lots of times in different ways, and I'm convinced it's not due to a bug in my program. Can someone help me with an intuitive picture of what is going on?