Selecting a valid hand configuration for Monte-Carlo simulation

[jukofyork]

Q) Given a distribution of hands for each player (stored as 52x52 triangular matrix where the weights sum to unity), what is the best way to assign each player a hand that fits the distributions without introducing bias?

(1) Surely there must be a better way to do this than simply assign each player a hand independently from their distribution, then check if any of them have been assigned the same cards and keep restarting until a valid configuration is reached?

(2) How much bias am I likely to introduce if I select the first player's hand from their distribution, then re-weight the 2nd player's distribution and select his hand, and so on?

(3) Also, how much bias will occur if I assign each player a hand using method (1) and then if two players have the same cards in their hand, ONLY reassign those two players a new hand and keep doing that until I get a valid configuration?

I'll take a method which introduces a small amount of bias over a mega-slow method like (1) any-day, but I assume others must have come across this before and found some way round the slowness - any ideas?

Juk [img]/images/graemlins/smile.gif[/img]