Selecting a valid hand configuration for Monte-Carlo simulation

[SixthSense]

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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?

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Juk,

I'm not sure if this would introduce bias, but why not just assign player #1's hand from the distribution, then assign player #2 and if there is a collision with player #1 then just reselect for #2, and repeat? E.g. for player #3 you'd have to check for a collision with player #1 and #2.

-Ben