Wrote a program to rate 2 hole cards (your hand) against a single random hand.

Your two hole card are combined with a common 5 card board to create the best 5 card hand. You can play the board. Each opponent does the same.

I remove the two cards from the 52 card deck. Run all the 5 card boards. And for each board run all the remaining 2 card hands = $\binom{45}{2} = 990$. And just sum the wins and losses.

Now my question is what about versus 2 random hands. Would I need to run $\binom{990}{2} = 489555$

It seems like there has to be a trick to get versus multiple random hands knowing the value for one random hand. I see poker calculators that do this very fast.

Versus one random hand at 50% then two random hands is 34% and three random hands 21% with the calculators.



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