The latest version of Deck-u-lator shows new math formulas for advanced calculations with two or three hands. Previously multi-hand calculations simply confirmed how many alternate hand combinations you were calculating. This is still the case for combinations with four or more hands.
To calculate your chances to draw alternate hands, Deck-u-lator performs the multivariate hypergeometric calculation for each hand and adds those probabilities together. What about draws that contain all the cards needed for two different hands? These get double counted by just summing probabilities for both hands. So we calculate the probabilities for all combinations of two hands and subtract those. This process continues, alternately adding probabilities for combinations of three hands, subtracting probabilities for combinations of four hands and so on.
The new formula gives a glimpse into this process. Enjoy!
$$ \frac{ H_{0} + H_{1} - H_{0} \cap H_{1} }{ \binom{ 52 }{ 2 } } = 95.0\% $$
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