Re: Short handsed (3 Player ) odds...
A) If you insist that Player 1 gets AA, Player 2 gets QQ and Player 3 gets JJ: (4*3 * 4*3 * 4*3)/(52*52 * 50*49 * 48*47) = 1:8,482,716
B) If you don't care which player gets the aces, queens or jacks: (12*3 * 8*3 * 4*3)/(52*52 * 50*49 * 48*47) = 1:1,413,786
C) If you'd be happy with any three pocket pairs, tens or better: (20*3 * 16*3 * 12*3)/(52*52 * 50*49 * 48*47) = 1: 141,378
In other words, if we assume that Party's million dollars in rake per day translates to something like four million Real Money hands a day (more hands are played at low stakes with small or infrequent rakes; tournaments can generate mere pennies per hand) then Case A should happen [roughly] every other day on average. Case B should happen several times a day, and Case C should happen hourly.
A lot of seemingly "impossible" hands seem less outlandish when phrased in terms of "average occurence per day on the Party Network"
[Edited to add: the above numbers apply equally well to the first three players at any table, regardless of how many other players are at the table -- or, for that matter, to any three players, selected before the deal.]
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