rreid you are absolutely right. The probability of a redraw royal = the probability of being dealt a hand that requires a 5 card draw • the probability of drawing a royal given the undealt 47 card subset. A very complicated problem. You have one idea wrong however. Given you're drawing 5 cards (jacks or better) the 47 card subset contains all the jacks, queens, kings and aces (might be missing exactly one 10). If you don't throw away a ten the probability of drawing a royal = 4/1533939=1/383484.75. If one 10 is thrown away the probability of drawing a royal= 3/1533939=1/511313. In both cases the probability of the redraw royal is quite a bit more than the probability of being dealt a royal (from a 52 card deck). I hope this helps everyone in this group.
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