I have had to analyze some multi-deck poker games recently. Suppose I am dealt 7 cards from an 8-deck “shoe”, and I have to make the best 5-card hand out of 7.
What is the probability my best hand is a flush (meaning no 5 of a kind, 4 of a kind, full house, straight flush, or royal flush are also obtainable)?
What is the probability my best hand is a straight (meaning no flush is attainable either)?
I solved this in a spreadsheet, but it was at the borderline, if it had been any more complicated I would have written a program.