Join Date: Nov 2009
Brett plays poker with a large group of friends. With so many friends playing at the same time, Brett needs more than the 52 cards in a standard deck. This got Brett and his friends wondering about a deck with more than four suits.
Suppose you have a deck with more than four suits, but still 13 cards per suit. And further suppose that you’re playing a game of five-card stud.
As the number of suits increases, the probability of each hand changes. With four suits, a straight is more likely than a full house. How many suits would the deck need so that a straight (not including a straight flush) is less likely than a full house?
Extra credit: Instead of five-card stud, suppose you’re playing seven-card stud. How many suits would the deck need so that a straight (not including a straight flush) is less likely than a full house?
I stole this from FiveThirtyEight.
I know we (and by "we" I mean someone other than me) could just brute-force it and count up the combos or run a simulation, but are there better ways to do this?