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        riddles >> medium >> What's Your Cut
        
(Message started by: fieldazed on Apr 17^th, 2012, 9:31am)

Title: What's Your Cut
Post by fieldazed on Apr 17^th, 2012, 9:31am

Coop is our weekly friendly poker games resident card counter and odds calculator. Fortunately, his poker face reads like a book and he can't keep an ash on his stogie when bluffing. As of late prop bets have been in favor at our game and last week Coop offered this one: "For five bucks I'll cut the deck, if it's a club I win, if not it's your turn and if you cut a Jack, Queen, King, or Ace the fiver's yours. We'll continue mano a mano until there's a winner shuffling after each cut if you want. I'll even agree to go around the table five times, twenty games in all. Everyone in?" Coop then pulled a c-note from his wallet and slapped it on the table. Huck, after a long pull on his bourbon and oblivious to the workout the ashtray was now getting, piped up first. "So thirteen clubs vs sixteen honors, I'm in." Rob, Vern and I reluctantly agreed even though we suspected Coop had an edge. Where we right?

Title: Re: What's Your Cut
Post by SMQ on Apr 17^th, 2012, 10:13am

Yes, you were right: [hide]going first[/hide] is enough to give him an advantage. If your friendly games don't use the jokers, he has a [hide]thirteen to twelve[/hide] advantage; if you do use the jokers, it's slightly less: [hide]351 to 328 or about 12.8 to twelve[/hide].

Edit to add: and even that relatively small margin is enough to give him almost a [hide]two-thirds[/hide] chance of ending up even or ahead after 20 games.

--SMQ

Title: Re: What's Your Cut
Post by fieldazed on Apr 18^th, 2012, 3:38pm

you are, of course, correct SMQ. perhaps this one belonged in a different forum. still feeling my way around here. also wanted to introduce the cast of characters for some hopefully more challenging future puzzles. thought the (mild) interest here was the more simple/insightful way of looking at the problem as a single repeated game which appears to be your approach vs solving an infinite series. will be back...