A practical lower bound on the time required to finish one game of Set: How fast would Rain Man be?
As many of you know, I’m kind of into the card game Set. If you’re unfamililar with the game, it works like this: you start with a deck of Set cards, each card uniquely patterned (see photo for examples), and you lay twelve cards face up on the table and look for “sets”. A set is defined as three cards that share certain characteristics; three cards that have one, two, and three solid red diamonds, for example, would constitute a valid set. When you find a set, you remove those three cards from the table and replace them with three new cards, and repeat the process until you reach the end of the 81 cards in the deck. When played in groups, the winner is the player with the most sets at the end of the game, but Set can also be played alone, and indeed this is how I like to spend my mornings at the breakfast table. It’s pretty addictive.
It takes me a while to finish a game of Set on my own, probably 8-10 minutes on average. Part of the time required to finish a game comes from the physical process of scooping up sets and dealing new cards, but mostly I’m limited by my ability to find sets: I’m brain-limited, not hand-limited. My question is this: given the constraints of the game as I play it — i.e., with physical cards that need to be dealt by hand, not with a computer that can deal virtual cards in a negligible amount of time — how fast can a game of Set be played? If I trained my brain really hard and turned into a Set savant, what’s the shortest time I could deal out and scoop up all the cards necessary to finish a game? How fast could Rain Man play Set?
To answer this question I timed myself on some test games this morning. In each game I started the stopwatch when I dealt the first card and stopped it after scooping up the 25th set, thereby leaving six cards on the table, which is the most common ending to the game (the Doc, personal communication). The crucial difference in these tests is that I did not seek true sets; each “set” I scooped up consisted merely of the three most easily accessible cards, in order to simulate instantaneous recognition of sets.
I played four of these test games, and finished with times of 85, 93, 85, and 85 seconds, for an average of 87 +/- 2 seconds (mean +/- s.e.). Although I could probably push these times down a little with more efficient dealing, I don’t think this lower bound would drop all that much; finishing a game in under a minute, for example, is highly improbable, but a minute and a half seems like a reasonable goal. All I need to do now is cultivate my inner Raymond Babbitt. I’ll start by writing my name on my boxers and using youtube to catch up on Wapner. In other words: Ton, you’re going down.