Nachos and Game Theory

nachos photo

Not yo cheese!

Last night during dinner I was reminded of an article about an optimal game theory strategy for playing Memory.1

Game theory is all well and good, but rarely does it intersect with real life situations.  Being a competitive sort, I’ve always enjoyed reading about game theory, but have had little chance to put that kind of knowledge to use – until now.

Memory, or Concentration, as it is sometimes called is a relatively simple game.  Players put a bunch of cards face down and take turns flipping over two cards, one at a time, trying to make a match.  Make a match and you get to flip over two more cards.  At the end of the game the player with the most pairs wins.

Apparently the optimal strategy was determined some time back in 1993.  This article does a really good job of explaining the theory in depth.  The strategy boils down to this – at any given moment during the game the player with more information and the ability to flip over a card has a slight edge.  Accumulate enough of these such edges, while minimizing your opponent’s opportunities, and you’ll be more likely to win.

In a more concrete sense, the strategy dictates that when you flip over a brand new card that you cannot now match to a card previously flipped over, it makes more sense for you to flip over a card everyone has already seen than to flip over a brand new card.  The reason is that you probably have a low probability of picking a match for your new card out of the whole lot – and a corresponding high probability of showing your opponent two cards they’ve never seen (or a card they’ve never seen and a card they can match with something they have seen).  Thus, you let your opponent uncover new cards and you use that information to make more matches, while simultaneously depriving them of additional information they can use to make more matches.2

How does this relate to nachos???

You see, I’m not the only competitive one in my family.  When it comes to the crispy salty greasy delicious fried bits of cheese that cover a tortilla chip, my lovely daughter is every bit as cutthroat as her father.  Last night I picked a veggie laden chip off the top of the nacho pile – to reveal a crispy nacho dripping with cheese underneath.  My hawk-eyed daughter was apparently monitoring the pile as I obliviously ate, spotted it instantly and grabbed it.  Meanwhile I was stuck holding a veggie nacho.  Like a chump.

Now, I’m not the least bit bitter.  I’m glad she spotted an opportunity and exploited it.  And, whether she realized it or not, she was using information and game theory to improve her dinner experience.  She was actively allowing me to take the most available nachos while she took the most satisfying nachos.

Damn it, I couldn’t be more proud.

  1. Photo by @joefoodie []
  2. Both of these articles are really great and do a much better job of explaining this all than I have.  If you’re interested in game theory at all they’re worth a read. []

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