XKCD solves Ghost

The XKCD guy not long ago wrote about the game Ghost.  You start the two-player game Ghost by saying one letter.  Then, your opponent says another letter.  Concatenate the letters together, they should not form a word.  Continue adding letters to the concatenation of letters one by one until somebody forms a word and thus loses.

The XKCD guy uses the Ubuntu dictionary in /usr/bin/words and creates a short program to calculate the optimal strategy to play the game.  He solves Ghost and publishes the solution.  Since that game no longer yields interesting results, he asks at the end of his post for users to recommend new games that he can play just using voice and memory.  None of the offered games seemed very interesting or innovative, so I will offer my own:

My brother Mark and I have spent many hours in cars together through our lives.  To fight boredom, we have invented some open-ended games.  I will mention only the most unique one: the Doubling Game.  How about the Perla Doubling Game, yes.

Doubling Game Rules

Nobody can be confused by the simplicity of the Perla Doubling Game.  Two players play, although I can easily see any number of people playing.  One begins by saying, “2 + 2 = 4.”  The second player takes the summand and adds it to itself, thus speaking “4 + 4 = 8.”  The first player continues with “8+ 8 = 16,” and so on until a player asserts an incorrect sum and thus loses.

Importantly, the game does not encourage adversarial deceit.  Once the game reaches the hundreds of millions, the digits become more difficult to store in short-term memory. I can ask my brother what he last said as a summand.  We double-check the sums with each other cooperatively.  Minor slip-ups slide, since continuing with ever-larger numbers exercises the brain much more than starting over at “2 + 2.”

We enforce no time penalties.  When the two players match up in skill-level, they both spend all of their energy and about the same amount of time performing all of the sums.  One player sums because it’s her turn, the other sums to check the other’s answer.  And, cooperatively, you remember many digits together.

Variants

Yes, you can begin with other primes, such as “7 + 7″ or “53 + 53″ (exercise for the reader: why start with primes?).  But, once you reach a very high level, the summands become as simple (and as difficult) as the “2 + 2″ path.  Moreover, these numbers tend to repeat the same chunks of numbers no matter where you start.

Fun

The Perla Doubling Game taxes you mentally, passes the time, and inspires both a competitive and cooperative spirit (how high can you go?).  I highly recommend the game to any two smart, bored car passengers.