One for the Math Geeks (alternative version)

Simon: Seven of Clubs

Julie: Four of Diamonds

Simon: Eight of Spades

Julie: Jack of Clubs

Simon: Three of Diamonds

Webb: That’s Spiderwang!

Audience: (canned laughter)

Julie sighed audibly. This was the 100th game she had lost in a row. On 57 occasions Simon called a card and it was Spiderwang. On the other 43 occasions, Julie called a losing card and the host declared it was Not Spiderwang. Yes, Julie could rot13(xvpx Fvzba’f nefr) at regular Spider Solitaire and a game with more dependency on luck was required to prevent things becoming boring. But a game show with unexplained rules was taking things too far. Julie had to reluctantly consider the possibility that Simon might be (gasp!) cheating with the cooperation of the host.

Julie discussed her predicament with her trusted group of Very Smart Friends. They eventually agreed on a plan. On the next few episodes her VSF would record the footage, take meticulous notes and work out the pattern. Once the pattern was figured out Julie could at least hope to fight on equal terms.

After burning much midnight oil, a pattern was found. Webb would declare Spiderwang whenever every card of a single suit was named at least once. Webb would declare Not Spiderwang if any single card was named for the third time.

Eventually some Math Ph. D.’s decided to join in the fun. They worked out that if nobody named the same card thrice and the probability of a new card being named was double the probability of a card already named once then Spiderwang should occur after 66.5 cards on average. The median was 67.0. The theoretical minimum was obviously 13 cards, and if e.g. no Kings were named within the first 96 cards we would achieve the maximum of 97 cards. On the last hand, Simon achieved Spiderwang after 60 cards, which corresponded to the 23rd percentile.

On the next day Julie is pleased when the host announces that Simon is going first. Her group of Very Smart Friends have done the math and with best play she would win her first game after 90 cards.

Julie takes out some pen and paper for round 1. Curiously neither Simon or Webb object to her taking copious notes during the game. Then again, nothing on this game show made much sense to her anyway.

Simon: Jack of Spades

Julie: Four of Diamonds

Simon: Queen of Clubs

Julie: Jack of Spades

Simon: Jack of Spades

Rot13(jung gur shpx) – why would Simon throw away round 1 just like that? Of course, it takes less than three nano-seconds for the host to confirm her worst fears.

Webb: That’s Wangerspy!

Audience: (canned laughter)

THE END