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Puzzled: Coin Flipping
Credit: Jacob Hamblin, Alex Kalmbach
- You have just joined the Coin Flippers of America, and, naturally, the amount of your annual dues will be determined by chance. First you must select a head-tail sequence of length five. A coin is then flipped (by a certified CFA official) until that sequence is achieved with five consecutive flips. Your dues is the total number of flips, in U.S. dollars; for example, if you choose HHHHH as your sequence, and it happens to take 36 flips before you get a run of five heads, your annual CFA dues will be $36. What sequence should you pick? HHHHH? HTHTH? HHHTT? Does it even matter?
- Now you have entered your first CFA tournament, facing your first opponent. Each of you will pick a different head-tail sequence of length five, and a coin will be flipped repeatedly. Whoever's sequence arises first is the winner. You have the option of choosing first. What sequence should you pick?
- Following the tournament (which you win), you are offered a side bet. You pay $1 and flip a coin 100 times; if you get exactly 50 heads, you win $20 (minus your dollar). If you lose, you are out only the $1. Even so, should you take the bet?
Footnotes
Readers are encouraged to submit prospective puzzles for future columns to [email protected].
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