Coin Flipping Game

Alice and Bob are playing a coin flipping game. Each of them will flip their own quarter 100 times and note the outcome of each flip on a line, in their own scoresheet: \(H\) for heads and \(T\) for tails.

If on any line Alice marks \(HH\), she will give herself 1 point, begin a new line, and continue flipping.

If on any line Bob marks \(HT\), he will give himself 1 point, begin a new line, and continue flipping.

After 100 flips each, who is more likely to have more points?

Clarification: Here is an example of a possible scoresheet for Alice after 25 flips, where she scores 3 points.

  • \(HTT \boxed{HH}\)
  • \(HTTTTHTHTHTT \boxed{HH}\)
  • \(TTT\boxed{HH}\)
  • \(T\)

Taken from a numberphile video

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