# Coin Flipping Game

Probability Level 2

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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