Two players are playing the following game:
- Player A picks a sequence of three consecutive coin toss results, e.g., Tails-Heads-Heads, and tells it to player B
- Player B picks another sequence of three consecutive coin toss results, e.g., Heads-Tails-Heads, and tells it to player A
- A coin is flipped repeatedly and results are written down until one of the sequences is observed
- The player who’s sequence is observed first wins
Is the game fair?
This is Penney’s game, in which player B has an advantage.
Monte-Carlo simulation using this program gives the following odds of winning: