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: