Puzzle Nekst 4

Now that the summer has come, Nekst provides you with a game and accompanying puzzle to amuse you when it is hot outside. All you need is a regular coin and someone to play with!

The game this puzzle is about is a variation of simply choosing heads or tails. Instead, each player will publicly announce a sequence of three outcomes, for example ‘heads, tails, heads’. Player 1 will first announce his choice, after which player 2 will announce his sequence.

The players will then start tossing a coin until one of their sequences has appeared. The player whose sequence appears first, wins the game. What is the probability player 1 will win this game when both players play optimally? And more importantly, what are the optimal strategies for both players?

Please send your solution to Nekst@Asset-Econometrics.nl before October 1. A crate of beer or a delicious pie, whichever the winner prefers, will be waiting for whoever has the best (partial) solution. Please note that as before, every recipient of this magazine is eligible to send in their solution, so members of the department are invited to participate as well. Good luck!

Robin Caljouw is the winner of the previous puzzle. As a reward, he can come and pick up a crate of beer or a pie at room E1.10. The answer of the previous puzzle was 15621.