This is a repost from my post at Math Stack Exchange
2 criminals A and B, were recently captured and brought to prison. They were then locked in two separate rooms.
Known for being exceedingly smart, the prison warden set a test for them. The Warden flips a fair coin an infinite number of times and tells the outcomes of odd numbered trials to A and even numbered trials to B.
Now A and B are separately told to pick a trial whose outcome they don't know, i.e., A is supposed to pick an even trial number, and B is supposed to pick an odd trial number. If the outcomes of the trials picked are the same, the prison warden will release them. If they are different, they will spend their life in jail.
Note: A and B don't know of each other's guesses.
The Warden told them what they were going to do and let them agree upon a common strategy in advance, but after that they can't communicate.
Find a strategy such that the chance of winning is higher than 0.5.
Strategies so Far
- 70% chance of winning by @Jaap Scherphuis
- 2/3 probability of winning by @Mike Earnest
- 62.5% chance of winning by @Teo Miklethun
I was told there was a greater chance to find an optimal solution on this platform. This problem was extremely intriguing to me! For reference, I'm a maths student and this was a problem in an extra class I take.
Edit: I realize that an optimal solution may be impossible at the moment, but any strategy that can beat 2/3 probability of winning would be interesting!