Life In 19x19

Redundant wrote:For a derivation of the probability in the prisoner puzzle see wikipedia.

better lay-out indeed. thx

entropi wrote:2- Is there a proof that this strategy gives the highest survival probability?
While understanding the strategy and how it works, I must admit that I don't get the feeling of it. Why would creating such a "linked list" maximise the survival probability?
Which information do you exploit for increasing the probability?

a. Eugene Curtain and Max Washauer have recently proved that this solution cannot be improved
upon. ( from link.pdf )
b. Why it works. Assume two prisoners. If they choose random their chance is 25 %. If they agree upon mr one choosing the first box and mr two the second box. Now their chance is 50%. They made sure they succeed or fail together.
If you next try 4 prisoners by hand you see why it works. If they fail as team at least 3 of them has failed personally.

cyclops wrote:1/51 + 1/52 + 1/53 + .. .. + 1/100 as the probability for failure.
Somehow this sum equals 1 - 1/2 + 1/3 - 1/4 .. + 1/100.

This can be proven quite easily by induction.