07 Mar '11 19:17

So we are in Tibet at the Holy Temple of Gangwolf and two novices are eagerly awaiting their final test before entering the order. Unfortunately the monastery is almost fully booked; there being only one vacancy.

In time honoured tradition they are given a challenge. Who can get highest up the temple stairway without stumbling?

The novices can stop at any stage. The one who has taken the most steps without stumbling is the winner. If it is known that there is a 10% chance of any step crumbling what is the best strategy? To attempt 10 steps and stop? Less? More?

(Yes this is a more complicated version of "Heads you win" problem)

A draw is NOT a win and they cannot see how their opponent has done.

Can you formulate a solution for P% chance of steps crumbling?

In time honoured tradition they are given a challenge. Who can get highest up the temple stairway without stumbling?

The novices can stop at any stage. The one who has taken the most steps without stumbling is the winner. If it is known that there is a 10% chance of any step crumbling what is the best strategy? To attempt 10 steps and stop? Less? More?

(Yes this is a more complicated version of "Heads you win" problem)

A draw is NOT a win and they cannot see how their opponent has done.

Can you formulate a solution for P% chance of steps crumbling?