played, won, lost

with changing

Imagine you're a canditate of a gameshow, so now you can test your strategy to maximize profit by drawing tickets for free. If you're in a hurry, let the computer play for you 300 rounds at once with the autoplay option. The computer chooses the tickets accidental and you can decide whether it always will change it's selection after the hint of the show master or not.
In a gameshow the candidate can choose between three doors. Behind one of them the prize is hidden, the others cover goats which are symbols for flops. After the candidate decided, the showmaster says: "I'll show you something" and opens one of the remaining doors from which he knows that it coveres a flop. "If you want, you can change your selection now."
Should the canditate keep his selection or choose the other remaining closed door?
Now think about it, decide on the wrong answer (of a 50%-chance) and be amazed at the solution.

With an average chance of 2/3 the prize will be behind one of the doors which are not chosen. Since the showmaster knows where it is and only opens a flop-door, the chance to win stays 1/3 if the candidate keeps on his first selection and raises to 2/3 if he changes.

On a party lately my uncle fooled me with that riddle and I was completely convinced the chances are always 50%. At home I got the right solution after thinking about it, so now I hope to have compensated my mistake by writing this interactive web page and the reputation of computer scientists is restored.

Philipp von Bassewitz, 8.4.99, -> Homepage