The Game Show Problem

The Game Show problem is when you are faced with 3 choices, one of which makes you a winner and 2 of which make you a loser. You make a choice and then one of the other 2 choices are revealed to you, a losing choice. You are now given the choice to stay with you original decision or swap for the as yet unrevealed prize. You would think your chance that you picked a winner to begin with was now 50/50 but you would be mistaken. If you swap, your chance of winning is 66% and 33% to lose if you stay with your original choice. Statistics are amazing! Its fun to play this and see it working or there is an AI that will play up to 100 games at a time so you can see this statistical quirk in action. Enjoy!