Your initial pick has a 1/100 chance of being right. If you switch, and you were right, you lose. On the other hand, your initial pick has a 99/100 chance of

Your initial pick has a 1/100 chance of being right. If you switch, and you were right, you lose. On the other hand, your initial pick has a 99/100 chance of being wrong, and if you were wrong, and you switch, you win. So switch.