For game 2, flip a coin and guess what is shows. If the original coin was heads, your chance to win is still 50%. But if the original was tails, and you only

For game 2, flip a coin and guess what is shows. If the original coin was heads, your chance to win is still 50%. But if the original was tails, and you only have to guess once correct, your chance to guess wrong twice is only 25%. So a 50% chance of winning half the time and a 75% chance half the time gives you an overall better chance that the 50% of sticking to one answer because it doesn't matter. It seems a random guess is the best solution for game 2.