You play a game where you toss two fair coins in the air. You always win $1. However, if you have tossed 2 heads at least once, and 2 tails at least once, you surrender all winnings, and cannot play again. You may stop playing at anytime. What’s your strategy?
My thoughts were that this seems similar to the coupon collector. We have two bad events (2H and 2T). So after the occurence of the first bad event the second one will occur in an expected number of 4 turns. So my strategy is to stop after 3 tosses from the moment the first bad event occured. However, I can't prove it.