You are offered the following bet. You pay one dollar. Two coins are flipped. If they both come up the same, you win two dollars. If the first coin lands heads and the second tails, you lose one dollar. In the case of first tails and second heads, a third coin is flipped. If the third coin lands heads, you win five dollars; if it lands tails, you lose four dollars.
Should you take this bet? Why or why not?
Submit your answer to Gene Wirchenko <email@example.com>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, January 10, 2018> at noon Pacific Time. I will post the answer shortly after.