You and I each roll 1 die each at the same time. I win if I roll a six on one roll, and then a five on the next. You win if you roll two sixes in a row. Who would you bet your money on? Note that You: 1, 1, 5 and I: 1, 6, 5 is a winning sequence for me, i.e. the six and the five (or two sixes) can appear as a subsequence in any position.
Isnt the fair price zero if payoffs are 1-1? Theres equal probability in getting "6-5" sequence and "6-6" sequence?