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?

  • $\begingroup$ Is the game played in distinct "games" of two rolls, or is the "win" condition just detected whenever it occurs in a unstructured sequence of rolls? If the latter, would the second player win twice if they rolled 6,6,6 in three rolls? $\endgroup$
    – Blckknght
    Jan 18, 2014 at 23:04
  • $\begingroup$ I believe its the first. If the second case is true, then my EV for the game is negative since it always takes at least 4 rolls for me to win twice and for the "6-6" sequence, it takes only 3 rolls to win twice. $\endgroup$
    – adfasdf
    Jan 18, 2014 at 23:23
  • $\begingroup$ what is your definition of fairness here? What are your assumptions on the risk aversion of the agents, or more generally the form of their utility function? $\endgroup$ Jan 19, 2014 at 22:47

1 Answer 1


$6-5$ is more likely to win. The expected occurrence of the first $6$ is equal for both sides, but then if you miss your second $6$, that throw was definitely wasted; whereas if I miss my $5$, I might have rolled a $6$ instead, in which case I stand better.


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