The probability of the shooter winning in craps is .493, slightly less than even, as we proved in the preceding section. In casinos, a bet that the shooter will win is a bet on what is called the “Pass” line. We could all become rich, it would seem, if only we bet consistently against the shooter, on the “Don’t Pass” line. But of course there is no such line; one cannot simply bet against the shooter, because the house will not take so unprofitable a bet. Yet usually one can place a bet called “Don’t Pass–Bar 3,” which wins if the shooter loses, unless the shooter loses by rolling a 3, in which case this bet loses also. What is the expectation value of a $100 bet on the “Don’t Pass–Bar 3” line?