Framing and Intentionality
If Brown hopes to throw a six in a game of dice and succeeds, we wouldn't say he threw the six intentionally. If Brown puts his last cartridge into a six-chambered revolver, spins the chamber as he aims it at Smith, his archenemy, pulls the trigger, and kills Smith, we'd say he killed him intentionally. Does that make sense? In both cases Brown hoped for a certain result, in both cases the probability of that result was the same. If Brown didn't intentionally throw a six, why did he intentionally shoot Smith?
By email, Neil Sinhababu suggests that this might be an example of the Knobe Effect. The Knobe Effect says that our moral evaluations of actions can influence our ideas about whether those actions are intentional. Specifically, Joshua Knobe found that people are much more likely to say that known-but-not-sought-out side effects are intentional if they were bad than if they were good. Here, we're calling the killing intentional because it was a bad thing (whereas rolling a 6 is not so bad). There's some plausibility to this hypothesis, but I don't think it really gets at what's going on. Imagine that Brown put $1000 in one of six plastic Easter eggs, mixed them up in his hat, and then handed one to a homeless man, and it turned out that egg had the money. My intuition is that in this good outcome version of the revolver case, my desire to say Brown gave out the money intentionally is perhaps not quite as strong as in the original revolver case, but certainly not as weak as in the dice case.
I think the difference in attributions of intentionality in the dice versus gun example could be explained as a framing effect. The difference is made by what we imagine the alternative scenario to be. In the dice-throwing case, we take the throwing of the dice for granted, and the question is whether the person got a 6 or some other number. So of course it seems like they didn't intentionally get a 6. But in the gun case, we're implicitly thinking of the alternative as one where Brown didn't pick up the gun at all. If we rephrase to say "did Brown intentionally shoot him with the chamber that had the bullet rather than an empty one?" our inclination to call it intentional goes away. And if the dice roll was, say, to determine whether an attack in a role-playing game was successful, then we highlight "don't attack at all" as the alternative scenario and thus the rolling of a 6 takes on an air of intentionality as part of the larger action -- you intentionally killed the monster that you were rolling to attack.