by choosing to roll, say, 3d8 instead of 3d6, it's possible to manipulate the shape of that bell curve
It's turtles all the way down.
This-you chose to roll 3d8 and other-you chose to roll 3d6 and yet more of other-yous chose to roll 1d10, 7d36, etc. etc. Yes, you manipulated the bell curve but in other timelines it also got manipulated, albeit in a different way. When you step in one direction, yes, the timelines spreading out from that step are biased in that direction. But the step itself, when you made it another-you also made a step, in a different direction, and biased another bunch of timelines in that different direction.
The set of all possible futures is the set of all possible futures -- you cannot change it.
I think I've run out of different ways to try to explain what I'm trying to get across; so we seem to have hit the door-wall debate limit. ("This is a door." "Yes, but /this/ is a wall." "Yes, but /this/...")
If I were to try to explain our difference to an outsider, I might describe your position as being that as there are an infinite number of timelines, any sub-portion of them also contains an infinite number of timelines, and thus any given infinity is equally as important as any other, so there's no reason to prefer any on...
I haven't been able to find the source of the idea, but I've recently been reminded of:
This is, of course, based on the Multiple Worlds Interpretation: if the lottery has one-in-a-million odds, then for every million timelines in which you buy a lottery ticket, in one timeline you'll win it. There's a certain amount of friction - it's not a perfect wealth transfer - based on the lottery's odds. But, looked at from this perspective, the question of "should I buy a lottery ticket?" seems like it might be slightly more complicated than "it's a tax on idiots".
But I'm reminded of my current .sig: "Then again, I could be wrong." And even if this is, in fact, a valid viewpoint, it brings up further questions, such as: how can the friction be minimized, and the efficiency of the transfer be maximized? Does deliberately introducing randomness at any point in the process ensure that at least some of your MWI-selves gain a benefit, as opposed to buying a ticket after the numbers have been chosen but before they've been revealed?
How interesting can this idea be made to be?