I don't have a model which I believe with certainty, and I think it is a mistake to have one, unless you know sufficiently more than modern physics knows.

Note that I said provided MWI is true.

Why do you think that your consciousness always moves to the branch where you live, but not at random?

I think that, given MWI, your consciousness is in any world in which you exist, so that if you kill yourself in the other worlds, you only exist in worlds that you didn't kill yourself. I'm not sure what else could happen; obviously you can't exist in the worlds you're dead in.

The thing I don't like about such way of winning quantum lotteries is that they require non-local physical laws.

I don't see why; MWI doesn't violate locality.

Imagine that a machine shoots you iff some condition is not fulfilled; you say that you will therefore find yourself in the branch where the condition is fulfilled. But the machine won't kill you instantly, so the choice of branch at time t must be done based on what happens at time t + dt.

You have a point; my scenario is different from that, but I guess it isn't obvious. So let me restate my quantum suicide lottery in more detail. The general case I imagine is as follows: I go to sleep at time t. My computer checks some quantum data, and compares it to n. If it doesn't equal n, it kills me. Say I die at time t+dt in that case. If I don't die, it wakes me.

So at time t, the data is already determined from the computer's perspective, but not from mine. At t+dt, the data is determined from my perspective, as I've awoken. In the time between t and t+dt, it's meaningless to ask what "branch" I'm in; there's no test I can do to determine that in theory, as I only awaken if I'm in the data=n branch. It's meaningful to other people, but not to me. I don't see anywhere that requires non-local laws in this scenario.