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The experiment, as defined, only leads to your survival by random chance. The experiment does not create any outcome except by random chance so it cannot be used to prove anything.
Every half life you survive is an experiment.
The chance you'll survive a half life is exactly the same whether MWI is real or not. It doesn't give you any useful information. You have no way of distinguishing between being just that lucky or MWI being true.
That's not the case with other experiments. If you assume your hypothesis is correct, the chance of the experiment being successful is higher than the chance of it happening by random chance if your hypothesis is not. That's a key difference.
You're right, of course. But it feels like science.