Due to constant MWI branching, delayed observation produces more exact copies which don’t know yet the result of the coin toss.
Applying Self-Sampling Assumption (SSA) to all exact copies, we get that I am more likely to be in the wining branch.
This isn’t how you should be doing anthropics in MWI though. You need to weigh each copy by the Born probability of its branch, which will make this effect disappear. It all adds up to normality!
I mean, sportsbooks can shut down your account if you’re too consistently successful so that seems like a major downside for “serious gamblers”. This is also a way that they’re pretty blatantly more predatory than PMs.