In this construction every configuration of ones and zeros have equal amplitude, yes. However, most of them are nonsensical; the sum of the measures of meaningful worlds are very very close to zero.
Meanwhile, the sum of measures in this scenario where you exist is, well, 1.
That you see each of the nonsensical numbers with equally low probability doesn't matter. If you roll a d1000 and get 687, the chance of that was the same as 1; you still wouldn't expect to get 1. In the same way, you wouldn't expect to get any particular configuration, but you're effectively summing over all the nonsensical ones, and that sum is pretty close to 1.
The part I don't get is why we should care if we observe the person suffering or not.
This conversation is confusing me; possibly this comment will help us understand each other.
From David Deutsch's The Beginning of Infinity:
I'm not so sure we have the computing power to "simulate a person," but suppose we did. (Perhaps we will soon.) How would you respond to this worry?