I just noticed this thread continued, but I'm not sure what you're worried about. The two things you said: * the final count will be about 50/50 * the remaini

I just noticed this thread continued, but I'm not sure what you're worried about. The two things you said: * the final count will be about 50/50 * the remaining part will be about 50/50 are actually the same thing (since we're talking about a limit). That is, we could flip a fair coin a billion times, get all heads, and still, in the long run, expect the total ratio to converge to 1/2 (imagine flipping the coin forever - that initial billion flips won't even be a blip on the graph).