I have a question, though, about Hawking Radiation. Given that the pairs pop up randomly at the event horizon, is the decay essentially a result of the gambler's dilemma-i.e. given infinite time, the gambler always loses because he can't bet when his funds drop below zero?

Correct me if I have this wrong, but from what I gather it would go like this.

Particle pair pops up at event horizon. Negative falls in, positive goes away. Black hole loses mass.

Particle pair pops up at event horizon. Positive falls in, negative goes away. Black hole gains mass.

Particle pair pops up at event horizon. Positive falls in, negative goes away. Black hole gains mass.

Particle pair pops up at event horizon. Positive falls in, negative goes away. Black hole gains mass.

Particle pair pops up at event horizon. Negative falls in, positive goes away. Black hole loses mass.

And so forth. The idea being that it's random, but eventually the black hole has its mass reduced to zero. Is this right, or is it the case that only the negative particles enter the singularity? And if so, can you explain why to me without having to resort to math that will go way over my head?

Thanks!