So what's the magic number of entries if $50 buys you 0.5% chance of winning $4500?

No, because then you're paying double for a pro. Maybe 75, or so. I'm not sure how to calculate it.

When I said magic number, I meant for one person to have the greatest chance of winning using as few entries as possible

One person - multiple entries.

At what point is the decrease in risk negated by the decrease in reward? This is all hypothetical, of course, because it's likely multiple entries would span two drawings

I'd be curious to even know the equation.

It appears to be a long summation of what you win vs what you lose

It does. So I guess the true magic number is 0. You don't win, you don't lose.

But with every entry, the government loses $50 and the charity gains $50... so maybe 200 is the magic number

I chose walking dead. I've heard nothing but great things!