I think my math works out.

It does, noone is arguing that, I believe. It's your assumptions that are slightly off

There was this statistics professor that started the first year class with the following pearl about averages (loosely translated):

"Statistics are like a bikini, showing almost everything but hiding the most important... If you and me both go and eat together, I eat two chiken and you eat none, on average we each had one, but I'll be stuffed and you'll be hungry."

The error, in my non educated opinion, is one of historical averages. Take the coin toss example:

you throw a coin 10 times, 8 of them it falls on tails. What would you say your chances are of hitting tails the 11th throw?

Amazingly, they are 50%. Every time 50%. Regardless of how many times you throw them. This is not true for a physical coin, as it may have unbalanced weight or whatever, but still the same applies.

You are assuming that if you keep betting all numbers all the time, chances are that your losses and your gains will accumulate to void one another. Each time you bet is a different time, same possibilities regardless of past prize history. It's a gamble, no matter how you dice your numbers (pun obviously intended)...

You can minimize you chances of loosing by betting less or not at all, but your chances of winning depend on all the betters, not just on your own actions.

I remember my statistics professor starting off with this well known problem now (before internet):

A car is behind 1 of 3 doors. the other 2 doors contain goats. You select a door at random, say door #2. The host (who knows where the car is) shows you a goat behind door #1. He gives you the chance to switch. Is it to your advantage to switch if you want a car? Answer: yes, 2/3 chance car is behind door #3.

At the time, I couldn't believe that was true, now I get it.

I am assuming that the draws are completely random, and that over time, my gains will overcome my losses by betting every number. This is a no-lose *long term* bet, given enough tries, I'll come out, at worst, break even if everyone employs the same strategy. As soon as someone 'takes a shot', I gain edge from him.