A very big issue with this thing, is that bingo isn't exactly a single-player "game". Someone will win, the question is who will win first. Or rather, who gets the luckiest the fastest.

This premise, especially given then examples in the body, is not even what we mean when we talk about a probability becoming 1 given infinite time.

In mathemathics, a 0 multiplied by anything, usually only results to 0, so for this fact to be true, there has to be at least some chance of it to happen.

This complete issue with your question being resolved, let's talk about probabilities. When calculating the probabilty of an event X to happen after a given amount of "tries", it is much easier to talk in terms of "how likely is it not to happen." as it is just shorter math to the same result.

When testing twice for a same probability, given you're only trying to get it to happen once, you multiply the odds of it by themselves. So, if something had a 10% chance to happen, it has a 90% chance not to happen, and when you try twice, it's 0.9 x 0.9, which is 0.81. It is lower than the original odds. If you try three times, for it not to happen at all would be 0.9 x 0.9 x 0.9, which is 0.729.

Then, to get the odds of it happening once, you get 1 - [the odds of it not happening]. Using my example, the odds of it happening once in two tries is then 0.19, or in three tries, it would be 0.271.

This trend of it getting lower and lower is what gets the odds of it never happening infinitely closer to 0, and thus the odds of it happening, given it has a chance to happen, AND infinite time, is always virtually 1.

It most definitely isn't that price tag, no.

Syphon Filter remake with more modern controls and (hopefully) at least one voice actor replaced to make the character at least sound French instead of bad French accent from a Quebecer would be great.