Imagine a coin with two sides with uneven chances. Heads has a probability of 0.9 and Tails has one of 0.1. Flipping this coin ten times will (on average) result in nine times Heads and one time Tails. But there is a small chance, that more than five of the flips will turn out Tails. If we flip the coin 100 times there's still a chance, that it will be mostly (>50) turn out Tails. There is a really small chance, that if we flip Tails 1000 times in a row. The more times we flip the coin the smaller the chance gets, that we will have more Tails than Heads.
The challenge is to have more Tails than Heads at some point.
If we imagine flipping the coin an infinite amount of times evaluating after every flip, we will at some point have 1000 Tails. If this leads to more Tails than Heads the challenge is completed. If not we must continue, and the score is likely 1000 to 9000. Luckily we will a some point hit 9001 tails in a row. If this happens right after we will accept, otherwise we continue. This can go on forever and the more flips made the chance of ever reaching more Tails than Heads decreases.
The question
Since this challenge is accepted or continued with every coin flip, does this mean that we at some point will accept, or is infinite necessary to describe that it will end at some point?
I don't know if my question makes sense, and I can't find any theories about it.
Thanks.
Just a comment as companion of your question and explanation. I don't answer your question. But I believe that my contribution is interesting:
In fact one can build such coins: take two coins with same diameter and different densities (steel and wood) and join them with glue.
After you can do experiments.