The probability for each win is separate from the others.

Suppose you flip a coin and get a thousand successive heads. The possibility of getting another head is 50%, it is not diminished by the thousand that preceded it.

OTOH the probability of getting a thousand heads is about one in 10^301.

Physicists don't talk about that fine-tuning question much anymore. It could be that there have been a vast number of universes before us, or that in the multiverse every possible tuning is represented in another eigencosmos.

These are more interesting questions.