[nhaehnle]

Your example is misleading, because the same can be said about the game where you roll a dice over and over again, and you win if you get a 6.

The probability that the game ends is 1, but it is not guaranteed to end. Yet no reasonable person will worry about this in practice.

Your example with 100 times 6 in a row is conceptually exactly the same, just the expected time until the game terminates is much, much larger.