In that episode, Isaac claimed, "Over an infinite period of time, anything that can happen will happen...". I agree that if the probability of that thing that "can happen" is static, then it will happen. What if the probability of that thing is not static but decreases over time? Will that thing happen eventually?
Imagine this game. You have a magic die that begins with 6 numbered sides. You win the game if you roll a 1. At the start of the game you have a 1 in 6 chance of winning. If you don't win the game after the first roll, the magic die increases by 1 side so on the next trial you have a 1 in 7 chance of winning. If you go on to a third trial the die has 8 sides, On the forth trial it has 9 sides and so on. Is it possible to roll such a die an infinite number of times and never roll a 1(win the game)? Its always possible to win the game but does an infinite number of tries guarantee you will win it?
Admittedly the above thought experiment is contrived. Nevertheless similar situations do happen in real life. Can a roulette player who starts a quest to quit gambling when he/she is even when they are currently down by $10000 ever have a winning steak that takes them back to even if they play the game for eternity? It could happen, but is it guaranteed? If they play for an eternity they will certainly have winning streaks that clear $10000 in losses. The problem for our degenerate gambler is while he/she is chasing that streak his/her losses are very likely to grow. After a billion spins our roulette player might have to run into a 100 billion dollar winning streak to get back to even and that is a much harder thing to accomplish..