This is the concept of ergodicity. The fun fact is that even if casinos offered a game with 50% odds players without unlimited bankrolls would still always bust

This is the concept of ergodicity. The fun fact is that even if casinos offered a game with 50% odds players without unlimited bankrolls would still always bust eventually[1]. It's similar to why betting $1 to make $1 million at million to one odds is a smart bet, but betting $1 million to make $1 at the equivalent odds isn't, unless you have an unlimited bankroll. [1] If they use the Kelly criterion they won't bust hard, but they'll still lose most of their bankroll.