I can not wrap my head around this ever. and I know people use this calculation and it may as well be right but my logic tells me that the "probability of losing in the last bet" is the same as probability of losing in the first bet. so for example if you have 50% chance of losing in bet #1 you still have 50% chance of losing in bet #80 and bet #1000000000 because bets are not connected to each other! when you roll the dice the system (the provably fair ones) doesn't check whether you won or lost the last bet it generates a completely random new number which has 50% chance of giving you the number you want (aka win) and 50% chance of giving you the number you don't want (aka lose).