Listen, casino has a house edge and in most cases, it's between 1-5%, which means that casino returns to player 99%-95% of the money back, which also means that, long-term, you shouldn't lose more than 95-99% of your capital.
Wrong. What you are missing here is compound interest working against you.
You are right, I'm actually shocked that I wrote that. When you place a bet of $100 and the house edge is 5%, casino expects to create a $5 profit.
If you deposited $1000 and lost $900, mathematically, you still have a chance to gain back those money.
Mathematically it is possible but most unlikely because you would need to make 1,000% on your bankroll playing a game that every time you bet has a minus 1-5% of expected value working against you.
Yes, if my bankroll is $100 and I place $1 for 1000 times, my expected lose is $50.
By the way, the most interesting thing is what happens when the house edge is 0%. Even with zero house edge and no negative compounding, it's still expected to lose, depending on your target. For example, if I start with $100 and I target $110, my chance to reach this target is 90.9% and the chance to go broke is 9.1%, assuming the game is completely fair. But if I target $1000, then my chance to reach the target is 10% but the chance to go broke is 90%.
Formula:
Start = $100 | target = $1,000
Reach target = 100 / 1000 = 10%
Go broke = 100% - 10% = 90
