the part that I found the most counter-intuitive is that if the casino is over-risking to the point that it expects to lose money, shouldn't it be profitable for a whale to play there?
And...? Don't leave us hanging! How did you resolve this? If the house expects to lose money because it's over leveraged, and the player expects to lose money because of the house edge, where is all the money expected to end up???
My guess is that the house never "expects to lose money". It's just that the probability of going bust gets higher. For example if the house has no maximum bet, and is always willing to risk its entire bankroll every roll, it will go bankrupt as soon as a suitably rich whale wins a single bet. But if the house is paying only 2x for a 49.5% bet, the house still expects to profit by 1% of the amount wagered. Consider the case where the house starts with 1 unit, and the whale bets the whole bankroll against the house up to 3 times in a row or until the house goes bust:
There's a 0.495% chance that the house goes bust on the first bet, losing 1 unit.
There's a 0.505*0.495 chance that the house goes bust on the 2nd bet, losing 1 unit.
There's a 0.505*0.505*0.495 chance that the house goes bust on the 3rd bet, losing 1 unit.
There's a 0.505*0.505*0.505 chance that the house wins all 3 bets, profiting 1 + 2 + 4 = 7 units.
Expected profit = (0.495 + 0.505*0.495 + 0.505*0.505*0.495) * -1 + (0.505*0.505*0.505) * 7 = 0.030301 units.
So while there's a 87.12% chance that the house goes bust in the first 3 bets, there's a 12.88% chance that it wins 1+2+4 from the first 3 bets, which means the expected profit is positive.