This is not what's happening though AFAIK. In the lottery illustration there will be a single payout. In derivatives the risk of default for a certain "class" i

This is not what's happening though AFAIK. In the lottery illustration there will be a single payout. In derivatives the risk of default for a certain "class" is treated as IID, and banks can leverage a certain amount on different risk classes (100x is not unusual). But as 2007 demonstrated the real world risk is not IID. And at 100x leverage a 1% movement can totally wipe out a bank. Also it's not like the 2007 crisis was fixed in any meaningful way. The FED just bought 1.4 trillion of MBS derivatives and is now sitting on them, actual value still unclear. Probably to be paid by the tax payer through 20 years of austerity.