> the starting point is always higher than the absorbing barrier.
true - also a tautology
> justifying the fact that people are more willing to bet with "house money" - this is clearly wrong
I don't think you exactly showed that.
true - also a tautology
> justifying the fact that people are more willing to bet with "house money" - this is clearly wrong
I don't think you exactly showed that.
But if I wanted to explain why treating house money differently from your own money was wrong I'd use the example of two people who entered the casino with different amounts of money but now have the same amount (somewhere in between where they each started). Then one is betting with house money and the other isn't. But I claim that it would be rational for them to behave the same way. This is because the consequences of having a certain amount of money will be the same for both of them, no matter where that money came from.
A is losing money they had put aside -- B is losing money he didn't have to begin with.
E.g. A might be playing with borrowed mafia money, or his kids college fund (and risks losing them), whereas B doesn't risk going anywhere below where he was when he entered the casino. If anything, he has a chance to make his winnings even bigger (or at worse, lose them).
In real life (as opposed to thought experiments treating those persons like abstract entities) the origin of those money has a story, so the A=B=100 state is not all that matters to determine the consequences.
You say it as it's some kind of cheating -- instead of enriching the in vitro abstract example with real world impact, and showing why its abstract conclusions don't apply to the real world.