I was hoping someone who voted fold in the AA thread said A1B2 here so I could yell at them.
Originally Posted by dj11
In the original post (OP), there is no down side to scenario 2, so obviously we all choose that.
In scenario 1, there is a serious gamble, with a devastating downside, it would be just like that munificent stranger never made the offer. But since the offer is made at those odds I prefer to profit with a 100 % win decision.
Yeah, this summarises everything pretty well. As I briefly mentioned in the thread but intentionally avoided going into any detail over, it's utility theory.
It's actually not all that different from the principles governing fluctuating chip values in tournaments. Invariably, the more of something you have, the less satisfying any additions of that particular something are, just as in a tournament the more chips you have, the less true value additional chips have.
Imagine a big box of chocolates. Compare the satisfaction you get from the first chocolate to the satisfaction you get from the 30th chocolate, and then try and plot a graph of 'satisfaction' for all the chocolates you eat in between (you fat bastard). You should get a downward-sloping curve - the gradient of which will level out close to (or at) zero after a certain point, depending on your tolerance for chocolates.
The same can be said of money. The inherent 'difference' between the two examples is the outcome should one take the coinflip and lose. Instead of thinking in terms of chocolates, now think in terms of millions of pounds. You gain a huge amount of satisfation from your first million pounds, but that diminishes for every consecutive million, so much so even only after a couple of million that in the examples given most people who want the guaranteed money in Scenario 1 are willing to take the 'gamble' in Scenario 2. For what it's worth, I agree. Although taking the guaranteed money in Scenario 1 is a -EV decision, the utility one gains from the first million is so far in excess of the utility one gains from the extra $500k in EV (this is, incidentally, assuming we're not very wealthy to start with), that taking the money is the most practical option.
As the utility curve mentioned above (except in terms of $m, not chocolates ^^) goes down and levels out, the EV of the decision becomes more important, so again, people will take the 'gamble' in Scenario 2.
The whole of Ron's AA thread hinges on the steepness of each person's specific $m utility curve. Some people will find a second million much more/less satisfying than others. The more satisfying one finds the second million, the more one should be inclined to fold, despite it being -EV. I'd argue that from my perspective the second million is worth nowhere near as much as the first million in terms of utility, and so EV should be the overriding concern in my decision-making at this point. That said, and despite what I've said and/or implied in the thread, I've come to the conclusion that there isn't really a 'wrong' answer to Ron's question, because ultimately it can be boiled down to a scenario not unlike the two in the OP. I'm too lazy to do the maths in order to do this, but it lies somewhere between the two above cases.