Sorry, but I'm not in the habit of taking one for the quantum superteam. And I don't think that it really helps to solve the problem; it just means that you don't necessarily care so much about winning any more. Not exactly the point.

Plus we are explicitly told that the coin is deterministic and comes down tails in the majority of worlds.

So here's why I prefer 1A and 2B after doing the math, and what that math is.

1A = 24000
1B = 26206 (rounded)
2A = 8160
2B = 8910

Now, if you take (iB-iA)/iA, which represents the percent increase in the expected value of iB over iA, you get the same number, as you stated.

(iB-iA)/iA = .0919 (rounded)

This number's reciprocal represents the number of times greater the expected value of iA is than the marginal expected value of iB

iA/(iB-iA) = 10.88 (not rounded)

Now, take this number and divide it by the quantity p(iA wins)-p(iB wins). This represents how much you have to value the first $24000 you receive over the next $3000 to pick iA over iB. Keep in mind that 24/3 = 8, so if $1 = 1 utilon in all cases, you should pick iA only when this quotient is less than 8.

1A/(1B-1A)/[p(1A wins)-p(1B wins)] = 369.92
2A/(2B-2A)/[p(2A wins)-p(2B wins)] = 1088

I have liabilities in excess of my assets of around $15000. That first $15000 is very important to me in a very quantized, thresholdy way, but it is not absolute. I can make the money some other way, but not needing to - having it available to me right now because of this game - represents more utility than a linear mapping of dollars to utility suggests, by a large factor.

The next threshold like this in my life that I can think of is "enough money to buy a house in Los Angeles without taking out a mortgage," of which $3000 is a negligible portion.

I'd say that the utility I assign the first $24000 because of this lies between 370 and 1080 times the utility I assign the next $3000. This is why I take 1A and 2B given that this entire thing is performed only once. Once my debts are paid, all bets (on 1A) are off.

If we're dealing with utilons rather than dollars, or I have repeated opportunity to play (which is necessary for you to "money pump" me) iB is the obvious choice in both cases.

I think that what really does my head in about this problem is, although I may right now be motivated to make a commitment, because of the hope of winning the 10K, nonetheless my commitment cannot rely on that motivation, because when it comes to the crunch, that possibility has evaporated and the associated motivation is gone. I can only make an effective commitment if I have something more persistent - like the suggested $1000 contract with a third party. Without that, I cannot trust my future self to follow through, because the reasons that I would currently like it to follow through will no longer apply.

MBlume stated that if you want to be known as the sort of person who'll do X given Y, then when Y turns up, you'd better do X. That's a good principle - but it too can't apply, unless at the point of being presented with the request for $100, you still care about being known as that sort of person - in other words, you expect a later repetition of the scenario in some form or another. This applies as well to Eliezer's reasoning about how to design a self-modifying decision agent - which will have to make many future decisions of the same kind.

Just wanting the 10K isn't enough to make an effective precommitment. You need some motivation that will persist in the face of no longer having the possibility of the 10K.