Button game

[Angrboda]

This is actually a fairly interesting subject. According to economics, the utility value of a 50% chance of 50 million is 25 million, yet we have biases against risk which lead us to disregard the expected utility. Daniel Kahneman and Amos Tversky have studied the subject in some depth. I had their book around here at one point, but I may have thrown it out. The long and short is that when faced with choices like that in the OP, we don't respond rationally. I don't know if they go into the psychology behind it, or if it is even known, but I'm reminded of Antonio Damasio's patient E who, due to some damage to his frontal lobes, demonstrated interesting deficits in his ability to make judgments about risk. If I recall correctly, Damasio postulated that certain emotional information was not being integrated into the decision-making process due to the frontal lobe damage. Given the OP, it seems to "make sense" that our emotions surrounding the potential unpleasantness of getting nothing by choosing the second button likely bias against that choice and towards the more emotionally safe first choice, regardless of the fact that, in doing so, we are "likely" losing $24 million dollars of expected utility. That loss is in a sense hidden from our emotional centers and so fails to affect the decision.