

If the song you listened to was “Why Does the Sun Shine,” you should know they didn’t actually write that one (it’s from a 50’s educational record they liked as kids) and it’s not very representative of their ouvre. They’ve even released a follow-up track (“Why does the sun really shine?”) which corrects a lot of that one. It starts with the line “The sun is a miasma of incandescent plasma, the sun’s not simply made out of gas, no no!”





Yeah. OP’s alternate scenario, where there’s not supposed to be a way to get the million, is a lot more fragile, since then there’s a huge incentive to get the intelligence to screw up its prediction.
In the original setup, where you can choose either the jackpot box or both the jackpot and $1000 boxes, that incentive basically goes away. Like, maybe you successfully change the odds to 25% $1M, 25% $1.001M, 25% $1000, and 25% $0 (assuming the intelligence’s ability to predict the coin flip is no better than chance). But in the original problem, depending on your analysis, you’ve either got a 99.999% chance of $1M (based on the one-box camp’s analysis of taking one box), or you’ve got a 100% chance of getting $1000 more than you would by taking one box (based on the two-box camp’s analysis of taking two boxes). It doesn’t seem to me that a 25% chance of getting $0 would seem like an improvement to either of those camps.
So yeah. The scenario OP describes would be a lot more broken, because people’s behavior would be much more chaotic.