Should you buy insurance at 0 EV?

[Three]

I believe the coefficient of Z in the first term should be 8/3, since it is 4/3+4/3.

Thanks DH. I was pretty sure someone would catch a mistake somewhere in there if they took the trouble to check. My brain woke up slowly today.

In this case, the X² coefficient might in fact be positive. Since X (the wager) is much larger than Y (the EV), would that change your result?

I makes it more likely but I think Z is far less than .50. I still the first addend it is negative.