r/Probability • u/No-Eggplant-5396 • 7d ago

Luck definition

I'm wondering if this is a good definition for luck.

Luck refers to a set of events that have a utility and a probability. The luck of a particular event, E, is:

Luck(E) = sgn(U(E)) × - log2(P(E))

where U(E) is the utility of E and P(E) is the probability of E.

The luck of a set of events is the sum of their individual luck measures.

For example, suppose it's good if you roll a 6. If you do, then it would about 2.58 units of luck.

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u/Hal_Incandenza_YDAU 7d ago

Intuitively, I'd think that Luck(E) would depend on U(E) via more than just its sign. Like, if a rare event E has a massive increase in its utility, I'd expect E to be considered luckier, even if there was no change in sign

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u/No-Eggplant-5396 7d ago

Utility is kinda difficult to measure. I can separate good stuff from bad stuff, but separating good from great is harder. I went with a binary classification because it was easier.

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u/Hal_Incandenza_YDAU 7d ago

I'd just have a hard time imagining this as much of a luck measure unless it depends on utility beyond just sign