The utility of money is sometimes claimed to be logarithmic.
More generally it’s that the marginal utility of money decreases, making buying insurance potentially an expected gain in utils even when the expectation of financial gain is negative.
Not if the marginal utility of money decreases as you have more.
If your utility function has convex parts then it might be possible, though. If you have $1000 but owe the Mafia $2000 and they’re coming to collect, betting it all on black might be a good idea.
More generally it’s that the marginal utility of money decreases, making buying insurance potentially an expected gain in utils even when the expectation of financial gain is negative.
Having this in mind, could it be possible to construct such roulette betting system, which have positive expected utility value?
Not if the marginal utility of money decreases as you have more.
If your utility function has convex parts then it might be possible, though. If you have $1000 but owe the Mafia $2000 and they’re coming to collect, betting it all on black might be a good idea.