The genie faces a single, static decision over probability distributions. There is no temporal sequence, no compounding, no intermediate node at which the genie might re-evaluate. The genie simply picks the best plan, and the best plan is the one whose probability distribution over outcomes ranks highest.
I don’t see how this is a contrast. Is this not what an ergodic strategy is doing, also? A resolute choice? All updateless decision theories are stepping outside time; there’s a reason the first step in that direction was called ‘timeless’ decision theory. Benja’s pretty explicit that these plans include probabilities; it is selecting choices that make sense at particular intermediate steps. If the correct strategy to make bets to achieve long-run growth, that optimizes the bankroll at the time labeled by the genie as ‘outcomes’ is to Kelly-bet, and that’s what you care about, the genie will choose to Kelly-bet.
However, it will not do that, because long-run growth is not what we care about. Optimizing long-run growth is correct, AIUI, only if losing your last dollar is infinitely bad and there is no bankroll size at which you cease to desire it to grow at the same strength you presently desire it. Certainly I prefer a quadrillion dollars to a trillion, but if I have a trillion (in 2025!USD-equivalent), I will cease to be particularly interested in what choice optimizes the long-run growth of that bankroll, and will instead be much more conservative.
I am far from certain. But I believe this thought experiment deviates from what you prescribe only in circumstances where you become the one relying on unnecessary and inappropriate assumptions. It looks to me like the argument there continues to hold for exactly the processes you suggest are superior.
I don’t see how this is a contrast. Is this not what an ergodic strategy is doing, also? A resolute choice? All updateless decision theories are stepping outside time; there’s a reason the first step in that direction was called ‘timeless’ decision theory. Benja’s pretty explicit that these plans include probabilities; it is selecting choices that make sense at particular intermediate steps. If the correct strategy to make bets to achieve long-run growth, that optimizes the bankroll at the time labeled by the genie as ‘outcomes’ is to Kelly-bet, and that’s what you care about, the genie will choose to Kelly-bet.
However, it will not do that, because long-run growth is not what we care about. Optimizing long-run growth is correct, AIUI, only if losing your last dollar is infinitely bad and there is no bankroll size at which you cease to desire it to grow at the same strength you presently desire it. Certainly I prefer a quadrillion dollars to a trillion, but if I have a trillion (in 2025!USD-equivalent), I will cease to be particularly interested in what choice optimizes the long-run growth of that bankroll, and will instead be much more conservative.
I am far from certain. But I believe this thought experiment deviates from what you prescribe only in circumstances where you become the one relying on unnecessary and inappropriate assumptions. It looks to me like the argument there continues to hold for exactly the processes you suggest are superior.