Sorry, but—it sounds like you think you disagree with me about something, or think I’m missing something important, but I’m not really sure what you’re trying to say or what you think I’m trying to say.
If you think this is a problem for Linda’s utility function, it’s a problem for Logan’s too.
IMO neither is making a mistake
With respect to betting Kelly:
According to my usage of the term, one bets Kelly when one wants to “rank-optimize” one’s wealth, i.e. to become richer with probability 1 than anyone who doesn’t bet Kelly, over a long enough time period.
It’s impossible to (starting with a finite number of indivisible currency units) have zero chance of ruin or loss relative to just not playing.
most cautious betting strategy bets a penny during each round and has slowest growth
most cautious possible strategy is not to bet at all
Betting at all risks losing the bet. if the odds are 60:40 with equal payout to the stake and we start with N pennies there’s a 0.4^N chance of losing N bets in a row. Total risk of ruin is obviously greater than this accounting for probability of hitting 0 pennies during the biased random walk. The only move that guarantees no loss is not to play at all.
Sorry, but—it sounds like you think you disagree with me about something, or think I’m missing something important, but I’m not really sure what you’re trying to say or what you think I’m trying to say.
Yeah, my bad. Missed the:
IMO neither is making a mistake
With respect to betting Kelly:
It’s impossible to (starting with a finite number of indivisible currency units) have zero chance of ruin or loss relative to just not playing.
most cautious betting strategy bets a penny during each round and has slowest growth
most cautious possible strategy is not to bet at all
Betting at all risks losing the bet. if the odds are 60:40 with equal payout to the stake and we start with N pennies there’s a 0.4^N chance of losing N bets in a row. Total risk of ruin is obviously greater than this accounting for probability of hitting 0 pennies during the biased random walk. The only move that guarantees no loss is not to play at all.