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.
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.