4 ms·
Kelly criterion is not the best strategy for one. It’s the best strategy for an ensemble of ones in many universes but you can only live in one universe. It’s a
by SnowHill9902 4y ago
Kelly criterion is not the best strategy for one. It’s the best strategy for an ensemble of ones in many universes but you can only live in one universe. It’s a nerd trap because it seems so elegant and reasonable.
- anonymoushn 4y agoThis isn't true? If you aggregate utility across universes using addition and have utility linear in wealth then you maximize your aggregate utility by going all-in on every favorable bet. Kelly turns out to be equivalent to maximizing expected log-wealth, if one stays within a single universe, or to maximizing the probability that one will eventually have more wealth than any agent in the same universe that employs any other strategy on the same sequence of opportunities.
- kwertyoowiyop 4y agoOnly on HN is it necessary to define that we are only discussing the single-universe case!
- SnowHill9902 4y agoYou are still using infinite universes: expected value and probability still are calculated across an ensemble of parallel universes.
- anonymoushn 4y agoThis is the worst comment I have ever read. There are reasonable definitions of expected value and probability that do not require infinitely many universes to figure out whether you should raise pre-flop with aces.
- SnowHill9902 4y agoCan you provide any such definitions or references?
- anonymoushn 4y agouse google next time https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/UltraF.html https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml...
- SnowHill9902 4y agoYou are conflating time-samples with ensembles. That lecture refers to finite time series which may be shown to converge for N < infinity. That’s fine.
- anonymoushn 4y agoI have not mentioned either of these things. You can find other finitist formulations of probability if you want. You replied to a post about aces. For any finite number of chips and players (n_players > 23 starts to raise some questions), there are finitely many games of NLHE anyway.