I like the social features. Good luck.

“take the regular kelly derivation and replace the losing trade term with min(account reset value, losing trade term), then re-maximize the whole thing.”

Basically, you use the regular Kelly strategy with one exception: if Kelly outputs a bet that might take you below the reset value, then go “all in” instead. But if Kelly does not put you in jeopardy of going below the reset value, then just stick with exactly what Kelly says.

Anyone care to prove it formally?

aj’s idea of opening 2^N accounts and Jason’s comments in his email to me that “the account values of the leader board are also important” inspire a further question:

What is the optimal strategy when managing multiple accounts in order to maximize the wealth of the largest account? I’m guessing that any improvement over Kelly will be at the beginning, to give yourself a faster running start, but in the limit, you’ll want to converge back to using Kelly strategy on whatever account is the largest. (Note I’m ignoring the option of “cheating” by transferring money from one account to another.)

The only thing I am sure of, is you *should* go “All-In” on the first bet. If we shrink the time to reload close to zero as well as the time to place a bet close to zero, we are effectively starting with double the bankroll. How is this not preferable? The question for me is when do you *stop* going “all in” and revert back to regular Kelly. In fact, if we shrink all transaction times to zero, then we can perform infinite number of bets, and should move “all in” on every hand.

Regarding Centsports, Since all bets are roughly 50/50 I am pretty sure going all in every bet is correct. I don’t think you will be able to beat this with any kind of modified Kelly.

With the play money prediction exchanges, there are many bets that are significantly better than 50/50. Still, I think the best strategy is to go all in for some set time, and then revert to standard Kelly based on your ultimate goals. Because the edges are bigger with play money exchanges we don’t want to risk our entire bankroll when we expect to double rather fast anyways.

One case when you can obviously improve on the Kelly criterion in the above circumstance: if Kelly says bet f% of your cash, c, then if (100%-f%)*c <= r, betting 100% of your cash is more optimal (you’ll win slightly more if you win, and by restarting with $r, you’ll be no worse off if you lose).

I can’t see any reason why the Kelly criterion would otherwise differ with play money though — it explicitly ignores any fundamental value to how much money you have and just aims to maximise the expected amount you have; and equally, in real life you can declare bankruptcy and sit on the street with a tin can until someone gives you ten cents.

Going all in everytime increases the maximum possible amount you can end up with, but reduces the liklihood of that to nothing. In a play money scenario, you could make use of that by creating 2^N accounts, and having them bet in a combinatorical way, so that you’re guaranteed exactly one of them will have placed the optimal series of bets. If you then pretend all the other accounts never existed, that could work…

I do play a little looser on that site than I do in my investment accounts, but there’s good reason to keep my bets spread around. OTOH, there have been people (outside the top fifty) who did risk everything on one bet, and ask to have their accounts reset to zero. But for the most part, they were better off before they made their big bet than they were a year later, for having started over.

I suspect there are many cases where it pays to play a slow and steady game. If there’s a prize for being in the top 100, and you aren’t close, then maybe you want to play a higher variance game, but otherwise, I’m not sure when you’d want to do that.

As you suggest, CentSports may be an interesting place to start looking for an answer, with real money at stake but in small enough amounts that you are much closer to play money values, whatever they are.