Quote from: nicolaennio on August 14, 2014, 06:29:50 PM

(see http://thehackensack.blogspot.fi/2009/11/half-kelly-bet.html)

Thanks for the link. I hadn't seen that post before; it's quite convincing.

Quote from: nicolaennio on August 14, 2014, 06:29:50 PM

My suggestion (as a tiny investor) is to cut the max bet to 0.5% or 0.25%.

In the past I have told people "if you want to risk 0.5% instead of 1%, just invest half as much".

The problem with that is that the two aren't equivalent.

If I invest 100 BTC at 1%, I'm risking 1 BTC per bet, and after a whale wins a max bet, I have 99 BTC left
I am risking 0.99 BTC on his next max bet.

If instead I risk 200 BTC at 0.5%, I'm still risking 1 BTC per bet, and after a whale wins a max bet, I have 199 BTC left.
I am risking 0.995 BTC on his next max bet.

So although the two strategies started out looking the same (risking 1 BTC per bet), they very quickly diverge (*).

Something I was considering for Just-Dice, but never actually implemented, was allowing people to "borrow" coins to invest. It would work like this:

All investments risk up to 0.5% per bet, but you are allowed to "borrow" up to N times the amount you have deposited (for some N, maybe 10).

This borrowed amount isn't available for betting or withdrawing - it can only be used to invest, and to repay your loan. Maybe you're not even allowed to withdraw at all which you have a loan outstanding.

Borrowed coins can be invested just like regular coins. The only difference is that if your investment does poorly, and you lose to the point where your total balance is close to being insufficient to cover your loan, you get auto-divested and your loan gets paid off from your remaining balance.

This would allow me to deposit 50 BTC to the site, "borrow" another 450, say, and invest a total of 500 BTC into the bankroll. I would be risking 0.5% of that 500 BTC per roll (2.5 BTC). If a whale came and won a bunch, I would get auto-divested when my 500 BTC investment reached 455 or so (2 max bet losses above me being unable to repay my 450 BTC loan). So my remaining 455 BTC investment would be divested, and the 450 BTC loan would be paid off, leaving me 5 BTC in my account.

This would allow those who want the high-risk, high-reward effect of full Kelly to approximate it (as shown above, marked (*), 2 half Kellys doesn't make a full Kelly), while also allowing the more conservative investor to use half-Kelly.

I never implemented this on JD because I was concerned that a few "whale" investors would use it to dominate the bankroll.

But now that I'm the whale investor, that doesn't seem so important. Wink