Noob question regarding "x Kelly" investment options. How does it really work? There's a 'more info' on the test site (in invest window) but nothing there yet.
I know 1/4 kelly is the least risky and 10x kelly the most risky, but how does it work in practice? What happens in the scenario:
Bankroll is 100 BTC, I have 1 BTC invested, player wins/loses 1 BTC. What's my profit/loss if:
a) I have 1 BTC invested on 1/4 kelly
b) 1 BTC invested on 10x kelly
Let's ignore all the operator commission for easier calculation.
Also, does it make any sense to spread the investment, say 0.5 BTC on 1/2 kelly and 0.5 on 2x kelly, or is it perfectly the same as investing 1 BTC on 1x kelly?
The leveraged kelly option is really to reduce counter party risk for investors.
Example, say you want to invest 10 Bitcoin at the normal risk of 1/2 kelly but don't want to have the risk of a site operator holding on to all your Bitcoin. You could instead deposit 0.5 Bitcoin and invest at 10x kelly.
This puts more of your investment at risk each bet and you may need to redeposit and top up your investment account frequently due to the variance of the game. So really you should have the coins in your own cold wallet to back up the desired investment total. Obviously some people may just want to gamble and risk their full 10 Bitcoin at 10x to try and maximise profit. This is not recommended though.
The maximum payout of the site is calculated by taking the sum of all the investments * risk * 0.01.
So imagine we had user A with 10 Bitcoins invested at 1/2 kelly, B with 10 at 5x and C with 10 at 10x.
The max payout would be:
(10*0.5*0.01) + (10*5*0.01) + (10*10*0.01) = 1.55 Bitcoin
The higher your risk the more you stand to win or lose each bet.
So each bet your investment will be updated like so:
i = i + ((-p * i * r * 0.01) / m)
Where:
p = the players profit for that bet
i = the amount you have invested
r = your risk
m = the current max payout
In the above example lets say a player bets 1 Bitcoin and wins.
The current investments would then be:
iA = 10 + ((-1 * 10 * 0.5 * 0.01 )/1.55) = 9.96774193
iB = 10 + ((-1 * 10 * 5 * 0.01 )/1.55) = 9.67741935
iC = 10 + ((-1 * 10 * 10 * 0.01 )/1.55) = 9.35483870
Max payout on the next bet would then be:
(9.9677*0.5*0.01) + (9.6774*5*0.01) + (9.3548*10*0.01) = 1.46919354
Again, you should only really be using this to reduce counter party risk and actually have the funds in your own cold wallet to replenish your investment as often as needed.
Feel free to test it out at
https://test.prcdice.eu (note you will get a certificate warning but it is safe (I can think of a better site I could be malicious on) and is due to just using a self signed certificate on the test site. Obviously live site won't be like this.
