Quote from: GOB on September 26, 2013, 06:01:02 AM

Quote from: Peter R on September 26, 2013, 03:14:28 AM

Quote from: VTC on September 26, 2013, 01:44:21 AM

The best would be set max bet to a flat 2%. And you can invest 1/2 of what you would have invested for 1% risk, or 1/8 of what you want to invest for .25% risk. Thoughts?

I think I am coming around to this logic. Let me know if we are on the same page:

The Kelly-criterion says that the optimal max bet is 1% of bankroll, but the "effective bankroll" is not what it says up there on the just-dice.com website. The effective bankroll must include the available funds from all the people that would jump in if the "posted" bankroll got small. Of course they would jump in (assuming no security breach) because each marginal bitcoin reinvested buys a larger slice of the pie than what it did before the whale attack. Thus, the first investors that move in to help battle the whale will have a higher-than-normal return until enough people re-build the site's "posted bankroll", thereby diluting things back to equilibrium.

Earlier in this thread, we showed that, under certain assumptions, reducing the max bet % has no advantage for the investors in aggregate. Total expected profit is simply volume * house_edge. We showed that instead, reducing max bet % has the effect of increasing the aggregate exposure to counter-party and legal risk (as a larger volume of BTC must be deposited to JD cold storage to support a given bet volume [aggregate profits]). Investors can pick there level of risk exposure simply by how much they invest. But they need to appreciate the expected variance of their investment in order to gauge how much exposure is appropriate, given their personal financial circumstances.

I am thinking that the optimal max bet % is high, but still low enough so that investors can jump in quickly after a whale attack to prevent the max bet (in absolute BTC terms) from jumping around too much [so that we don't annoy the whales]. I think 2% would be a good start too.

I was just reading up on the Kelly Criterion (KC) and saw something interesting. Just as the KC maximizes bankroll growth, apparently risking 2x KC (in our case 2%), results in ZERO expected bankroll growth. Beyond 2x KC, expected bankroll growth is negative. So just keep that in mind when speaking of setting max profit to 2%.

So, what do you think about the idea that the "effective bankroll" is not what is displayed on the JD website, but is actually a greater number due to the "sideline" money that would come in should the JD bankroll become depleted?

This was my argument for why it may make sense to have a max bet % greater than 1% of the funds physically held by JD.