Just-Dice.com : Invest in 1% House Edge Dice Game

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organofcorti:
Quote from: Peter R on September 27, 2013, 06:37:50 AM

Quote from: organofcorti on September 27, 2013, 06:22:46 AM

Quote from: Peter R on September 27, 2013, 04:40:54 AM

Can anyone help me justify why stdev would be the square root of entropy?

I have a vague memory of variance and entropy having a monotonous relationship for some continuous distribution, and I think that for gaussian distributions variance == entropy, and stdev = sqrt(variance). I wouldn't have thought the relationship would hold for a discrete distribution though.

Thanks organofcorti. If variance = entropy for Gaussian distributions, then I think we use the central limit theorem to justify a bunch of discrete Bernoulli processes morphing into a process with a Gaussian PDF.

Check it out first though - information theory is not really my area and it might be a false memory. If so I'm just glad it didn't involve priests.

geofflosophy:
Quote from: Peter R on September 27, 2013, 06:37:50 AM

Quote from: organofcorti on September 27, 2013, 06:22:46 AM

Quote from: Peter R on September 27, 2013, 04:40:54 AM

Can anyone help me justify why stdev would be the square root of entropy?

I have a vague memory of variance and entropy having a monotonous relationship for some continuous distribution, and I think that for gaussian distributions variance == entropy, and stdev = sqrt(variance). I wouldn't have thought the relationship would hold for a discrete distribution though.

Thanks organofcorti. If variance = entropy for Gaussian distributions, then I think we use the central limit theorem to justify a bunch of discrete Bernoulli processes morphing into a process with a Gaussian PDF.

The number of plays doesn't have to be very high for a discrete distribution to approximate a Gaussian, something like n=8 if I remember correctly, though it's been at least 11 years since I've studied it. I'm probably in over my head in saying this; so take it with a grain of salt; but the central limit theorem is about the distribution of the means of samples, and holds regardless of the underlying distribution. I think that you can basically consider this data to be a mean of many n=1 samples.

organofcorti:
Quote from: geofflosophy on September 27, 2013, 06:54:14 AM

Quote from: Peter R on September 27, 2013, 06:37:50 AM

Quote from: organofcorti on September 27, 2013, 06:22:46 AM

Quote from: Peter R on September 27, 2013, 04:40:54 AM

Can anyone help me justify why stdev would be the square root of entropy?

I have a vague memory of variance and entropy having a monotonous relationship for some continuous distribution, and I think that for gaussian distributions variance == entropy, and stdev = sqrt(variance). I wouldn't have thought the relationship would hold for a discrete distribution though.

Thanks organofcorti. If variance = entropy for Gaussian distributions, then I think we use the central limit theorem to justify a bunch of discrete Bernoulli processes morphing into a process with a Gaussian PDF.

The number of plays doesn't have to be very high for a discrete distribution to approximate a Gaussian, something like n=8 if I remember correctly, though it's been at least 11 years since I've studied it. I'm probably in over my head in saying this; so take it with a grain of salt; but the central limit theorem is about the distribution of the means of samples, and holds regardless of the underlying distribution. I think that you can basically consider this data to be a mean of many n=1 samples.

Don't forget that the CLT doesn't necessarily mean that sums of random variables eventually become normally distributed. It just means that the sums of iid RVs tend toward a stable distribution.

For example, sums of Pareto distributed RVs for example emphatically do not tend to a normal distribution (as I found out to my dismay while working on Ozcoin's PoT reward method last year).

I have no idea if that's the case here, and probably not. I just thought it a good idea to point out that the CLT doesn't necessarily mean sums of iid RVs tend to normality.

Lohoris:
Quote from: mechs on September 25, 2013, 03:04:55 PM

I personally agree with the change as a stopgap solution and I am down more than anyone I think since I never divested. This site was not intended to have so much variance for the investor. I am fine with losing coins, it is an investment. But this investment was never designed to be one where someone can go fro +10% to -25% in 5 days. I would not expect it to similarly gain.

The high max bet has increased the variance to astronomical levels. It may not effect gambler luck, but that is not the goal. A high max profit with a player who now has more coins likely than the entire bankroll, can truly break the bank and has practicallly done so.

The key for J-D to stay competitive is to still over the best interface and best odds of any reputable online casino. Whales will continue to come to J-D since Dooglus has proven time and again to be honest and always payout. Noone is going to deposit 10k bitcoins on LetsDice (would you trust them not to steal it all?).
The max bet at our nearest competitor is 20 BTC (Primedice). There is a reason for this. For sites such as Satoshi Dice which allow higher max profit the house edge is 1.9%. These are the #s we need to beat.

I agree a better strategy would be to increase house edge for big potential profit bets. The site will lose nothing since these players have no other trustworthy place to go with better odds. I like a sliding scale house edge which inceases by .02% for every 1 BTC potential profit over 50 BTC up to a max of 1.9%. Eg. 60 BTC max profit bet has a house edge of 1.2%, 90 BTC max profit bet has a house edge of 1.9%. Beyond that, I would not increase the house edge further. With these changes I would increase the max profit per bet to 0.5%

This change will not even effect 99.99% of players since few ever make bets with max protits greater than 50 BTC. Those very few who do, have nowhere better to go, since J-D still offer the best odds out there in bitcoinland. Decisions should not be made on whether one player (nakowa) returns or not. He has shown the site's design is flawed from its intended design - this level of variance was never intended. Doing otherwise would just be the gambler's fallacy in reverse on the house.

In summary I recommend:
0.5% Max Profit per Bet
1% House edge up intil max profit 50 BTC, then increase 0.02% per 1 BTC up until a max of 90 BTC profit at 1.9% house edge
Max Investment of 50,000 BTC - this will in effect lead to a cap of the max bet and less likely investor divestment in bad runs (since if you divest and someone else invests back up to the max, you lose your spot). This would still allow 250 BTC max profit bets (at an edge of 1.9%) - still a very large amount and better than the competition.

Btw, looks today like most of Nakowa's bets in the 30 - 60 BTC range, even he would be minimally effected by these changes with his "current" playing style.

Fullquote and BIG +1.

Except for the cap at 1.9% edge: since we are the only one offering such a small max bet, I feel we really need no cap on increasing the edge.

dooglus:
Quote from: Lohoris on September 27, 2013, 08:37:38 AM

Fullquote and BIG +1

Except for the cap at 1.9% edge: since we are the only one offering such a small max bet, I feel we really need no cap on increasing the edge.

I don't really like the idea of charging big players a higher house edge. For one we should be encouraging big play, not punishing it. And for two it's nice to be able to advertise "1% house edge" without having to put in small print "* unless you're a serious player, in which case it's up to double that, determined by some complex formula or other"

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