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

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Lohoris:
Quote from: Professor James Moriarty on September 25, 2013, 04:44:34 PM

I want to have a no-limit casino to invest , like you can bet all the investment , which was like 30k or something , be able to bet 30k than. Thats more fun , casinos should take some courage to run , even if its not your money to run , even better if its like that.

You would have no investors, only gamblers.
Makes no sense, not even a bit.
(unless you were being ironic, of course)

GOB:
Quote from: dooglus on September 27, 2013, 08:41:01 AM

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"

Fullquote and BIG +1 ;)

broolstoryco:
Quote from: organofcorti on September 27, 2013, 08:27:57 AM

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.

clt applies in our case as the distribution is independent and identical.

Rampion:
Quote from: dooglus on September 27, 2013, 10:12:35 AM

Whoever said we should cuddle our whale... it sounds like he needs a big hug right about now:

https://bitcointalk.org/index.php?topic=301412.msg3246012#msg3246012

I was the one saying we should "cuddle" our whales, but I just mean to be fair with them by not changing how the casino works when they are playing precisely to "stop" them from winning. Honestly, that's lame, I assume that everybody should understand what 1% edge + 1% max profit means (high variance). I don't think we should adulate our whales (you can see how in other threads I tell Nakowa very clearly I think he is delusional and he will eventually go busto), I just think we should just let them play and follow "their strategy" without messing with them and the reason why is veyr clear for me: the fundamentals of the casino (1% edge, Kelly criterion) are sound and solid, and gambler's mentality is definitely our ally.

As it was obvious, now Nakowa justifies his losses by the change in the rules, and it's possible he won't play as much as before because he feels his "strategy" has been cheated. IMO he is delusional, I don't think he is as smart as you seem to think (otherwise he wouldn't believe he found "a flaw in sha256" and that he can "spot patterns"), and I strongly believe he would have played over and over until he lost everything. You say he might win and "never come back", that is a possibility but IMO very small, I've seen many gamblers in my life and Nakowa is just the prototypical one (big rush when gambling lots of money, denies he is a gambler, believes he has a strategy that beats the house, etc. etc. etc.) They just come back, and they come back more when they are losing, that is what happens 99% of the times. Now that we "changed the rules" while he was playing, precisely to stop him (this is very obvious Doog, and hardly justifiable), we just gave him an excuse to feel cheated, and we just gave him a reason to never play again. In his mind is not his "strategy" not working any more, is US that messed up with it.

I still think he will eventually play again (gamblers are gamblers), but nevertheless as I said many times before I think changing the max profit while he was playing was a very bad, rushed move.

Finally: 1/2 Kelly is much better than 1/4 Kelly, and probably this situation will just make that important changes (like variable risk) will be implemented sooner. I for one fully support you, I just increased my investment, and probably will continue to do so.

organofcorti:
Quote from: broolstoryco on September 27, 2013, 12:22:25 PM

Quote from: organofcorti on September 27, 2013, 08:27:57 AM

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.

clt applies in our case as the distribution is independent and identical.

You missed the point - I wasn't disagreeing. My point is that CLT != normality.

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