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

<< < (514/1005) > >>

Peter R:
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.

I think it is normal. Maybe Bugpowder can superimpose a normal distribution on his histogram:

geofflosophy:
Quote from: Peter R on September 27, 2013, 08:53:04 AM

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.

I think it is normal. Maybe Bugpowder can superimpose a normal distribution on his histogram:

Okay so let's assume for a second that it is normal; in that case we're talking about a slightly >12% event to this point, which while lucky isn't THAT lucky. Certainly not unlikely enough to start screaming cheater...

Peter R:
Quote from: geofflosophy on September 27, 2013, 09:07:13 AM

Okay so let's assume for a second that it is normal; in that case we're talking about a slightly >12% event to this point, which while lucky isn't THAT lucky. Certainly not unlikely enough to start screaming cheater...

Indeed. We have no evidence that Nakowa ever cheated.

wachtwoord:
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"

This. To me, increasing the edge is worse than not going full Kelly.

Navigation

 Message Index