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

[organofcorti]

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]

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]

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]

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]

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"

[Peter R]

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]

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]

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]

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.

[dooglus]

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

In what I am sure is a totally unrelated incident, the Just-Dice chat has recently been spammed with LD ads:

02:28:10 (159120) <alison> PLAY LETS DICE | MORE REWARDS | PROGRESSIVE JACKPOT | REFERRAL PROGRAM | https://lets-dice.com/?invite_info=7829
02:28:51 (159120) <alison> RECOMMENDED > bit.ly/1fLPMeq PLAY LETS DICE | MORE REWARDS | PROGRESSIVE JACKPOT | REFERRAL PROGRAM | http://bit.ly/1fLPMeq
02:29:14 (159120) <alison> VOUCHED > bit.ly/1fLPMeq PLAY LETS DICE | MORE REWARDS | PROGRESSIVE JACKPOT | REFERRAL PROGRAM | http://bit.ly/1fLPMeq
02:29:32 (159120) <alison> GO > bit.ly/1fLPMeq PLAY LETS DICE | MORE REWARDS | PROGRESSIVE JACKPOT | REFERRAL PROGRAM | http://bit.ly/1fLPMeq
02:29:58 (159120) <alison> BETTER > bit.ly/1fLPMeq PLAY LETS DICE | MORE REWARDS | PROGRESSIVE JACKPOT | REFERRAL PROGRAM | http://bit.ly/1fLPMeq
02:30:53 (159120) <alison> NEW & BETTER : http://bit.ly/1bgY4vz | LETS DICE | CLEAN DESIGN | MORE REWARDS | PROGRESSIVE JACKPOT | CASH BACK | BEST DICE | REFERRAL PROGRAM | http://bit.ly/1bgY4vz
02:39:45 (159140) <alison> NEW & BETTER : http://bit.ly/1bgY4vz | LETS DICE | CLEAN DESIGN | MORE REWARDS | PROGRESSIVE JACKPOT | CASH BACK | BEST DICE | REFERRAL PROGRAM | http://bit.ly/1bgY4vz
02:43:18 (159147) <alison> NEW & BETTER : http://bit.ly/1bgY4vz | LETS DICE | CLEAN DESIGN | MORE REWARDS | PROGRESSIVE JACKPOT | CASH BACK | BEST DICE | REFERRAL PROGRAM | http://bit.ly/1bgY4vz

Ho hum...

[Lohoris]

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]

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]

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]

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]

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.

[Lohoris]

That's the same as me betting on a nfl game

TOTALLY not the same.

If you place a 10 bet, or two 5 bets, on an nfl game, the result will be the same.

If you roll dice at 10, or roll dice twice at 5, the result is much different.

Higher house edge on big rolls compensates variance, variance is bad for investors, so investors want to be paid more.
Easy.

[integrity42]

The edge should under no circumstances be changed.  The 1% edge is why just-dice has a market advantage and 2 million BTC wagered.

If he raises it, gamblers will instantly go play at a competitor with 1%.   Adjust the max bet if you'd like, but changing the edge would be a terrible business decision.

[integrity42]

Right.

Maybe it would have been better if they were called 'Bankrollers' instead of 'Investors'. 

It seems like people here think the term 'Investor' somehow means that no risk is being taken and they should have guaranteed profits.

[rarefied]

It seems like people here think the term 'Investor' somehow means that no risk is being taken and they should have guaranteed profits.

Yeah, just like in the stock market :-P

[chriswen]

But *now*, what is the max bet for the whale's second roll?  There are two ways to calculate this and it depends on whether you "trust" Investor B:

If you *don't* trust Investor B, then I think you would say:

  max profit = 1% of 99 BTC + 1% of 9 BT * 10X = 0.99 BTC + 0.9BTC = 1.89 BTC,

and, should the whale lose the next bet, it would only be fair to give Investor A more of the winnings than Investor B (remember, we don't trust that he is good for the "bankroll" he claims to hold off site).

I think if you do it that way, it is exactly the same as if "offsite" reserves weren't implemented at all, and investor B just invested 10 BTC at 10% risk.  After losing his first bet he would have 9 BTC left, risk 10% of it, ie. 0.9 BTC, as in your working above.  The point of the "offsite" reserve is that it doesn't shrink with losses.  He deposited 10 BTC, claims to have 90 BTC more at home, and we take him on his word.

If you *do* trust Investor B, then I think you would say

  max profit = 1% of 99 BTC + 1% of 99 BTC = 0.99 BTC + 0.99BTC = 1.98 BTC,

in which case both investors would share equally in the win.  

And that is how it is meant to work.  "offsite" investment is a way for player B to invest his whole 100 BTC without having to trust us with more than 10 BTC of it at a time.  It should be exactly equivalent to investor A investing the whole 100 BTC at once.

So can we trust Investor B?  Or should it be Investor B's responsibility to "keep up his margin" as required.  

We don't care whether he really has the other 90 BTC or not.  If he loses the first 10 BTC without topping it up, he gets divested.

The only downside I can see to this is that it can cause sudden changes in the available max profit.  To mitigate that, we limit the amount of leverage investors are allowed access to.

As a way of limiting the leverage - have you considered restricting people's total investment to the max they had deposited at any one time?
That way - they demonstrate they had the funds, by only 'risking' it with you for a short time.
Sure - people could game it a little.  e.g friends lending around the same 100BTC for deposit/withdraw into different accounts - but you're still limiting it to people who at some point had access to that sort of money.

I guess that sort of eligibility criterion favours the wealthy - but would help put an overall cap on use of leverage.. and help with promoting the image of 'responsible gambling' by only offering the higher leverage to those who can afford it.

It wouldn't completely stop the issue of big fluctuations in available max profit... but I guess big investors can already instantaneously influence that quite heavily anyway.

I think its okay to allow people to leverage.  They're exposing themselves to more risk.  But, there should be a limit.  And I'll discuss this later tonight but I think leveraging will bring some new problems.