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

[mechs]

I think all the fancy math and assumptions unneeded.  Variance is extreme due to a very small # of very large bets.  The answer is to lessen the max bet size while still staying significantly bigger than competition so as not to lose players.  Nearest competition is 20BTC max profit.  We were as high as 550 BTC.

[bobboooiie]

Well seems like not many people have experience with grinding poker otherwise you would know this is not even close to extreme in variance world 

[Deprived]

@usagi

That being said my rates are exceedingly cheap.

what is cheap? as I want to open an online casino I would be interested in Your opinion. I know what is wrong with JD. lets say I think I know and as I want to be sure I really would be interested in Your opinion. so how much  

cheers

I think the answer is to simply put in a hard cap for the max profit.  So it can be 1% of the bankroll up until X.  X can be 50 BTC or 100 BTC or whatever.  This would decrease variance significantly. At the same time, Just-Dice would still have the highest max profit of any site.  I mean, when put nearest competitors have a max profit of 20BTC and we were over 550 BTC, something is maybe wrong.

Then simply multi-accounting would bypass the limit.

I think the issues is the cap is so high that martingales are highly probably to work for those with extremely large bankrolls.  A more sane limit would decrease the effectiveness of that strategy.  We just need to be a better deal than the competition (which as I said has a max profit of 20 BTC per bet).  Having a straight 1% max profit is extreme.  

I would also be interested in determining if the results we have seen are statisically probable but I do not have the statistics background to do so confidently.  I do not think Dooglus is cheating or the server is compromised (meaning is playing under alt names are giving out server seed).  In that case, if the results turn out to be statistically improbable, is there any explanation as to why beyond a compromised server seed?

The results we've seen aren't statistically probable - in that they aren't a likely outcome.  But what valid math I've seen indicates that they aren't so unlikely as to suggest a problem.  If something has a 1 in 10 or 1 in 20 chance of happening then is there a problem if it happens?  Is it (your phrase) "statistically probable"?

If there is a problem then, ignoring server compromise/dooglus cheating, then the obvious issue would be if the RNG had a (even small) flaw in it.  For example if the odds of a high number after 2 low rolls was different than the odds of a high number after 2 high rolls.  Any flaw such as that could potentially make an otherwise normal (i.e. losing) strategy into a winning one (one with a positive expectation) - either through blind luck or as the result of careful analysis.

[Rannasha]

You are correct. But the problem is much much deeper than this. Let me begin by asking the simple question; since the KC maximizes profit over number of bets, and since variance decreases with bet size, how many max bets would we need to make in order to decrease variance to get, say, 0.9% < profit < 1.1% assuming all bets were max bets? Going with a set max bet size, say 500 BTC, guarantees we will find a sample size more than sufficient to limit profit in this way. Let's further simplify by going after the RNG and not the house edge.

Variance definitely does not decrease with bet size (assuming total amount wagered is kept constant). The standard deviation for a binomial process is calculated by:
s = sqrt( n * p * (1 - p) )
(s = standard deviation, n = number of samples, p = probability)
If every bet is the same (size b), we can obtain the standard deviation for the total profit (S):
S = b sqrt( n * p * (1 - p) )
If we increase bet-size (b), we decrease n (number of bets) proportionally. But since S is proportional to b and proportional to sqrt(n), we see that with increased bet-size, the standard deviation of the expected total profit goes up.

Which is exactly what he said. Lol.
If you increase bet size, you increase variance.
If you decrease bet size, you decrease variance.

=> Variance is decreasing with bet size.

Ah duh, you're right, my reading comprehension sucks. I've removed that part of my post. The rest of the post is still valid though.

[RationalSpeculator]

I think all the fancy math and assumptions unneeded.  Variance is extreme due to a very small # of very large bets.  The answer is to lessen the max bet size while still staying significantly bigger than competition so as not to lose players.  Nearest competition is 20BTC max profit.  We were as high as 550 BTC.

What about Satoshi Dice? What is max bet there?

[mechs]

@usagi

That being said my rates are exceedingly cheap.

what is cheap? as I want to open an online casino I would be interested in Your opinion. I know what is wrong with JD. lets say I think I know and as I want to be sure I really would be interested in Your opinion. so how much  

cheers

I think the answer is to simply put in a hard cap for the max profit.  So it can be 1% of the bankroll up until X.  X can be 50 BTC or 100 BTC or whatever.  This would decrease variance significantly. At the same time, Just-Dice would still have the highest max profit of any site.  I mean, when put nearest competitors have a max profit of 20BTC and we were over 550 BTC, something is maybe wrong.

Then simply multi-accounting would bypass the limit.

I think the issues is the cap is so high that martingales are highly probably to work for those with extremely large bankrolls.  A more sane limit would decrease the effectiveness of that strategy.  We just need to be a better deal than the competition (which as I said has a max profit of 20 BTC per bet).  Having a straight 1% max profit is extreme.  

I would also be interested in determining if the results we have seen are statisically probable but I do not have the statistics background to do so confidently.  I do not think Dooglus is cheating or the server is compromised (meaning is playing under alt names are giving out server seed).  In that case, if the results turn out to be statistically improbable, is there any explanation as to why beyond a compromised server seed?

The results we've seen aren't statistically probable - in that they aren't a likely outcome.  But what valid math I've seen indicates that they aren't so unlikely as to suggest a problem.  If something has a 1 in 10 or 1 in 20 chance of happening then is there a problem if it happens?  Is it (your phrase) "statistically probable"?

If there is a problem then, ignoring server compromise/dooglus cheating, then the obvious issue would be if the RNG had a (even small) flaw in it.  For example if the odds of a high number after 2 low rolls was different than the odds of a high number after 2 high rolls.  Any flaw such as that could potentially make an otherwise normal (i.e. losing) strategy into a winning one (one with a positive expectation) - either through blind luck or as the result of careful analysis.

That should be easy to check since Dooglus has a datafile with all  bets ever rolled.

[Rannasha]

I think all the fancy math and assumptions unneeded.  ...

I disagree.  I think we need fancier math. 

If dooglus can make a database-dump with all bets-by-size-and-chance again, we can compute what the expected standard deviation of the profits is and how (un)likely our current situation is. The previous time we had such a dump, the site was at -2 sigma, so the conclusion was that the house was very unlucky, but not unreasonably so. At that time, we had around half the amount wagered, so it's been a while.

[Deprived]

I think all the fancy math and assumptions unneeded.  Variance is extreme due to a very small # of very large bets.  The answer is to lessen the max bet size while still staying significantly bigger than competition so as not to lose players.  Nearest competition is 20BTC max profit.  We were as high as 550 BTC.

Max bet will sort itself out - as investors who can't take the variance withdraw.

If max bet is lowered then less bank-roll is needed.  There's a mechanism in place that already adjusts max bet down to whatever variance investors are willing to accept.  And remember that loweing the max bet (unless done massively) doesn't actually change the range of likely outcomes all that much - it just means its done with smaller numbers.  Most bets will still be tiny compared to the max and the outcome will still be determined by the few players betting near the new max.  Just expected profit will be lower and actual profit/loss will be smaller.

If you try to design something where there's low variance then you're explicitly trying to define parameters that make the site unattractive to gamblers.  High variance is what they want - the chance that the house can lose - as without that they're just donating money.

[DomenicoRomano]

I think all the fancy math and assumptions unneeded.  ...

I disagree.  I think we need fancier math. 

If dooglus can make a database-dump with all bets-by-size-and-chance again, we can compute what the expected standard deviation of the profits is and how (un)likely our current situation is. The previous time we had such a dump, the site was at -2 sigma, so the conclusion was that the house was very unlucky, but not unreasonably so. At that time, we had around half the amount wagered, so it's been a while.

That is what I want but I was too lazy to write it out.

[drawingthesun]

Nakowa is now at least 10,000 bitcoin up. Incredible.

[maqifrnswa]

The Kelly Criterion derives from a model that differs from JD's real situation in a couple of important ways.

First, in the Kelly model, the player with the edge controls the betting.  Since he has an edge, he keeps on betting.  In contrast, with JD the house has the edge but must wait passively for the whales to bet.  Since the whales don't have an edge, they can and should stop when they're ahead.

Second, the Kelly model runs on "bet time", where the unit of time is one bet.  The Kelly Criterion maximizes the return over the number of bets.  In contrast, JD runs on "calendar time".  Investors count their return in percent per day or month or year, and count their opportunity cost the same way.

Because of these differences, it does not follow that setting the maximum bet based on the Kelly Criterion will maximize JD's return in calendar time. 

The maximum bet policy has been questioned before, and it's always been answered by an appeal to the Kelly Criterion, or to simulations based on the Kelly model.  I'm suggesting that the model doesn't match the reality, so it's time for a fresh look.

this is really bad math. kelly model has no distinction between house and player, and no distinction between calendar time and bet time. Kelly criterion is perfectly applicable to the house for JD to maximize profits.

The derivation isn't that hard to prove it, I think it's even on wikipedia...

[usagi]

The math is all wrong - or, rather, irrelevant.

The volume the site has had of large bets is nowhere near millions.  The millions of tiny bets become pretty much irrevelant compared to the much smaller number of large bets when looking at variance.

No, if you look at the variance for a number of smaller bets totaling the same wagered amount the variance will go down. When you compare the error from this to the error we were looking for (0.9% to 1.1%) you have numbers x and y such that 0.9% < x < profit < y < 1.1%. The math isn't wrong, it's just less precise. However it restrains the profit just as well. The fact is that if we used many smaller sized bets we would actually be closer to 1% profit than if we used fewer larger bets.

Try looking at what happens if you have 3 million bets at 1 satoshi and 1 bet at 500 BTC.  How likely is it that profits would be anywhere near expectation?  It's not just unlikely, it's impossible.

You are off by four orders of magnitude. 3 million one satoshi bets is 0.03 bitcoins. What my example represents is fifty thousand million (50,000,000,000) one satoshi bets compared to one bet of 500:

0 < 4.95 < profit in btc < 5.05 < 500

(where 0 is the loss from 500, 4.95 is -1% from house odds, 5.05 is +1% from house odds, and 500 is the profit from a single lost bet @ 500).

Point being precisely correct math is a waste of time, it is easier to calculate looser bounds which restrain the profit in the desired fashion and are just as mathematically sound.

As there's no way to get hundreds of people playing at high stakes then the choices are either:

1.  Allow large max bets - getting the most possible expected profit but also taking on huge variance.
2.  Don't allow large bets - the smaller you reduce the max bet the lower variance becomes (as the max bet becomes progressively nearer to the mean bet and the long-term arrives faster).

I'm fine with #1 - as it currently is.  If you reduce max bets not only do you lose the few players who use them but also those who come to the site to watch them and one of the biggest factors differentiating J-D from other sites.

This isn't what I had in mind, I wouldn't make this kind of offer unless I felt I had something worthwhile to share tho. To answer elm, given that dooglus should have site profits of ten million btc by now but is struggling to hold 2000, I think what I have to say is worthwhile to him.

[drawingthesun]

given that dooglus should have site profits of ten million btc by now

ten thousand bitcoin. :p

but is struggling to hold 2000

Have you seen recently, site profit is negative right now.

[Deprived]

To answer elm, given that dooglus should have site profits of ten million btc by now but is struggling to hold 2000, I think what I have to say is worthwhile to him.

Not sure where the 10 million btc expected profit comes from.  That's got a few too many 0s in it.

[elm]

@usagi

To answer elm, given that dooglus should have site profits of ten million btc by now but is struggling to hold 2000, I think what I have to say is worthwhile to him.

hmmm IMHO something looks wrong here. and I think that it is not only for dooglus but also for all investors important and worthwhile to know the error he implemented.

[usagi]

To answer elm, given that dooglus should have site profits of ten million btc by now but is struggling to hold 2000, I think what I have to say is worthwhile to him.

Not sure where the 10 million btc expected profit comes from.  That's got a few too many 0s in it.

Lol, 10,000 not 10 million. Still, 10,000 is a lot of money and the site is negative now. I feel bad for dooglus.

[elm]

To answer elm, given that dooglus should have site profits of ten million btc by now but is struggling to hold 2000, I think what I have to say is worthwhile to him.

Not sure where the 10 million btc expected profit comes from.  That's got a few too many 0s in it.

Lol, 10,000 not 10 million. Still, 10,000 is a lot of money and the site is negative now. I feel bad for dooglus.

JD had a few days ago the 10,000 BTC profit

[infested999]

I think all the fancy math and assumptions unneeded.  ...

I disagree.  I think we need fancier math. 

If dooglus can make a database-dump with all bets-by-size-and-chance again, we can compute what the expected standard deviation of the profits is and how (un)likely our current situation is. The previous time we had such a dump, the site was at -2 sigma, so the conclusion was that the house was very unlucky, but not unreasonably so. At that time, we had around half the amount wagered, so it's been a while.

How large was the filesize for such a database-dump?

[cowbay]

Not a welcome sight for investors.  This illustrates how one whale can dominate the action and skew the stats with just a handful of significant bets.

[juhakall]

Has a stop-loss feature been discussed before? Surely I'm not the only investor who has doubts about being exposed to this kind of variance, especially just after big losses. Why not have a user-settable investment threshold, and if a user's investment falls below that level they'd be auto-divested?