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

[dooglus]

Do you think there will be a potential issue with investors using all their margin to gain a larger percentage of the smaller bets then divesting or reducing margin (manually or with a bot) when a whale comes along? I feel that if you do implement margin it will greatly inflate the bankroll as investors will try to get a larger percentage of the smaller (less volatile) bets.

Perhaps this is a non issue since it is similar to someone doing the same without margin. I suppose it could depend on how much margin you allow. As you said, it will probably cause large swings in the max profit when a whale starts betting.

I think we'll have to see what happens.  If it's a problem, we'll address it.

The two issues I see:

1) allowing large leverage will permit large investors to monopolise the bankroll in a way that they currently don't feel comfortable doing due to CP risk

2) increased volatility in max profit isn't a good thing for gamblers.  they will feel like we're reducing the max profit to stop them winning their losses back

Both of these can presumably be addressed by putting limits on the allowed leverage multiplier.

[dooglus]

I made the point about the robbing. I'm glad you took it in the spirit in which it was intended. I was worried it would come off... I dunno, mean or tasteless.

Not at all, it's a real issue.

I don't think people know my exact location, and I'm pretty hard to find.  I take reasonable measures to be able to protect myself, but of course there's always a risk.

[Rampion]

Leverage is a very tricky thing, if implemented it should be done with the utmost care and I'd personally avoid it.

I agree that implementing well variable risk is the top priority ATM.

[mechs]

Yup, since doog seems persistent to keep the max bet lower, I'd like to also request for at least 0.5% max bet for the time being.

While I work on the change, I am happy to put the max profit back up to 0.5%.  Half Kelly seems like a reasonable compromise.

How do I do this in a way that doesn't piss anyone off?  Changes without notice are "out of order".  Where do I announce it?  I don't have any way of contacting most of the investors.

Do I just post here "max profit will be adjusted to 0.5% of bankroll at (midnight tonight, UTC)" and leave it at that?  How much notice does it need?  That's only 2 hours away, and so probably not long enough.

What about "midnight pacific"?  That's 9 hours away.

Thoughts?  How much notice do people need?  And where's a good place to put such annoucements?

Announce it here, in the blog and in the FAQ and don't do it until Sunday UTC. That gives a few days for investors to divest if they wish.

[jgarzik]

Are there (or can there be) additional trusted parties outside a single physical location?  (rhetorical question, no need to answer publicly)

Bitcoin supports M-of-N transactions, for example, where two-of-three signatures could be required to unlock cold storage.

There are other variations on this idea with Shamir's Secret Sharing.  Decentralize the risk, eliminate "single points of failure" (or "key man risk").

[Gatekeeper]

I would say adjusting max profit up to 0.5% is ok to do anytime when Nak isn't playing or waiting on a deposit to arrrive in the middle of a session as it only really affects him anyway, so don't worry about giving too much notice.

I would probably leave it at 0.25% though as it seems to be doing quite well and with investment going back up the max bet will soon be 100btc. Don't feel pressured into raising it back up a bit if it proves that 0.25% is working well.

[mechs]

I would say adjusting max profit up to 0.5% is ok to do anytime when Nak isn't playing or waiting on a deposit to arrrive in the middle of a session as it only really affects him anyway, so don't worry about giving too much notice.

I would probably leave it at 0.25% though as it seems to be doing quite well and with investment going back up the max bet will soon be 100btc. Don't feel pressured into raising it back up a bit if it proves that 0.25% is working well.

It does seem that Nakowa's "strategy" less effective at the lower 0.25% max profit, variance certainly is.

[romerun]

Is there a way to see history of bets ? who broke the bank while I was sleeping and how they played ?

[Dabs]

I'm not a copy cat, but as a player, I would prefer seeing 1%, even though I will probably never reach that amount. I mean, realistically, I've only been playing with single and double digit BTC bets (although my current plan is to wait until I have 3 digits and make a bet.)

@akka, dunno what to say, I don't believe in ghosts. Satoshi or otherwise. But I have magic seeds. (I'm just playing, okay.)

[chriswen]

It isn't that simple. If it's the most profitable but you can spend 6 months in the red because of the high variance of the rare big bets, it loses one of its most attractive features, liquidity. And no, it isn't necessarily "being scared".

And remember it not a fixed bankroll.  When whales play, many players divest increasing variance of those remaining.  When bankroll goes down a lot, many new people reinvest and dilute the share of bankroll and therefore ROI of those that stayed invested. The 1% Kelly assumes a fixed bankroll for the house.

The 1% Kelly assumes a fixed bankroll for the house. = fixed min & max bets!

The 1% Kelly assumes a fixed bankroll for the house.

This is NOT TRUE.

Min and max bets is a terrible idea. That is why this website is so damn beautiful! Where else in the world can you bet anywhere between 0 and 8,500,000,000 units (satoshi, in this case) of anything? Don't lobby to kill one of the defining characteristics of the place!

min & max for a casino with any edge is a must and a healthy way for investors and OP to earn money in the long run.

Where else in the world can you bet anywhere between 0 and 8,500,000,000 units
in this case the investors are gambling and investors dont want to gamble IMHO

1) "Investors don't want to gamble" I beg to differ. Like someone said, this is a startup casino using startup money which is highly volatile. That's gambling. Just with a 1% edge. So I reject that premise. Plus it's real simple-- most investors on the site gamble some too.

2) We use the Kelly Criterion to determine the max profit, which is 1% of your investment (or .25% now). But that's the max. In reality, we're almost never risking full kelly, except on the occasional times when someone makes a bet that pays full max profit (usually a whale, but sometimes somebody going for a longshot, betting little for a big payoff). So when someone bets 0.008 when max profit is 80BTC, that wager is actually 0.0001x Kelly. Hardly relevant. And individual satoshi, even less. Look at the awesome Kelly chart someone uploaded a couple pages ago. Look how little volatility 0.0001x Kelly contributes. Thus, no need for a minimum, maximum is already taken care of rationally. Done.

EDIT: Keep in mind that casinos have minimums for several other reasons that are irrelevant here: segregate high-rollers from us poor folk, there are fixed costs to having dealers, it's physically difficult and risky to have the dealer have to handle wildly different denominations on one table (imagine having stacks or 1 cent chips next to a stack of $10,000 or $500,000 chips. That's a recipe for disaster!). Again, none of this is relevant at JD!

Another reason casinos have minimum bets is because they have to pay for employees and dealers.  It actually cost money to run a casino.  This is different from a online casino, where the costs are a lot less.  But, smaller bets do cost the server a bit and hog up cpu time so theres a delay on small bets.

[chriswen]

24 hours Doog - remember this is world wide you got people sleeping in Europe.

Post here and JD chat at minimum preference on front of site

Actually good compromise imo at 0.5% for now

OK, so I'm announcing it.  At midnight UTC Friday I'll change max profit to 0.5%.  (half Kelly).

That's in 25 hours.  I'll have the site spam this news to the chat periodically too.

Thank you doog!  Just wondering, you also work right?

[usagi]

Anyways, I've stopped begging a long time ago. The ones who "invested" in my "gambling security" did it willingly and contacted me directly. No one ever contributed to the "Group Bet" I started even earlier.

Oh. That was you?

I never really paid much attention to those messages o_o

I have a slight suggestion for dooglus in the way he implements the lucky number generation. Use the nonce twice. Once as concatenated input to the "secret", and second as concatenated input to the "message".

There is a better way, and one which doesn't require much coding or a reduction to kelly/4.

Remember, dabs, vegas rule #1: never talk a sale. Do you know what I mean?

[Bugpowder]

While I think full Kelly is still the best approach, half Kelly is a pretty good alternative, you really cut the variance in half and only sacrifice a quarter of the profit.

[julz]

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.

[Peter R]

Changing the topic a bit, but check out this graph of Nakowa's winnings over time:




Bugpowder had made some very nice histograms via simulation over 100,000 trials that show where on a PDF Nakowa's gambling profits were when he stopped (see p. 106 of this thread).  I wanted to devise an analytic way to do the same thing *over time* and I think I may have.  But I need some of the experts here to confirm or refute  

The variance of a *single* bet is

  V = B^2 * p * (1-p)

But the rule-of-thumb "variances add" does not apply to individual dice rolls: individual dice rolls are Bernoulli processes which do not have Gaussian PDFs.  (If you assume that variances add, then Nakowa's win shown above would be > 4 sigma, which would be really disconcerting!)

Borrowing some concepts from information theory, the entropy of a Bernoulli process is defined as:

  H(p) = -p log_2 (p) - (1-p) log_2 (1-p)

and entropy *does* add.  The entropy cloud above was calculated by accumulating the entropy from Bet #1 to Bet n:

  H_accumulated = H(.495)*B1^2 + H(.495)*B2^2 + ... + H(.495)*Bn^2

Here is my question: if I take the square root of H_accumulated at Bet n, it seems to give me standard deviation at that particular point in the bet sequence.  My PDF matches Bugpowder's results almost exactly.  

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

[geofflosophy]

Changing the topic a bit, but check out this graph of Nakowa's winnings over time:




Bugpowder had made some very nice histograms via simulation over 100,000 trials that show where on a PDF Nakowa's gambling profits were when he stopped (see p. 106 of this thread).  I wanted to devise an analytic way to do the same thing *over time* and I think I may have.  But I need some of the experts here to confirm or refute  

The variance of a *single* bet is

  V = B^2 * p * (1-p)

But the rule-of-thumb "variances add" does not apply to individual dice rolls: individual dice rolls are Bernoulli processes which do not have Gaussian PDFs.  (If you assume that variances add, then Nakowa's win shown above would be > 4 sigma, which would be really disconcerting!)

Borrowing some concepts from information theory, the entropy of a Bernoulli process is defined as:

  H(p) = -p log_2 (p) - (1-p) log_2 (1-p)

and entropy *does* add.  The entropy cloud above was calculated by accumulating the entropy from Bet #1 to Bet n:

  H_accumulated = H(.495)*B1^2 + H(.495)*B2^2 + ... + H(.495)*Bn^2

Here is my question: if I take the square root of H_accumulated at Bet n, it seems to give me standard deviation at that particular point in the bet sequence.  My PDF matches Bugpowder's results almost exactly.  

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

Your visualization shows him pretty much riding the 2 sigma line most of the way, no?

[Dabs]

Remember, dabs, vegas rule #1: never talk a sale. Do you know what I mean?

I'm sorry, what's that? Or what do you mean? Or maybe I'm dense and I don't get it.

Yes, that was me. You said in chat (or you PM'd me) to include you in the messages. Don't worry, didn't miss much. It was full of my gambler's fallacy as a constant reminder to all "investors" that it really was just a fun gamble and not a serious investment. Or maybe it was because of the mining stuff, I forget already.

[Peter R]

Your visualization shows him pretty much riding the 2 sigma line most of the way, no?

Yeah, I wish I could ride the 2 sigma line on $20,000+ bets!  He was one lucky SOB indeed!  

But notice that he was off to a good start early, and near Bet #33,000 he had fallen near the 1 stdev line.  So, what he did was not *that* improbable: he tries to "stop" at a time when he is in a high sigma zone.

I really hope he comes back when doog ups the max bet % to 0.5%.

[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.

[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.