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

[rarefied]

Fun little paper on the Gambler's ruin problem that you can play around with: http://www.columbia.edu/~ks20/FE-Notes/4700-07-Notes-GR.pdf

Of course these equations need some modification to take into account the varying max bet size, but I figure there's only a 0.9% chance of someone with a bankroll equal to the house's winning 90% of the bankroll before losing 90% of his bankroll at a 1% max bet and 2x payout.

[Rampion]

100% agree with watchwoord and RationalSpeculator.

(3) You're still free to *prefer* that maxbet = Kelly value. But it's a preference, nothing more, nothing less. Right now, investors are obviously not of the same opinion about this. But you need to stop calling those who have a different preference from your own "irrational". It's disingenious, and rather insulting.

I strongly disagree on this. As soon as dooglus changed the max profit to 1%, a violent riot started on JD's chat. Only mechs supported that decision.

After that somebody made a poll, and 2/3 of people said that going to 0.25% max profit was a mistake.

Just read these forums, the vast majority of investors is annoyed by the sudden change - let's remember that we all signed up for a site that had 1% edge and 1% max profit.

That said, we all know dooglus NEEDS support, and we all like him. You'll see how mechs took most of the heat, basically because most people feels bad attacking dooglus, I guess the reason is that he demonstrated he is extremely capable, smart and trustworthy.  

So, let me ask you: what investors do prefer fractional kelly instead of optimal kelly? Those who voted in the poll prefer optimal kelly. Those writing in here (except a few exceptions) prefer optimal kelly.

[DumbFruit]

This is how you do a sliding scale:

1.) Max return is whatever the highest investor(s) is willing to lose. Doesn't matter if it's percentage or a literal number.

Edit: A lower tier could possibly crowd out a higher tier, but I don't think that's a problem. They would just get lumped together in the payout.  
Edit2: Removed the stupid.
Max Return = (Tier1Limit*Tier1Bankroll)+(Tier2Limit*Tier2Bankroll)... etc
or
Max return = (.0025*2000)+(0.005*2000)+(0.01*2000)

2.) If a gambler loses the bet, divide the sum by the number of "tiers" that intersect it.

Example:
All investors have 400btc stake, and there are 5 investors in each tier.

35 btc max return, and 35 btc lost by the gambler.
1% tier = 17.5btc

.5% tier = 8.75btc

.25% tier = 8.75btc

Note: Tiers do not necessarily need to be percentages.

Edit: Also, the distribution could be very different due to different bankrolls in the tiers.

3.) The top tier is divided among the top investor(s) in proportion to their bankroll.

4.) Each following tier is divided equally among every investor in the tier and all tiers above, in proportion to their portion of these tier(s) bankroll.

Continued Example:
1% tier would yield 3.5 bitcoins for all 1% investors. 17.5*(400/2000)
.5% tier would yield .875 bitcoins for every tier .5% investors and tier 1% investors. 8.75*(400/4000)
.25% tier would yield .58 btc to each .25% investor and all tiers above.  8.75*(400/6000)

Totals:
.25% investor --> .58btc
.5% investor --> 1.45btc
1% investor --> 4.95btc

The losses propagate samesies. Each person gets a return/loss in proportion to the amount they "contribute" to the bet.

My example doesn't quite come out to 35, because I did some rounding for brevity, but that's the idea. While theoretically you could have an arbitrary amount of tiers, you likely would want to limit them.

Edit: Updated numbers to something more realistic.

[oda.krell]

100% agree with watchwoord and RationalSpeculator.

(3) You're still free to *prefer* that maxbet = Kelly value. But it's a preference, nothing more, nothing less. Right now, investors are obviously not of the same opinion about this. But you need to stop calling those who have a different preference from your own "irrational". It's disingenious, and rather insulting.

I strongly disagree on this. As soon as dooglus changed the max profit to 1%, a violent riot started on JD's chat. Only mechs supported that decision.

After that somebody made a poll, and 2/3 of people said that going to 0.25% max profit was a mistake.

Just read these forums, the vast majority of investors is annoyed by the sudden change - let's remember that we all signed up for a site that had 1% edge and 1% max profit.

That said, we all know dooglus NEEDS support, and we all like him. You'll see how mechs took most of the heat, basically because most people feels bad attacking dooglus, I guess the reason is that he demonstrated he is extremely capable, smart and trustworthy.  

So, let me ask you: what investors do prefer fractional kelly instead of optimal kelly? Those who voted in the poll prefer optimal kelly. Those writing in here (except a few exceptions) prefer optimal kelly.

Bullshit. It's pointless to argue further on this, I'm out of the discussion. Seriously rampion, you lost a lot of my respect today (not that it really matters).

[RationalSpeculator]

Once you do that you'll see that 1% max bet is the optimal balance.

RationalSpeculator: 1% of what?  The amount physically deposited at JD, or the amount an investor is willing to risk [which may be larger than what they physically deposited with JD in an effort to further reduce counter-party risk]?

Thanks for the question Peter

Indeed 1% max bet of the capital you are willing to risk on the gambling adventure, not perse deposited on JD.

[Rampion]

100% agree with watchwoord and RationalSpeculator.

(3) You're still free to *prefer* that maxbet = Kelly value. But it's a preference, nothing more, nothing less. Right now, investors are obviously not of the same opinion about this. But you need to stop calling those who have a different preference from your own "irrational". It's disingenious, and rather insulting.

I strongly disagree on this. As soon as dooglus changed the max profit to 1%, a violent riot started on JD's chat. Only mechs supported that decision.

After that somebody made a poll, and 2/3 of people said that going to 0.25% max profit was a mistake.

Just read these forums, the vast majority of investors is annoyed by the sudden change - let's remember that we all signed up for a site that had 1% edge and 1% max profit.

That said, we all know dooglus NEEDS support, and we all like him. You'll see how mechs took most of the heat, basically because most people feels bad attacking dooglus, I guess the reason is that he demonstrated he is extremely capable, smart and trustworthy.  

So, let me ask you: what investors do prefer fractional kelly instead of optimal kelly? Those who voted in the poll prefer optimal kelly. Those writing in here (except a few exceptions) prefer optimal kelly.

Bullshit. It's pointless to argue further on this, I'm out of the discussion. Seriously rampion, you lost a lot of my respect today (not that it really matters).

Sorry for that Oda, but I see what I see. Care to elaborate about where is the BS?

Just read J-D's chat logs. Just check the forum. Just check the poll.

I hope you also realize that the level of investment during Nakowa's "raid" was still 30k, which means that max. 1/3 of the investor divested, which is quite a big sum (and I guess that made doog very nervous), but the majority of investors (2/3) kept the money on the line, meaning they were OK with the risk.

Finally, don't you agree that we have ALL signed up for a site that had 1% max profit? That was VERY CLEAR on the "invest" page. I personally did my calculations, projecting roughly a 100% return in one year. If some of the few investors that whined about Nakowa do not understand what 1% max profit means, or what variance is, or they just send their money blindly without thinking, we should just add a big disclaimer explaining that investing in a casino = variance.

I will keep supporting dooglus, and in fact I increased my investment x4 just after the max profit was reduced to 0,25%. It was the only way to recoup my loss, and in fact I succeeded and covered it today thanks to Nakowa coming back. But I'm still an investor, I think I have the right to explain my position. You might think that I already recovered my loss, so why I'm still whining? Just because I had to risk and tie to the site 4x the coins I initially wanted to invest - that's not cool at all in my book.

[RationalSpeculator]

I see. The circlejerk continues. Let me try again:

(1) Our favorite whale is back. Please stop repeating the argument that somehow Dooglus chased him away. That obviously didn't happen.

(2) Kelly value is not the "only rational value" to base maxbet on. It's dead simple: it's provably the correct value for optimal growth. That's all. If you don't see the difference between that and "the only rational choice", you're hopeless.

(3) You're still free to *prefer* that maxbet = Kelly value. But it's a preference, nothing more, nothing less. Right now, investors are obviously not of the same opinion about this. But you need to stop calling those who have a different preference from your own "irrational". It's disingenious, and rather insulting.

(4) The long-term solution seems to be clear: Dooglus will (probably) implement a market determined maxbet, i.e. investors choose their own exposure. The details are maybe still open (what's then percent range investors can chose? will there be a forced delay to limit wild maxbet swings?), but in principle, the idea is fantastic and should satisfy all.

(5) In the meantime, if you prefer maxbet to go up again, go ahead, lobby for it. But keep your arguments somewhat respectful (see points 2 and 3 above).

... and now something that I really feel needs to be said in all of this:

(6) Dooglus, you're doing a fantastic job. Most of us investors know this, even if we don't always show it. Maybe some of us didn't completely agree with your sudden maxbet reduction yesterday, but seriously, j-d is the first gambling site that I feel comfortable with both as an (occasional) gambler and as an investor. Keep that in mind please, whenever you start doubting your project.

Oda, I see you are getting tired with this too. I think I got it finally, bare with me if you will.

Problem: volatility risk too high

Solution 1: Reduce Kelly Size
- Reduces volatility risk = yes
- Reduces returns = yes
- Reduces counterparty risk = no

Solution 2: Reduce invested amount
- Reduces volatility risk = yes
- Reduces returns = yes
- Reduces counterparty risk = yes

[xypos]

I hope you also realize that the level of investment during Nakowa's "raid" was still 30k, which means that max. 1/3 of the investor divested, which is quite a big sum (and I guess that made doog very nervous), but the majority of investors (2/3) kept the money on the line, meaning they were OK with the risk.

Totally BS.
How can you argue by imagining what other people thinks? You have no idea why they did not divest, and I can see plenty of reasons. It does not mean at all that they were OK with the risk.



3 months: (expected profit) = 20 k btc.
Profit = - 780 btc.


WTF? Only doog got some cash from JD

[Keyser Soze]

I think your deductions are incorrect though since you exclude counterparty risk.

Once you do that you'll see that 1% max bet is the optimal balance.

Those that want less volatility are better off investing less than reducing Kelly Size. Because reducing Kelly Size reduces returns so you need to increase your investment to have the same returns again. Reducing one risk, and increasing another means no reduction of your overall risk, whereas just investing less but keeping the optimal balance would actually have reduced your risk.

Am I explaining this correctly?

This is assuming that both risks are equal. The counterparty risk is difficult to quantify and will differ for each investor.

[romerun]

1% max bet is alright to give a few extra miles to martingale folks, "once in a while" max 1% bet is not so dangerous to the house, but it's so hairy when it's abused. Every time Nak is full-on starting his base at 100, everybody leaving coin invested is as risky as making bet himself.

[maqifrnswa]

This is how you do a sliding scale:

1.) Max return is whatever the highest investor(s) is willing to lose. Doesn't matter if it's percentage or a literal number.

2.) If a gambler loses the bet, divide the sum by the number of "tiers" that intersect it.

Example:
100 btc max return, and 100 btc lost by the gambler.

1% tier = 50btc.

.5% tier = 25btc.

.25% tier = 25btc.

Note: Tiers do not necessarily need to be percentages.
...

why are people so obsessed with tiers? why can't it be continuous? The counter argument was that not using tiers would be computationally intensive. I believe it is as difficult as the current implimentation and introducing tiers is computationally intensive (and confusing to investors/players). Right now JD keeps track of a player's fraction of the bankroll and distributes accordingly. Instead, with "set your own max bet percentage," JD needs to keep track of the player's fraction of the max bet and distribute accordingly. No need to introduce any other changes, no need for delays nor fractional reserve... everything stays the same as it is, no additional complicated rules.

Players get to tune their variance and return to maximize their own utility, gamblers have a high maximum bet in a very similar fashion as before with the same edge.

[Peter R]

I will keep supporting dooglus, and in fact I increased my investment x4 just after the max profit was reduced to 0,25%.

Ha! I did the same thing!!  I figured now that there is 4X less worst-case variance, I am willing to risk 4X as much (well, actually 3X as much, b/c I also accounted for the additional counter-party risk). So, I am now earning a larger % of the pie than the investors avoiding the variance  

So, if everyone does this, I guess we'll all end up in a similar position as before, but with WAY more exposure to counter-party and legal risk.

[Rampion]

I hope you also realize that the level of investment during Nakowa's "raid" was still 30k, which means that max. 1/3 of the investor divested, which is quite a big sum (and I guess that made doog very nervous), but the majority of investors (2/3) kept the money on the line, meaning they were OK with the risk.

Totally BS.
How can you argue by imagining what other people thinks? You have no idea why they did not divest, and I can see plenty of reasons. It does not mean at all that they were OK with the risk.



3 months: (expected profit) = 20 k btc.
Profit = - 780 btc.


WTF? Only doog got some cash from JD

Well, Oda is the one saying "investors wanted to go to fractional kelly", and I'm just piling up facts that seem to indicate the opposite. I'm also asking where are those investors, and who they are. I see forums and J-D chat full of people wanting to keep optimal kelly, polls with 2/3 of people wanting optimal kelly, and I didn't see such an amount of divestments. That's all. Plus, everybody who invested sent their money to a site that had 1% max profit. I want to assume the majority of people think before investing, and calculate what kind of returns they will probably get. I for one did it, and the hard cold fact is that the expected yearly return is now MUCH lower than when I invested.

I will keep supporting dooglus, and in fact I increased my investment x4 just after the max profit was reduced to 0,25%.

Ha! I did the same thing!!  I figured now that there is 4X less worst-case variance, I am willing to risk 4X as much (well, actually 3X as much, b/c I also accounted for the additional counter-party risk). So, I am now earning a larger % of the pie than the investors avoiding the variance  

So, if everyone does this, I guess we'll all end up in a similar position as before, but with WAY more exposure to counter-party and legal risk.

Well, that was the obvious way to try to recoup the losses *if* Nakowa showed up again (which he did), as the max profit was taken dpwm to 0.25%. What really sucks is that you are suddenly forced to either commit 4x the amount of coin, or to get stuck with a big loss. That's basically why all this turmoil started (plus the fact that you just don't treat like sh*t your best customers).

[Peter R]

Oda, I see you are getting tired with this too. I think I got it finally, bare with me if you will.

Problem: volatility risk too high

Solution 1: Reduce Kelly Size
- Reduces volatility risk = yes
- Reduces returns = yes
- Reduces counterparty risk = no

Solution 2: Reduce invested amount
- Reduces volatility risk = yes
- Reduces returns = yes
- Reduces counterparty risk = yes

+10000000

[Bitsinmyhead]

Actually the only people who should lobby for a 1% max bet is those who already have all their coins invested in JD. Everyone else would be better off by the site using less than full Kelly and just increasing their amount invested...

That can only be true if you think the chances of Dooglus running with the money, or being hacked, or losing all backups is exactly zero. Otherwise full-Kelly is and always will be optimal.

It is correct that the risk of Dooglus running will impact the optimal bet size, your conclusion is however wrong. This little example will illustrate for you:

Lets assume risk of Dooglus running with all the money is 5%. You invest 100BTC when max bet is 1% (lets assume this gives a 50% expected growth) so expected growth after 1 year is 50BTC. And lets assume your investment will have an expected variance of 0.1 so here the variance is 0.1*100 = 10BTC.

Now lets say you instead invest 150BTC when max bet is 0.5%. Growth of this investment will be 150*50%*0.75 = 56.25BTC. Variance will be 150*0.1*0.5 = 7.5BTC.

However we need to adjust for the fact that Dooglus might run with all the money. This is costing you 50*5%=2.5BTC extra in equity with the now 50BTC extra investment. It will also add a little extra variance to your situation, but because the chances of him running are small the variance will still be less than 10BTC.

Conclusion: Even with 5% chance of Dooglus running with all your money investing 150BTC instead of 100BTC at 0.5% max bet instead of 1% max bet will give you higher expectation and a lower variance.

Another benefit of a lower max bet is that if a player is cheating or has hacked the site the investors will lose less before it is discovered. I actually think these benefits might even totally cancel out the risks of Dooglus running.

[nicolaennio]

https://bitcointalk.org/index.php?topic=301412.0

I am getting more and more convinced that nakowa is one of the main investors of just-dice and he is just advertising the website

[Rampion]

https://bitcointalk.org/index.php?topic=301412.0

I am getting more and more convinced that nakowa is one of the main investors of just-dice and he is just advertising the website

Nakowa was/is indeed one of the best promos for the site. I was there while he was playing and the max profit was suddenly reduced to STOP him. That's unfair and lame, it was a rushed decision driven by emotions - and it was a very BAD decision. You want to cuddle and support Nakowa, he is the best customer you can have.

[DumbFruit]

why are people so obsessed with tiers? why can't it be continuous?

I think if you walked through the algorithm I proposed, you could see very clearly why having a substantial amount of tiers would add significantly to the computations.

Every step down in the tier requires a new reiteration across the users in every tier above it.

[nicolaennio]

https://bitcointalk.org/index.php?topic=301412.0

I am getting more and more convinced that nakowa is one of the main investors of just-dice and he is just advertising the website

Nakowa was/is indeed one of the best promos for the site. I was there while he was playing and the max profit was suddenly reduced to STOP him. That's unfair and lame, it was a rushed decision driven by emotions - and it was a very BAD decision. You want to cuddle and support Nakowa, he is the best customer you can have.

Yes, in this sense just-dice has collected many players into a single one which is now playing against an almost equivalent one. For sure this was not the intention of dooglus and attracted a lot of attention and perplexities that were not initially considered. What I mean is that possibly nakowa himself has a lot of money invested in the website (partly playing against himself, yeah) and in that case his bankroll may be, in total, even larger than the one of all the others players all together. Thus it would be a rational plan to bet a lot against a small player (even if he is in advantage with probabilities) and he would not be the victim of the gambler fallacy at all.

Please Rampion tell me your opinion on this hypothesis.

[utens]

I'll like to see max bet at .5%