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

[GOB]

Example 3: SUPER DUPER CRAZY NAKOWA^2 whale shows up and bets 20,580BTC at 98%, which pays 210BTC with 98% probability, and loses 20,580BTC with 2% probability. (this is * from above, there is an implicit "max bet" which is defined the maximum bet at 98% such that it pays the max profit.)

LOL   I'd love to see THAT bet.

I'd love to see that bet...lose.  

There is a tamer version of that scenario that did happen, though. If you look at the list of significant bets, the highest bet ever was 640btc at 90% and it lost! I believe that's still the record. I'd like to challenge nakowa to dethrone that bet... I suggest a 1000btc bet at 82% (profit=207btc). Are you man enough celeste/allover/nakowa?

[GOB]

Investor lowRisk: 10 000 BTC @ 0.25%, Investor highRisk: 10 000 BTC @1%.

Plan A: my Assumption which is actually flawed.
Plan B: GOB's implementation.
Plan C: An Alternative that is slightly modified version of GOB's.

Computation: A - difficult
B: Actually quite simple.
C: A bit more difficult than B.

Max Profit:
A: 25 + 100 = 125
B: 0 + 100 = 100
C: 25 + 100 = 125

Case 1: Bet 0.25% of house roll.  Bets 50 BTC @ 49.5%
A: LowRisk = ±10, HighRisk = ±40
B: LowRisk = ±25, HighRisk = ±25
C: LowRisk = ±25, HighRisk = ±25
A isn't exactly fair for risk-averse investors.  They're okay with risking 25 BTC.

Case 2: Bet 100 BTC @49.5%
A: LowRisk = ±20, HighRisk = ±80
B: LowRisk = ±0,  HighRisk = ±100
C: LowRisk = ±25, HighRisk = ±75

Case 3: Bet 125 BTC @49.5%
A: LowRisk = ±25, HighRisk = ±100
B: Bet too high
C: LowRisk = ±25, HighRisk = ±125
B - Without lowRisk helping out, the bet can't go as high.
Note for C that low risk can only win up to 25 btc.

Great summary.

It is true that with scenario B you don't get as high of a max profit. I knew that going in and I don't see it as a negative-- I think investors should be paid fairly/what makes sense/etc., and max profit will be what it'll be. The goal is not necessarily to maximize max profit, after all.

Despite that I see the value in your scenario C. However, I think what I posted a couple posts above still stands. In Case 3, without investor HighRisk being willing to risk 100BTC on each roll, site Max Profit would have been 25, and that bet might never have been made. Thus, LowRisk is profiting, or benefiting, or deriving value, from risk Highrisk was willing to provide.

However, now that I write that out, I'm realizing that is true of this site in general, in concept: the reason my tiny investment is able to profit is because a bunch of other people have invested an additional 40kbtc that draws bettors to the site.... hmmmm. I'm stumped.

Can I ask you a favor? Could you make a Case 4: Bet 110 BTC @49.5%? Specifically for Plan C? i.e. would LowRisk make 10 or 25 btc?

[organofcorti]

A while back I was trying to derive a function to describe how the site's profits change with maximum bet size and maximum player bank. I hit a double integral, fiddled with it for a while and moved on to something else.

Now that I'm about 50btc down as an investor, I thought I might take a shortcut and simulate the results.

The first chart  shows how the site investment changes as a function of number of bets,  the second hows how the site investment changes as a function of average bet size, and the final one is dedicated to a Nakowa, betting an average of 50% of the max 0.5% of the site investment.

I hope this provides some insight to investor, and allows you to estimate your risk a bit better. I might not have explained this well, so post any questions.

[Deprived]

Investor lowRisk: 10 000 BTC @ 0.25%, Investor highRisk: 10 000 BTC @1%.

Plan A: my Assumption which is actually flawed.
Plan B: GOB's implementation.
Plan C: An Alternative that is slightly modified version of GOB's.

Computation: A - difficult
B: Actually quite simple.
C: A bit more difficult than B.

Max Profit:
A: 25 + 100 = 125
B: 0 + 100 = 100
C: 25 + 100 = 125

Case 1: Bet 0.25% of house roll.  Bets 50 BTC @ 49.5%
A: LowRisk = ±10, HighRisk = ±40
B: LowRisk = ±25, HighRisk = ±25
C: LowRisk = ±25, HighRisk = ±25
A isn't exactly fair for risk-averse investors.  They're okay with risking 25 BTC.

Case 2: Bet 100 BTC @49.5%
A: LowRisk = ±20, HighRisk = ±80
B: LowRisk = ±0,  HighRisk = ±100
C: LowRisk = ±25, HighRisk = ±75

Case 3: Bet 125 BTC @49.5%
A: LowRisk = ±25, HighRisk = ±100
B: Bet too high
C: LowRisk = ±25, HighRisk = ±125
B - Without lowRisk helping out, the bet can't go as high.
Note for C that low risk can only win up to 25 btc.

Great summary.

It is true that with scenario B you don't get as high of a max profit. I knew that going in and I don't see it as a negative-- I think investors should be paid fairly/what makes sense/etc., and max profit will be what it'll be. The goal is not necessarily to maximize max profit, after all.

Despite that I see the value in your scenario C. However, I think what I posted a couple posts above still stands. In Case 3, without investor HighRisk being willing to risk 100BTC on each roll, site Max Profit would have been 25, and that bet might never have been made. Thus, LowRisk is profiting, or benefiting, or deriving value, from risk Highrisk was willing to provide.

However, now that I write that out, I'm realizing that is true of this site in general, in concept: the reason my tiny investment is able to profit is because a bunch of other people have invested an additional 40kbtc that draws bettors to the site.... hmmmm. I'm stumped.

Can I ask you a favor? Could you make a Case 4: Bet 110 BTC @49.5%? Specifically for Plan C? i.e. would LowRisk make 10 or 25 btc?

Scenario B makes no sense - as the low-risk investors aren't adding anything.  The high risk ones can cover all of the low bets anyway - so the low-risk are leeching profits without adding anything to max-bet.  And if there's a lot more low-risk than high-risk then you end up with choosing high-risk not making any difference (try it with 20k low-risk and 5k high-risk to see what I mean).

And not sure how case A isn't fair for low-risk because they're willing to risk 25 BTC.  High-risk are willing to risk 100 BTC.  Both are risking the same percentage of their maximums.

[Rampion]

Interesting to see how investment skyrocketed to 45k from 30k when Doog took max profit to 0,25%, and how it decreased to 42k when he took it up to 0,5%. People is indeed investing/divesting to adjust their risk and expected return depending on a given max profit.

About variable risk: I think we should think about setting up a limit, and run simulations on different scenarios. For example, if it's going to be possible to set up  something as high as 10% max profit (which would be reckless gambling, not investing), I have the impression that a very big portion of the investors would choose very high max profit - wouldn't that potentially create huge swings in the bankroll?

About leverage: formulas to reduce C-P risk are always welcome, but I'd proceed with a lot of care when implementing leverage. IMO, hard limit should be enforced. When leverage is possible I expect a super-inflated bankroll, and this could lead to many bad situations.

Doog, any thoughts on that?

[Skinnkavaj]

Does it matter how much BTC I have invested?
I had around 2,5 BTC invested and have made around 0.5 BTC profit.
Then I deposited 10 BTC more, pretty much nothing has changed I'm not seeing an increase in profit.
Should I just leave 2,5 BTC invested?

[broolstoryco]

Does it matter how much BTC I have invested?
I had around 2,5 BTC invested and have made around 0.5 BTC profit.
Then I deposited 10 BTC more, pretty much nothing has changed I'm not seeing an increase in profit.
Should I just leave 2,5 BTC invested?

Of course it matters how much you've invested. Your investment earns profit over time, it not like you will see an instant jump in profit once you invest. However, I would advise you to get a better understanding before committing your money in this way.

[Skinnkavaj]

Does it matter how much BTC I have invested?
I had around 2,5 BTC invested and have made around 0.5 BTC profit.
Then I deposited 10 BTC more, pretty much nothing has changed I'm not seeing an increase in profit.
Should I just leave 2,5 BTC invested?

Of course it matters how much you've invested. Your investment earns profit over time, it not like you will see an instant jump in profit once you invest. However, I would advise you to get a better understanding before committing your money in this way.

Isn't it enough understanding that I will make a profit of 1% of everything I have invested? What more do I need to know?

[broolstoryco]

Does it matter how much BTC I have invested?
I had around 2,5 BTC invested and have made around 0.5 BTC profit.
Then I deposited 10 BTC more, pretty much nothing has changed I'm not seeing an increase in profit.
Should I just leave 2,5 BTC invested?

Of course it matters how much you've invested. Your investment earns profit over time, it not like you will see an instant jump in profit once you invest. However, I would advise you to get a better understanding before committing your money in this way.

Isn't it enough understanding that I will make a profit of 1% of everything I have invested? What more do I need to know?

No, it is not, because that's not true. That is not how it works. You have an expected profit of 1% of bet volume times your share of the bankroll (the volume that users bet DURING your investment period). This profit is not guaranteed and can take wild swings (potentially into losses), as we have seen in the recent past.

[marcovaldo]

Does it matter how much BTC I have invested?
I had around 2,5 BTC invested and have made around 0.5 BTC profit.
Then I deposited 10 BTC more, pretty much nothing has changed I'm not seeing an increase in profit.
Should I just leave 2,5 BTC invested?

Lol, use your brain and read how it works.
The more you invest, the more you will win (or lose) if the casino win (or lose).

[Professor James Moriarty]

 I love how most of the investors here have the mentality of wall street guys. This is bitcoin and a gambling website , I first invested just because I had the coins and liked the idea , knew it would make money just because I liked it and there was interest in it. Not because of some charts.

[broolstoryco]

 I love how most of the investors here have the mentality of wall street guys. This is bitcoin and a gambling website , I first invested just because I had the coins and liked the idea , knew it would make money just because I liked it and there was interest in it. Not because of some charts.

we prefer to use facts to justify our 'investment' positions, not just our gut feelings.

[marcovaldo]

 I love how most of the investors here have the mentality of wall street guys. This is bitcoin and a gambling website , I first invested just because I had the coins and liked the idea , knew it would make money just because I liked it and there was interest in it. Not because of some charts.

But you are not representative of most investors and never will be.

[penta]

Investor lowRisk: 10 000 BTC @ 0.25%, Investor highRisk: 10 000 BTC @1%.

Plan A: my Assumption which is actually flawed.
Plan B: GOB's implementation.
Plan C: An Alternative that is slightly modified version of GOB's.

Computation: A - difficult
B: Actually quite simple.
C: A bit more difficult than B.

Max Profit:
A: 25 + 100 = 125
B: 0 + 100 = 100
C: 25 + 100 = 125

Case 1: Bet 0.25% of house roll.  Bets 50 BTC @ 49.5%
A: LowRisk = ±10, HighRisk = ±40
B: LowRisk = ±25, HighRisk = ±25
C: LowRisk = ±25, HighRisk = ±25
A isn't exactly fair for risk-averse investors.  They're okay with risking 25 BTC.

Case 2: Bet 100 BTC @49.5%
A: LowRisk = ±20, HighRisk = ±80
B: LowRisk = ±0,  HighRisk = ±100
C: LowRisk = ±25, HighRisk = ±75

Case 3: Bet 125 BTC @49.5%
A: LowRisk = ±25, HighRisk = ±100
B: Bet too high
C: LowRisk = ±25, HighRisk = ±125
B - Without lowRisk helping out, the bet can't go as high.
Note for C that low risk can only win up to 25 btc.

Great summary.

It is true that with scenario B you don't get as high of a max profit. I knew that going in and I don't see it as a negative-- I think investors should be paid fairly/what makes sense/etc., and max profit will be what it'll be. The goal is not necessarily to maximize max profit, after all.

Despite that I see the value in your scenario C. However, I think what I posted a couple posts above still stands. In Case 3, without investor HighRisk being willing to risk 100BTC on each roll, site Max Profit would have been 25, and that bet might never have been made. Thus, LowRisk is profiting, or benefiting, or deriving value, from risk Highrisk was willing to provide.

However, now that I write that out, I'm realizing that is true of this site in general, in concept: the reason my tiny investment is able to profit is because a bunch of other people have invested an additional 40kbtc that draws bettors to the site.... hmmmm. I'm stumped.

Can I ask you a favor? Could you make a Case 4: Bet 110 BTC @49.5%? Specifically for Plan C? i.e. would LowRisk make 10 or 25 btc?

Scenario B makes no sense - as the low-risk investors aren't adding anything.  The high risk ones can cover all of the low bets anyway - so the low-risk are leeching profits without adding anything to max-bet.  And if there's a lot more low-risk than high-risk then you end up with choosing high-risk not making any difference (try it with 20k low-risk and 5k high-risk to see what I mean).

And not sure how case A isn't fair for low-risk because they're willing to risk 25 BTC.  High-risk are willing to risk 100 BTC.  Both are risking the same percentage of their maximums.

+1 anything but case A would make no sense.

[chriswen]

Investor lowRisk: 10 000 BTC @ 0.25%, Investor highRisk: 10 000 BTC @1%.

Plan A: my Assumption which is actually flawed.
Plan B: GOB's implementation.
Plan C: An Alternative that is slightly modified version of GOB's.

Computation: A - difficult
B: Actually quite simple.
C: A bit more difficult than B.

Max Profit:
A: 25 + 100 = 125
B: 0 + 100 = 100
C: 25 + 100 = 125

Case 1: Bet 0.25% of house roll.  Bets 50 BTC @ 49.5%
A: LowRisk = ±10, HighRisk = ±40
B: LowRisk = ±25, HighRisk = ±25
C: LowRisk = ±25, HighRisk = ±25
A isn't exactly fair for risk-averse investors.  They're okay with risking 25 BTC.

Case 2: Bet 100 BTC @49.5%
A: LowRisk = ±20, HighRisk = ±80
B: LowRisk = ±0,  HighRisk = ±100
C: LowRisk = ±25, HighRisk = ±75

Case 3: Bet 125 BTC @49.5%
A: LowRisk = ±25, HighRisk = ±100
B: Bet too high
C: LowRisk = ±25, HighRisk = ±100  - OOOPS it's 100 here
B - Without lowRisk helping out, the bet can't go as high.
Note for C that low risk can only win up to 25 btc.

Great summary.

It is true that with scenario B you don't get as high of a max profit. I knew that going in and I don't see it as a negative-- I think investors should be paid fairly/what makes sense/etc., and max profit will be what it'll be. The goal is not necessarily to maximize max profit, after all.

Despite that I see the value in your scenario C. However, I think what I posted a couple posts above still stands. In Case 3, without investor HighRisk being willing to risk 100BTC on each roll, site Max Profit would have been 25, and that bet might never have been made. Thus, LowRisk is profiting, or benefiting, or deriving value, from risk Highrisk was willing to provide.

However, now that I write that out, I'm realizing that is true of this site in general, in concept: the reason my tiny investment is able to profit is because a bunch of other people have invested an additional 40kbtc that draws bettors to the site.... hmmmm. I'm stumped.

Can I ask you a favor? Could you make a Case 4: Bet 110 BTC @49.5%? Specifically for Plan C? i.e. would LowRisk make 10 or 25 btc?

Case 4: bet 110 BTC @49.5%
Break into two bets.  50 btc and 60 btc.
lowRisk ±50 , High Risk ±75

Okay, and the problem with Investment B, is what if there are multiple tiers.  Like 5 or even 3.  And what if the ratios were different.  It wouldn't scale and the top tier (most risk) investors would not actually have a bigger bankroll than the next lower tier.  You understand what I'm trying to say.  Its a great concept but what if the high risk doesn't even have enough money to go above the max profit for the low risk investors.  They wouldn't be attracting any whales.  SO it is the low risk investors helping high risk.

[Dabs]

No Guts, No Glory.
No Pain, No Gain.
No Charts, No Investments.
No Money, No Honey.
No Whales, No Profits.

(Ok, they're not all true.)

[Peter R]

Great charts, organofcorti!  These kind of contributions really help the discussion. 

Some commentary about your first chart:

This is basically a test of the Kelly-criterion, correct?  [For viewers out there like me who may have missed this at first, when interpreting these results notice that the vertical axis on each chart is scaled differently]

And it looks like your charts confirm that 1%-Kelly produces the largest expected returns. 

What I found interesting was your 2% case.  The Kelly-curve that GOB posted shows that expected profits is exactly 0 at 2% Kelly.  But the 50% line in your curve is negative.  I think both plots are correct, but *median* profit and *mean* profit are not the same thing.  The 2% Kelly distribution has negative median profit and zero mean profit. 

[organofcorti]

Great charts, organofcorti!  These kind of contributions really help the discussion. 

Cheers!

Some commentary about your first chart:

<img snip>

This is basically a test of the Kelly-criterion, correct? 

I still don't really understand how the Kelly Criteria works in this circumstance, so I'm not keen to call it a Kelly Criterion test. Call it an illustration of site profit as a function of average win size.

And it looks like your charts confirm that 1%-Kelly produces the largest expected returns. 

I hadn't taken that away from the charts at all - how do you see that? The average return is 1% per roll (so I didn't bother charting it), so I can't see how the expected return would change by changing the max % bet. Or did I miss something? It's complicated, so I might have.

What I would expect to change is the percentiles. As the max bet increases, a negative site profit is more likely than a positive one. But there will be huge outliers that will make up for it.

What I found interesting was your 2% case.  The Kelly-curve that GOB posted shows that expected profits is exactly 0 at 2% Kelly.  But the 50% line in your curve is negative.  I think both plots are correct, but *median* profit and *mean* profit are not the same thing. 

Can you link to the curve you mention? I haven't seen it.

But what you say is quite true - mean and median are not the same, and there are lots of high variance distributions where this happens (distribution of income for example median is much less than the mean).

The 2% Kelly distribution has negative median profit and zero mean profit. 

Honestly I can't see how this could possibly happen? Zero median maybe, but not zero mean. Even if the max bet was 100 percent, the expected return would still be 1%

[Peter R]

Organofcoti, here is the chart that GOB posted:



It blows my mind too for the reasons you mentioned, but I think it still applies to just-dice.

I may have overreached, but I think if you were to plot your 0.25%, 0.5%, 1% and 2% curves with a vertical-axis that had the same scaling for each plot, and if, somehow, you could also plot a line for the mean profit, then I think it would verify the Kelly curve shown above. 

Your vertical axis is on a log scale.  So, I think it follows that the stuff above the 50% percentile line contributes more to the profit than the stuff below the 50% line.  So the mean *must* be greater than the median for the Kelly distribution. 

[dooglus]

If you pick 0.25% and I pick 1%, then I make (or lose) 4 times as much as you.  Simple as that.  

It's not as simple as that though.

If you both invest 100 BTC, and a whale constantly bets to win the max profit, and loses, then the 1% guy wins more than 4 times that of the 0.25% guy:

       A (   p/l)        B (   p/l)     roll    max    ratio
-------- (------) -------- (------) -------- ------ --------
100.2500 (0.2500) 101.0000 (1.0000) 200.0000 1.2500 4.000000
100.5006 (0.5006) 102.0100 (2.0100) 201.2500 1.2606 4.014981
100.7519 (0.7519) 103.0301 (3.0301) 202.5106 1.2714 4.030050
101.0038 (1.0038) 104.0604 (4.0604) 203.7820 1.2822 4.045206
101.2563 (1.2563) 105.1010 (5.1010) 205.0642 1.2931 4.060451
101.5094 (1.5094) 106.1520 (6.1520) 206.3573 1.3042 4.075785
101.7632 (1.7632) 107.2135 (7.2135) 207.6614 1.3153 4.091208
102.0176 (2.0176) 108.2857 (8.2857) 208.9767 1.3265 4.106721
102.2726 (2.2726) 109.3685 (9.3685) 210.3033 1.3379 4.122325
...
127.4046 (27.4046) 262.5266 (162.5266) 387.0141 2.9170 5.930639
127.7231 (27.7231) 265.1518 (165.1518) 389.9311 2.9438 5.957197
128.0424 (28.0424) 267.8033 (167.8033) 392.8749 2.9708 5.983919

After 100 or so whale losses, the 1% guy's profit is almost 6 times that of the 0.25% guy.  His share of the bankroll keeps increasing relative to the more timid guy.

The converse is also true.  If the whale wins, then the 1% guy loses less than 4 times as much as the 0.25% guy, and after around 100 whale wins has lost around 3 times as much as the 0.25% guy.  His share of the bankroll keeps decreasing relative to the more timid guy.

       A (   p/l)        B (   p/l)     roll    max    ratio
-------- (------) -------- (------) -------- ------ --------
 99.7500 (-0.2500)  99.0000 (-1.0000) 200.0000 1.2500 4.000000
 99.5006 (-0.4994)  98.0100 (-1.9900) 198.7500 1.2394 3.984981
 99.2519 (-0.7481)  97.0299 (-2.9701) 197.5106 1.2289 3.970050
 99.0037 (-0.9963)  96.0596 (-3.9404) 196.2818 1.2184 3.955206
 98.7562 (-1.2438)  95.0990 (-4.9010) 195.0633 1.2081 3.940449
 98.5093 (-1.4907)  94.1480 (-5.8520) 193.8552 1.1979 3.925778
 98.2631 (-1.7369)  93.2065 (-6.7935) 192.6574 1.1878 3.911192
 98.0174 (-1.9826)  92.2745 (-7.7255) 191.4696 1.1777 3.896691
 97.7724 (-2.2276)  91.3517 (-8.6483) 190.2919 1.1678 3.882275
 97.5279 (-2.4721)  90.4382 (-9.5618) 189.1241 1.1579 3.867943
...
 78.4426 (-21.5574)  37.7237 (-62.2763) 116.7439 0.5776 2.888855
 78.2464 (-21.7536)  37.3464 (-62.6536) 116.1662 0.5733 2.880154
 78.0508 (-21.9492)  36.9730 (-63.0270) 115.5929 0.5691 2.871500