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

[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.

Um, I think there's an error in your case 4. You have LowRisk at ±50, but their max profit was 10,000 * 0.25% = 25btc

Yeah, that's a good point. I do understand what you're saying.

Yeah, I don't know what I was thinking.
Scenario C:
Case 1: lowRisk ±25, highRisk ±25
Case 2: lowRisk ±25, highRisk ±75
Case 3: lowRisk ±25, highRisk ±100
Case 4: lowRisk ±25, highRisk ±85

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[dooglus]

I understand the max bet part, but what if a player bets 1BTC and wins (way below a max bet).  Do the 0.25% and 1% guy participate equally based on portion of the bankroll or does the 1% person get 4X more than the 0.25% investor?

People who run 100% kelly get 4 times the action of people running 25% kelly, yes.  By definition, pretty much.

A says "I'm willing to risk up to 0.25 BTC".  B says "I'm willing to risk up to 1 BTC".  We sum those two, and present to the gambler "the site is willing to risk up to 1.25 BTC".

If the gambler comes back and says to the site "I'll take 50% of what you're offering", we say to each investor "he's taking 50% of your offer".

I don't see how any other way would be fair.

[wachtwoord]

I understand the max bet part, but what if a player bets 1BTC and wins (way below a max bet).  Do the 0.25% and 1% guy participate equally based on portion of the bankroll or does the 1% person get 4X more than the 0.25% investor?

People who run 100% kelly get 4 times the action of people running 25% kelly, yes.  By definition, pretty much.

A says "I'm willing to risk up to 0.25 BTC".  B says "I'm willing to risk up to 1 BTC".  We sum those two, and present to the gambler "the site is willing to risk up to 1.25 BTC".

If the gambler comes back and says to the site "I'll take 50% of what you're offering", we say to each investor "he's taking 50% of your offer".

I don't see how any other way would be fair.

Thanks Dooglus, this method is completely fair.

[dooglus]

roll    max    ratio
200.0000 1.2500 4.000000

In this example, you're setting the max bet to 1% of the total bankroll (20,000 on the first roll).  But this is wrong!  The .25% people are willing to risk .25% of their 10,000, or 25.  The 1% people are willing to risk 1% of their 10,000, or 100.  The max bet on the first roll is 125, not 200.

I think you're reading my table wrong.  I've deleted all but the relevent parts in the quote above.

On the first bet, the bankroll is 200 and the max bet is 1.25

I'm using dot as a decimal point, not a thousands-separator in case that's the issue.

[Deprived]

I understand the max bet part, but what if a player bets 1BTC and wins (way below a max bet).  Do the 0.25% and 1% guy participate equally based on portion of the bankroll or does the 1% person get 4X more than the 0.25% investor?

People who run 100% kelly get 4 times the action of people running 25% kelly, yes.  By definition, pretty much.

A says "I'm willing to risk up to 0.25 BTC".  B says "I'm willing to risk up to 1 BTC".  We sum those two, and present to the gambler "the site is willing to risk up to 1.25 BTC".

If the gambler comes back and says to the site "I'll take 50% of what you're offering", we say to each investor "he's taking 50% of your offer".

I don't see how any other way would be fair.

The other ways also only work in certain ratios of high:low risk investors.

If you try looking at a situation with 20k invested low-risk and 2k invested high-risk in some of the other proposals you immediately see that there ends up being no difference between them.

[dooglus]

I'm hoping and expecting the latter.

You're right.

Then this really is not so much a set your own kelly % more more a set your own leverage.

I don't think so.  Leverage would be if I was to consider your bankroll to be N times bigger than you've actually deposited.

But that's not what this is.  What you're doing here is deciding what percentage of your investment you want to risk at most, and then, when the player decides to only bet X% of the maximum, you get to risk X% of the most you're willing to risk.

[mechs]

I'm hoping and expecting the latter.

You're right.

Then this really is not so much a set your own kelly % more more a set your own leverage.

I don't think so.  Leverage would be if I was to consider your bankroll to be N times bigger than you've actually deposited.

But that's not what this is.  What you're doing here is deciding what percentage of your investment you want to risk at most, and then, when the player decides to only bet X% of the maximum, you get to risk X% of the most you're willing to risk.

Why would I invest 500 BTC at 0.25% when I can just invest 125BTC at 1% then and not have the CP risk for the othet 375 BTC?

[Peter R]

I understand the max bet part, but what if a player bets 1BTC and wins (way below a max bet).  Do the 0.25% and 1% guy participate equally based on portion of the bankroll or does the 1% person get 4X more than the 0.25% investor?

People who run 100% kelly get 4 times the action of people running 25% kelly, yes.  By definition, pretty much.

A says "I'm willing to risk up to 0.25 BTC".  B says "I'm willing to risk up to 1 BTC".  We sum those two, and present to the gambler "the site is willing to risk up to 1.25 BTC".

If the gambler comes back and says to the site "I'll take 50% of what you're offering", we say to each investor "he's taking 50% of your offer".

I don't see how any other way would be fair.

Thanks Dooglus, this method is completely fair.

+1

[chriswen]

I'm hoping and expecting the latter.

You're right.

Then this really is not so much a set your own kelly % more more a set your own leverage.

I don't think so.  Leverage would be if I was to consider your bankroll to be N times bigger than you've actually deposited.

But that's not what this is.  What you're doing here is deciding what percentage of your investment you want to risk at most, and then, when the player decides to only bet X% of the maximum, you get to risk X% of the most you're willing to risk.

But, this means that the low risk investors are susceptible to just as much bet size variance. 

[dooglus]

Why would I invest 500 BTC at 0.25% when I can just invest 125BTC at 1% then and not have the CP risk for the othet 375 BTC?

Because you would get less variance.

Suppose a whale bets max bet and wins 20 times.  If you invest 500 BTC at 0.25%, you'll still have 95% of your bankroll left:

>>> a=500
>>> for i in range(20): a *= (1-0.0025); print "%.2f" % (a*100/500,),
99.75 99.50 99.25 99.00 98.76 98.51 98.26 98.02 97.77 97.53 97.28 97.04 96.80 96.56 96.31 96.07 95.83 95.59 95.36 95.12

But if you invest 125 BTC at 1%, you'll have only 82% of it left:

>>> a=125
>>> for i in range(20): a *= (1-0.0100); print "%.2f" % (a*100/125,),
99.00 98.01 97.03 96.06 95.10 94.15 93.21 92.27 91.35 90.44 89.53 88.64 87.75 86.87 86.01 85.15 84.29 83.45 82.62 81.79

Your risk of ruin is much greater if you invest at 1% than if you invest at 0.25%.

[dooglus]

But, this means that the low risk investors are susceptible to just as much bet size variance. 

Yes, because bets vary in size...

Forcing the 1% investors to take all the variance so the 0.25% investors don't have to isn't fair on the 1% investors.

Investing at 0.25% allows you to risk less of your investment per roll.  It doesn't change the fact that most bets aren't near the maximum.  It allows you to select your own risk of ruin as you see fit.

[Deprived]

Why would I invest 500 BTC at 0.25% when I can just invest 125BTC at 1% then and not have the CP risk for the othet 375 BTC?

Because you would get less variance.

Suppose a whale bets max bet and wins 20 times.  If you invest 500 BTC at 0.25%, you'll still have 95% of your bankroll left:

>>> a=500
>>> for i in range(20): a *= (1-0.0025); print "%.2f" % (a*100/500,),
99.75 99.50 99.25 99.00 98.76 98.51 98.26 98.02 97.77 97.53 97.28 97.04 96.80 96.56 96.31 96.07 95.83 95.59 95.36 95.12

But if you invest 125 BTC at 1%, you'll have only 82% of it left:

>>> a=125
>>> for i in range(20): a *= (1-0.0100); print "%.2f" % (a*100/125,),
99.00 98.01 97.03 96.06 95.10 94.15 93.21 92.27 91.35 90.44 89.53 88.64 87.75 86.87 86.01 85.15 84.29 83.45 82.62 81.79

Your risk of ruin is much greater if you invest at 1% than if you invest at 0.25%.

Not sure that's true in the second case - as their BR is what they have left of the 125 plus the untouched 375 they have in cold storage.

Broadly speaking having the two risks is similar to (but not quite the same) as if the people wanting low variance did what they should have done in the first place - and withdrew 3/4 of their BR.  But as they can't do BR management themselves, you're having to do it for them.

For those who want to avoid massive losses, the amusing thing is that a high risk level SHOULD be their friend.  Their optimal strategy if they want to avoid large downswings is to invest a small percentage of their BR at a very high level risk level - giving them tiny CP risk AND a stop-loss to curtail losses if a whale hits a large winning streak.  Of course they then also give up a lot in situations where a large down-swing is followed by a large up-swing - but until they accept they can't get the benefits of massive variance in an upward direction without accepting the reverse nothing is going to make them happy.  Unless you were to specifically cater for them by allowing them to only cover small bets (where their money isn't needed) out of some sense of charity.

[mechs]

Why would I invest 500 BTC at 0.25% when I can just invest 125BTC at 1% then and not have the CP risk for the othet 375 BTC?

Because you would get less variance.

Suppose a whale bets max bet and wins 20 times.  If you invest 500 BTC at 0.25%, you'll still have 95% of your bankroll left:

>>> a=500
>>> for i in range(20): a *= (1-0.0025); print "%.2f" % (a*100/500,),
99.75 99.50 99.25 99.00 98.76 98.51 98.26 98.02 97.77 97.53 97.28 97.04 96.80 96.56 96.31 96.07 95.83 95.59 95.36 95.12

But if you invest 125 BTC at 1%, you'll have only 82% of it left:

>>> a=125
>>> for i in range(20): a *= (1-0.0100); print "%.2f" % (a*100/125,),
99.00 98.01 97.03 96.06 95.10 94.15 93.21 92.27 91.35 90.44 89.53 88.64 87.75 86.87 86.01 85.15 84.29 83.45 82.62 81.79

Your risk of ruin is much greater if you invest at 1% than if you invest at 0.25%.

Not sure that's true in the second case - as their BR is what they have left of the 125 plus the untouched 375 they have in cold storage.

Broadly speaking having the two risks is similar to (but not quite the same) as if the people wanting low variance did what they should have done in the first place - and withdrew 3/4 of their BR.  But as they can't do BR management themselves, you're having to do it for them.

For those who want to avoid massive losses, the amusing thing is that a high risk level SHOULD be their friend.  Their optimal strategy if they want to avoid large downswings is to invest a small percentage of their BR at a very high level risk level - giving them tiny CP risk AND a stop-loss to curtail losses if a whale hits a large winning streak.  Of course they then also give up a lot in situations where a large down-swing is followed by a large up-swing - but until they accept they can't get the benefits of massive variance in an upward direction without accepting the reverse nothing is going to make them happy.  Unless you were to specifically cater for them by allowing them to only cover small bets (where their money isn't needed) out of some sense of charity.

The system seems very complicated as opposed to just staying at the current 0.5%.  Personally, I will divest when the new system first comes out and see how it goes for a couple of weeks before re-investing and deciding what risk tier to be in.  It hard not to see unanticipated consequences result from such a complicated approach.

[chriswen]

Okay, it seems like I can't convince you doog.

@mechs his system is not that complicated.

Dooglus, i just feel that this wouldn't solve that many problems and it doesn't scale as much.  You can't really have a 2% option because it would be really unfair to low risk investors, but if you implement it how I suggested than a 2% scenario would be possible.  Right now your method is susceptible to day traders stealing profit from risk-averse investors.  Actually my scenario is totally resistant to day traders.

[Oleander]

I think you're reading my table wrong.  I've deleted all but the relevent parts in the quote above.

On the first bet, the bankroll is 200 and the max bet is 1.25

You're right, my mistake.  We are in agreement!

I think it is inevitable that different max profit settings will lead to changes in the relative proportions of the bankroll, which will tend to amplify or dilute people's returns.  That's not different in principle from what we have now, when the investments or divestments of other people affect my return.  I don't see this as a problem, as long as the process is transparent and people have enough information to make decisions.

[geofflosophy]

I've lost track of exactly how you're planning on implementing it, when it was first suggested I thought that the obvious implementation would be that the 0.25% people would be in for their share of the bankroll on all bets and the impact would only be on the bets above this threshold of the bankroll. How does the math work out that people with higher thresholds would be getting 4x return of the nits on all bets? As I see it this would only happen on max bets.

FWIW I will be at full Kelly regardless.

[chriswen]

I understand the max bet part, but what if a player bets 1BTC and wins (way below a max bet).  Do the 0.25% and 1% guy participate equally based on portion of the bankroll or does the 1% person get 4X more than the 0.25% investor?

People who run 100% kelly get 4 times the action of people running 25% kelly, yes.  By definition, pretty much.

A says "I'm willing to risk up to 0.25 BTC".  B says "I'm willing to risk up to 1 BTC".  We sum those two, and present to the gambler "the site is willing to risk up to 1.25 BTC".

If the gambler comes back and says to the site "I'll take 50% of what you're offering", we say to each investor "he's taking 50% of your offer".

I don't see how any other way would be fair.

Okay, so I just thought of a great analogy of why you should use my option.

So say there are two investors.  Investor A has invested 100 BTC. Investor B has invested 100 BTC also.

Right now the max profit is set to 0.5%.

If someone bets 0.1btc at 49.5%
Then they both are able to gain 0.05 btc. (or lose)

Now you implement your method.  Investor B decides to risk 1% instead.

So now if someone bets 0.1 btc,
Investor A can win ±.33 and investor B can win ±.67.

This doesn't seem fair.  Investor A is still okay with betting at this risk level.  Why does investor B take some of his bet?

[chriswen]

I understand the max bet part, but what if a player bets 1BTC and wins (way below a max bet).  Do the 0.25% and 1% guy participate equally based on portion of the bankroll or does the 1% person get 4X more than the 0.25% investor?

People who run 100% kelly get 4 times the action of people running 25% kelly, yes.  By definition, pretty much.

A says "I'm willing to risk up to 0.25 BTC".  B says "I'm willing to risk up to 1 BTC".  We sum those two, and present to the gambler "the site is willing to risk up to 1.25 BTC".

If the gambler comes back and says to the site "I'll take 50% of what you're offering", we say to each investor "he's taking 50% of your offer".

I don't see how any other way would be fair.

No, because low risk investors are just as okay as high risk investors for lower bets.  They're okay with it.  But, they're not okay with betting more than 0.25% in one shot.  That is the definition of kelly.

[Deprived]

I've lost track of exactly how you're planning on implementing it, when it was first suggested I thought that the obvious implementation would be that the 0.25% people would be in for their share of the bankroll on all bets and the impact would only be on the bets above this threshold of the bankroll. How does the math work out that people with higher thresholds would be getting 4x return of the nits on all bets? As I see it this would only happen on max bets.

FWIW I will be at full Kelly regardless.

Think you're misunderstandign what the 0.25% and 1% are.

They're the amount each investor is PERSONALLY willing to risk per bet - and what their investment adds to the MAX WIN.  With all alternatives suggested there are ratios of HIGH:LOW risk investments where someone coming in with new investment doesn't increase MAX WIN - making their investment fundamentally useless as it dilutes profit for everyone else without adding anything.

Worse still, in some suggestions, if low risk investment is a lot larger than high risk then high risk end up being forced into being low risk - as MAX WIN gets set based on low-risk.  Just try looking at something like 20K low-risk investment, 5K high-risk for some of the proposals - and you'll see it works out that low-risk get to force high-risk into also only risking 0.25% of investment at most.

A proposal that relies on assumptions about the ratio of low to high risk investment is NOT a valid proposal.
Nor is one which can allow more investment to join without raiding MAX WIN - as by definition existing investors are already willing to cover any bet up to current MAX WIN - so no more investment is wanted if it doesn't raise it.

This whole debate is largely about a minority of investors who want some way to only personally accept small bets whilst passing all big bets to others.  Which is based on some sort of entitlement belief that they should be allowed a disproportionate share of low-risk action whilst leaving higher-risk action to others.

What would totally amuse me right now is if dooglus said : "OK - mechs and co have convinced me that it's fine for some people to only partake in the first part of bets and leave the high-variance stuff completely to others.  So I'll personally cover 100% the first 1 BTC of every bet and the rest of investors can have everything above it."  And then the really juicy low-variance stuff would go to someone who actually had some entitlement rather than to those with a mistaken belief that they have a right to only back the stuff that doesn't need backing (as those willing to cover all the action could back it without their money).

[oda.krell]

I've lost track of exactly how you're planning on implementing it, when it was first suggested I thought that the obvious implementation would be that the 0.25% people would be in for their share of the bankroll on all bets and the impact would only be on the bets above this threshold of the bankroll. How does the math work out that people with higher thresholds would be getting 4x return of the nits on all bets? As I see it this would only happen on max bets.

FWIW I will be at full Kelly regardless.

Think you're misunderstandign what the 0.25% and 1% are.

They're the amount each investor is PERSONALLY willing to risk per bet - and what their investment adds to the MAX WIN.  With all alternatives suggested there are ratios of HIGH:LOW risk investments where someone coming in with new investment doesn't increase MAX WIN - making their investment fundamentally useless as it dilutes profit for everyone else without adding anything.

Worse still, in some suggestions, if low risk investment is a lot larger than high risk then high risk end up being forced into being low risk - as MAX WIN gets set based on low-risk.  Just try looking at something like 20K low-risk investment, 5K high-risk for some of the proposals - and you'll see it works out that low-risk get to force high-risk into also only risking 0.25% of investment at most.

A proposal that relies on assumptions about the ratio of low to high risk investment is NOT a valid proposal.
Nor is one which can allow more investment to join without raiding MAX WIN - as by definition existing investors are already willing to cover any bet up to current MAX WIN - so no more investment is wanted if it doesn't raise it.

This whole debate is largely about a minority of investors who want some way to only personally accept small bets whilst passing all big bets to others.  Which is based on some sort of entitlement belief that they should be allowed a disproportionate share of low-risk action whilst leaving higher-risk action to others.

What would totally amuse me right now is if dooglus said : "OK - mechs and co have convinced me that it's fine for some people to only partake in the first part of bets and leave the high-variance stuff completely to others.  So I'll personally cover 100% the first 1 BTC of every bet and the rest of investors can have everything above it."  And then the really juicy low-variance stuff would go to someone who actually had some entitlement rather than to those with a mistaken belief that they have a right to only back the stuff that doesn't need backing (as those willing to cover all the action could back it without their money).

Oy gevalt. Aren't you an entitled little bugger.

Anyway, count me in as part of the "minority" who's in favor of being able to set their own risk percentage. I'll probably leave mine at 1%, but I see absolutely no reason why dooglus' brilliant idea of a market-determined maxwin shouldn't be implemented.