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Author Topic: Just-Dice.com : Invest in 1% House Edge Dice Game  (Read 435291 times)
Bitsinmyhead
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September 26, 2013, 05:05:03 PM
 #2501

This is a great graph. Thanks so much for sharing.

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 risk are better off investing less than reducing Kelly Size. Both measures reduce volatility risk and reduce returns but reducing Kelly Size keeps counterparty risk the same whereas just investing less also reduces counterparty risk.

Please see my last post. The counterparty risk will influence optimal bet size, but not enough for it to be 1%. This is assuming people have not invested all their coins and the chances of Dooglus running are somewhat low. After all you probably wouldn't invest at all if you thought they were very high.

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September 26, 2013, 05:11:47 PM
 #2502


That's why the second part of Doog's plan is so key. Allowing you to leave a fraction of your investment offsite, allows you to always keep your investment at the KC as your investment evolves.

Cheers.



Thanks again GOB.  

Now could you help me with this.  Assume there are only 2 investors on JD:

- Investor A deposits 100 BTC at 100% reserves, 1% max profit per bet

- Investor B deposits 10 BTC at 10% reserves, 1% max profit per bet

[by "deposits" I mean signs over his BTC so that they are in JD control]

Max profit at this moment in time:

   max profit = 1% of 100 BTC + 1% of 10 BTX * 10X = 1 BTC + 1 BTC = 2 BTC.

...a whale comes along....

...first bet: whale wins big and Investor A and Investor B both lose 1 BTC.  Straightforward, right?  Now we have:

- Investor A has 99 BTC at 100% reserves, 1% max bet

- Investor B has 9 BTC at 10% reserves, 1% max bet


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).

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.  

So can we trust Investor B?  Or should it be Investor B's responsibility to "keep up his margin" as required.  

Cheers,
Peter

Hey Peter. Thanks.

I'm gonna skip down to your second example, the *do trust investor B* scenario.

This *IS* the scenario that will be done (the way Doog is conceiving it). The site will track your full "investment", only a fraction of which ail be on hand at JD. Max Profit (not max bet!) is still calculated as a fraction of your full investment, including offsite coins.

I understand the confusion, but trust is not an issue. The reason we don't need to trust in this system is because if Investor B's investment drops significantly (say a whale wins 10 max profit bets in a row, dropping investment to 100*0.99^10=90.xx%), then investor B will be auto divested of his whole amount, until he replenishes his onsite deposits (using your definition). So at no point is he getting free returns on risk-free investments. Also, at no point would there be a situation where an investor "owes" the site btc. Thus no trust.

A real concern with this scenario is that say investment is at 50k, and suddenly a whale kills it and wins 20 max profits in a row. Conceivably, many of the more "leveraged" (lower reserves, your definition) would hit the bottom of their deposits (your definition, coins held on site) and get auto divested. So you could see investment suddenly come crashing down to say, 25k, leaving only more risk-averse investors.

This scenario worries some, I assume, because it might cause a loss of confidence in the site. However, I think this is overblown because:

A) you could have the site show: "Invested: 32,040.12312844 BTC (15,349.19494033 pending)", thus reassuring that we're just waiting for people to deposit more coins to maintain their investment. *ooooohhh.... I like this idea! Just thought of it*

B) Max Profit may drop dramatically, but I don't see this as a negative. As it leaves just the fully deposited and most likely more risk-averse (running fractional Kelly), the site will automatically turn more conservative and act as an automatic cushion to massive downward swings

C) This will be risk-averse investor's wet dream! Suddenly they'd have a much higher percentage of total invested, low risk ('cause of their probably fractional kelly), and could reap some outsized rewards. This will tend to draw back the investors that got margin-called out, and new investors.


I think all this will have a stabilizing effect on investment, whale-impact, etc. I just keep seeing win-win-win scenarios in this new system.

Cheers!



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September 26, 2013, 05:22:37 PM
 #2503

Please see my last post. The counterparty risk will influence optimal bet size, but not enough for it to be 1%. This is assuming people have not invested all their coins and the chances of Dooglus running are somewhat low. After all you probably wouldn't invest at all if you thought they were very high.

When you speak of counterparty risk, you postulate that it is low because the chances of Dooglus running off with the coins or losing them due to incompetence are low. I agree. But you are forgetting a huge factor of CP risk: he could be robbed, threatened, etc. (heaven forbid). This is a huge risk:

* Banks have armed guards, vaults, local/city/state/federal law enforcement, etc.

* Just Dice is just Dooglus and in his girlfriend, apparently in a rural area in Canada (maybe some people even know precisely who/where he is, I don't know). He controls anywhere from $4,000,000 to up to $7,500,000 (potentially much much more) after just three short months of operation. This is scary. I worry for him and Deb as people, and to ignore that risk for investors as well is to be willfully blind.

I think allowing the offsite coins/fractional investment/whatchamacallit will be great because it reduces the risk to investors AND it reduces the risk to Doog, who will be holding less of hundred's of strangers coins. That's win-win.

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September 26, 2013, 05:23:05 PM
 #2504


A) you could have the site show: "Invested: 32,040.12312844 BTC (15,349.19494033 pending)", thus reassuring that we're just waiting for people to deposit more coins to maintain their investment. *ooooohhh.... I like this idea! Just thought of it*


+1

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September 26, 2013, 05:31:09 PM
 #2505


That's why the second part of Doog's plan is so key. Allowing you to leave a fraction of your investment offsite, allows you to always keep your investment at the KC as your investment evolves.

Cheers.



Thanks again GOB.  

Now could you help me with this.  Assume there are only 2 investors on JD:

- Investor A deposits 100 BTC at 100% reserves, 1% max profit per bet

- Investor B deposits 10 BTC at 10% reserves, 1% max profit per bet

[by "deposits" I mean signs over his BTC so that they are in JD control]

Max profit at this moment in time:

   max profit = 1% of 100 BTC + 1% of 10 BTX * 10X = 1 BTC + 1 BTC = 2 BTC.

...a whale comes along....

...first bet: whale wins big and Investor A and Investor B both lose 1 BTC.  Straightforward, right?  Now we have:

- Investor A has 99 BTC at 100% reserves, 1% max bet

- Investor B has 9 BTC at 10% reserves, 1% max bet


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).

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.  

So can we trust Investor B?  Or should it be Investor B's responsibility to "keep up his margin" as required.  

Cheers,
Peter

Hey Peter. Thanks.

I'm gonna skip down to your second example, the *do trust investor B* scenario.

This *IS* the scenario that will be done (the way Doog is conceiving it). The site will track your full "investment", only a fraction of which ail be on hand at JD. Max Profit (not max bet!) is still calculated as a fraction of your full investment, including offsite coins.

I understand the confusion, but trust is not an issue. The reason we don't need to trust in this system is because if Investor B's investment drops significantly (say a whale wins 10 max profit bets in a row, dropping investment to 100*0.99^10=90.xx%), then investor B will be auto divested of his whole amount, until he replenishes his onsite deposits (using your definition). So at no point is he getting free returns on risk-free investments. Also, at no point would there be a situation where an investor "owes" the site btc. Thus no trust.


OK, I see now.  "Trust" had nothing to do with it. 

I can't quite explain it, but for some reason I feel what I called the "don't trust investor B" scenario is more fair/better/preferred [although I agree now that trust was never the issue].  Maybe it is because this scenario does not require memory of the previous state. 

Either way, I now think fractional reserves is a great way to reduce counter-party risk.


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September 26, 2013, 05:39:59 PM
 #2506

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

(ffs, I can't keep myself out of the discussion... compulsive gambling, compulsive discussing, it's all the same Tongue)

I don't disagree with your table, but as was pointed out before, there's no way to exactly quantify the counter-party risk here, so from what we *can* quantify (volatility, returns) Bitsinmyhead's point still stands.

And in any case, the point I tried to get across before was a different one anyway: the entire j-d system is dynamic, not static, and influenced by human reaction. Ignoring those (possibly irrational) reactions is *irrational* itself. Maybe the most relevant case: when bank size starts dropping because of the high variance, people get nervous and pull out, bank size drops further, people will get even more nervous, etc.

Granted, we weren't quite there yet yesterday, but we were getting close, with all those paranoid remarks like "Dooglus = nakowa", or "nakowa cracked SHA".

Can you please try to at least see my point, even if you ultimately won't agree with it: this entire discussion reducies the correct maxbet size to the Kelly formula, but doing so ignores an important aspect in managing profit and risk -- that not all actors asses risk the same way. All other things being equal, higher maxbet means higher variance, which means the bank can be brought closer to zero. Some of us (me included) are willing to sit that out and trust that the whale will eventually run out of luck, and will be harpooned by the 1% edge, but for other actors, this swing is too much. I'm not saying we have to agree with them, but it's not correct either to say they're acting "irrational".


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 said no such thing. I said opinions are divided on this -- though not necessarily equally. Even if the ratio of opinions on this would be 2/3 to 1/3, it would ridiculous to claim that *all* the investors share the same opinion. By the way, please include me in "dissenting opinion": *personally* I would have preferred that maxbet stays 1%, or maybe goes to 0.5%, but *considering other investors and how they might react*, I was sort of okay with the decision, as long as it isn't permanent.

Plus, can we please not entirely ignore the fact that site profit went from around -0.1% yesterday back to about -0.03%? No guarantee yet that it'll all work out just fine, but we're certainly on the right track.

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September 26, 2013, 05:44:00 PM
 #2507

Oda: for what is worth I agree on the fact that many investors are just clueless of what investing in a casino means (some of them dared to write that for them J-D is a "long term, stable investment" - LOL so hard at that, they do not even understand what the business model of a casino is). This can lead to panic, FUD and bank runs. In fact I already wrote about it in another thread yesterday, agreeing with your point:

I believe there are two factors we should consider when discussing this matter:

MATHS:

Kelly Criterion works just fine, but the fact is that Nakowa's bankroll is many orders of magnitude bigger than the average player's, and so is his average bet. He is virtually the only one going nowhere near the "max profit". This just means that himself alone can provoke huge variance - but if he plays long enough, it will even out.

PSYCHOLOGY:

From one side, its definitely the casino's ally. If you understand this business, you simply know that Nakowa is either a) a cheater or b) the absolute best customer you can probably EVER have. Let's remember that there's absolute no evidence for a), and that:

Nakowa is the kind of guy willing to gamble $40k every 5 seconds during 3/4 hours

From the other side, you have a mob of whiners or angry "investors" who treat JD as a bank, and these guys are obviously ready to spread FUD about JD and Dooglus if they see their investment shrink by %25 in a few days due to variance. Some of this "investors" are ready to crap their pants by disinvesting probably because they do not understand in what they were investing in the first place, and this could create a "bank run" effect if the whale has another lucky strike.

The latter is something difficult to factor when calculating the probability of "bankruptcy of the house", but anyhow I'm sure Doog took his decision considering also this difficult to weight but very real "bank run" scenario.

IMO, a "market for risk" is a brilliant concept. I also hope more investors understand now what does it means to invest in a gambling site: who is your average customer, who is your STAR customer, and how your expected result can fluctuate wildly.

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September 26, 2013, 05:47:41 PM
 #2508

Oda: for what is worth I agree on the fact that many investors are just clueless of what investing in a casino means (some of them dared to write that for them J-D is a "long term, stable investment" - LOL so hard at that, they do not even understand what the business model of a casino is). This can lead to panic, FUD and bank runs. In fact I already wrote about it in another thread yesterday, agreeing with your point:

I believe there are two factors we should consider when discussing this matter:

MATHS:

Kelly Criterion works just fine, but the fact is that Nakowa's bankroll is many orders of magnitude bigger than the average player's, and so is his average bet. He is virtually the only one going nowhere near the "max profit". This just means that himself alone can provoke huge variance - but if he plays long enough, it will even out.

PSYCHOLOGY:

From one side, its definitely the casino's ally. If you understand this business, you simply know that Nakowa is either a) a cheater or b) the absolute best customer you can probably EVER have. Let's remember that there's absolute no evidence for a), and that:

Nakowa is the kind of guy willing to gamble $40k every 5 seconds during 3/4 hours

From the other side, you have a mob of whiners or angry "investors" who treat JD as a bank, and these guys are obviously ready to spread FUD about JD and Dooglus if they see their investment shrink by %25 in a few days due to variance. Some of this "investors" are ready to crap their pants by disinvesting probably because they do not understand in what they were investing in the first place, and this could create a "bank run" effect if the whale has another lucky strike.

The latter is something difficult to factor when calculating the probability of "bankruptcy of the house", but anyhow I'm sure Doog took his decision considering also this difficult to weight but very real "bank run" scenario.

IMO, a "market for risk" is a brilliant concept. I also hope more investors understand now what does it means to invest in a gambling site: who is your average customer, who is your STAR customer, and how your expected result can fluctuate wildly.

Right, I remember reading that post. I'm okay with making that distinction, calling it 'math' vs. 'psychology'. I will just continue to get cranky when decisions based on the latter category are called "irrational". (sorry for the outburst by the way. low blood sugar, I bet)

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September 26, 2013, 05:48:20 PM
 #2509

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.

that's my point: don't use any tiers, don't use reiteration since it increases complexity, use a simpler algorithm...

right now % of total bankroll is computed for each player. Winnings are assigned proportional to % of bankroll. Do the same exact thing, but with variable max bets...

Example:

Right now A invests 100 BTC, B invests 50 BTC.
1) Site keeps track of total invested (100=A, 50=B)
2) Site calculates total bankroll = 150 (sum of deposits)
3) Site keeps track that A gets 2/3 of winnings/loss (invest/bankroll), B gets 1/3 (invest/bankroll)

Proposed:
A invests 100 BTC at 0.96% max bet, B invests 50 BTC at 0.77% max bet
1) Site keeps track of total "invested" (A=100*.0096=0.96, B=0.385)
2) site calculates maximum bet = 1.345 (sum of "invested")
3) Site keeps track that A gets 71% of winnings/loss ("invested"/maximum bet), B gets 29% ("invested"/maximum bet)


no tiers, and it uses the same calculations and computations as currently being done - but "invested" (in quotes) is now what is available for maximum bet.
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September 26, 2013, 05:49:37 PM
 #2510

The investors that whine really annoy me.

All these people came, diluting our investment and expected an constant risk free return. Very annoying. I expected swings like this where I could lose 20% in a day. I have made a lot of money off of Just Dice as an investor.

However this investment got worse and worse returns because of all these people who had NO idea what they were getting themselves into.

I have revised my thoughts on the matter.

Max bet should be 0.5% or 1% no lower, and investors can leave their coins with dooglus, any investors too scared of dooglus they can invest elsewhere and let us risk takers play this game.

To be clear: Why should we nanny and cater to those who want secure, safe, happy, comfortable high returns? Why?

Let the scared little hands leave. Please.
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September 26, 2013, 05:55:39 PM
 #2511

Right, I remember reading that post. I'm okay with making that distinction, calling it 'math' vs. 'psychology'. I will just continue to get cranky when decisions based on the latter category are called "irrational". (sorry for the outburst by the way. low blood sugar, I bet)

to some people, it is mathematical rational to not operate at full kelly. People are optimizing their utility, not their profit. To some investors, variance decreases their overall utility - therefore it is rational for them to want to exchange decrease in profit for decrease in volatility.

It's sub-optimal for profit, but optimal for maximizing their own utility. It is irritation only if they declare their strategy to be maximum growth then ask for non-optimal max bets.
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September 26, 2013, 06:00:52 PM
 #2512

Right, I remember reading that post. I'm okay with making that distinction, calling it 'math' vs. 'psychology'. I will just continue to get cranky when decisions based on the latter category are called "irrational". (sorry for the outburst by the way. low blood sugar, I bet)

to some people, it is mathematical rational to not operate at full kelly. People are optimizing their utility, not their profit. To some investors, variance decreases their overall utility - therefore it is rational for them to want to exchange decrease in profit for decrease in volatility.

It's sub-optimal for profit, but optimal for maximizing their own utility. It is irritation only if they declare their strategy to be maximum growth then ask for non-optimal max bets.

Excuse me, but I need to ask: so why these people invested in a casino that has a 1% house edge, plus an optimal kelly (1%) max profit? Complaining about variance knowing those parameters is like complaining because at 3AM is dark.

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September 26, 2013, 06:05:52 PM
 #2513

Right, I remember reading that post. I'm okay with making that distinction, calling it 'math' vs. 'psychology'. I will just continue to get cranky when decisions based on the latter category are called "irrational". (sorry for the outburst by the way. low blood sugar, I bet)

to some people, it is mathematical rational to not operate at full kelly. People are optimizing their utility, not their profit. To some investors, variance decreases their overall utility - therefore it is rational for them to want to exchange decrease in profit for decrease in volatility.

It's sub-optimal for profit, but optimal for maximizing their own utility. It is irritation only if they declare their strategy to be maximum growth then ask for non-optimal max bets.

Excuse me, but I need to ask: so why these people invested in a casino that has a 1% house edge, plus an optimal kelly (1%) max profit? Complaining about variance knowing those parameters is like complaining because at 3AM is dark.

It's possible that JD is the closest thing to the risk/reward they want and are asking for it to be changed closer to how they'd like it. My stance: Doog made and is running an awesome site. Investors disagree over the risk profile they'd like the site to take, and it is rational to have that discussion. User level max bet implementation will allow for everyone to play with the risk/reward tolerance they are comfortable with.
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September 26, 2013, 06:06:28 PM
 #2514

Did you ever consider that maybe we want to find a compromise, to keep those "weak hands" in?

Sure, they dilute your profits, you could say. But those unwashed mathematically uneducated masses sure add to the total bank size, this making the place more attractive for big players.

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September 26, 2013, 06:07:04 PM
 #2515

I also think the measures being discussed here are just too complicated, and introduce a risk of mistakes in the code (c.f. casinobit fiasco) and also makes it harder for investors to understand their risk and variance.

I think dooglus should just settle on a max bet and then investors who want to go less than that can just divest and risk less.  1% seems like a good amount to me and in that case, since my personal preference is a 0.5% max bet, so I will probably divest 50% of my assets in order to reach my target of 0.5%

Complexity is a bad thing, we should avoid it if possible.

Will

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September 26, 2013, 06:18:35 PM
 #2516

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.
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September 26, 2013, 06:21:56 PM
 #2517

(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.
+100 to this

Also I would rather raising the max bet to 0.5% as a compromise between investors rather than rush in this new complicated "choose your own risk option" until it fully tested for no us intended consequences.
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September 26, 2013, 06:23:43 PM
 #2518

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!
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September 26, 2013, 06:24:03 PM
 #2519

Right, I remember reading that post. I'm okay with making that distinction, calling it 'math' vs. 'psychology'. I will just continue to get cranky when decisions based on the latter category are called "irrational". (sorry for the outburst by the way. low blood sugar, I bet)

to some people, it is mathematical rational to not operate at full kelly. People are optimizing their utility, not their profit. To some investors, variance decreases their overall utility - therefore it is rational for them to want to exchange decrease in profit for decrease in volatility.

It's sub-optimal for profit, but optimal for maximizing their own utility. It is irritation only if they declare their strategy to be maximum growth then ask for non-optimal max bets.

Perhaps the JD-economy has one less degree of freedom than what most people think.  

You pick the variance you are OK with and, over time, you earn the expected profit stream.   You're just picking what % you want of the biased random walk that is the JD profit curve.    

Assuming all investors are rational and respond instantly to put the system back to equilibrium:

At max profit per bet = 1%, reserve ratio = 100%, and deposit amount (controlled by JD) = 100 BTC, an investor expects to earn "P" and expects variance "V"

***JD changes max profit per bet to 0.25%***

Now, each investor sees that to generate "P" while subject to "V", they need to increase their deposit to 400 BTC (but they are unhappy because they have more counter-party risk, and dooglus is worried about getting robbed)

***JD changes to allows reserve ratios as low as 25% but keeps max profit per bet at 0.25%***

Now, each investor cuts their deposit back to 100 BTC, and leverages up to the max (because this minimizes counter-part risk but keeps "P" and "V" the same)

***JD allows the investors to choose their max profit per bet, and puts reserve ratios back to 100%***

Now, each investor keeps their deposit at 100 BTC, and they all choose 1% max-profit per bet (again, this minimizes counter-party risk but keeps "P" and "V" the same).  And we are back where we started  Smiley





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September 26, 2013, 06:59:14 PM
 #2520

Right, I remember reading that post. I'm okay with making that distinction, calling it 'math' vs. 'psychology'. I will just continue to get cranky when decisions based on the latter category are called "irrational". (sorry for the outburst by the way. low blood sugar, I bet)

to some people, it is mathematical rational to not operate at full kelly. People are optimizing their utility, not their profit. To some investors, variance decreases their overall utility - therefore it is rational for them to want to exchange decrease in profit for decrease in volatility.

It's sub-optimal for profit, but optimal for maximizing their own utility. It is irritation only if they declare their strategy to be maximum growth then ask for non-optimal max bets.

Perhaps the JD-economy has one less degree of freedom than what most people think.  

You pick the variance you are OK with and, over time, you earn the expected profit stream.   You're just picking what % you want of the biased random walk that is the JD profit curve.    

Assuming all investors are rational and respond instantly to put the system back to equilibrium:

At max profit per bet = 1%, reserve ratio = 100%, and deposit amount (controlled by JD) = 100 BTC, an investor expects to earn "P" and expects variance "V"

***JD changes max profit per bet to 0.25%***

Now, each investor sees that to generate "P" while subject to "V", they need to increase their deposit to 400 BTC (but they are unhappy because they have more counter-party risk, and dooglus is worried about getting robbed)

***JD changes to allows reserve ratios as low as 25% but keeps max profit per bet at 0.25%***

Now, each investor cuts their deposit back to 100 BTC, and leverages up to the max (because this minimizes counter-part risk but keeps "P" and "V" the same)

***JD allows the investors to choose their max profit per bet, and puts reserve ratios back to 100%***

Now, each investor keeps their deposit at 100 BTC, and they all choose 1% max-profit per bet (again, this minimizes counter-party risk but keeps "P" and "V" the same).  And we are back where we started  Smiley



Again, some of these points aren't exactly correct, but rather then dwelling on that, I just wanted to say: The whole point of these new coming changes is each will be able to pick what they want!!! No need for more discussions! yay! Smiley

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