Topic: Just-Dice.com : Invest in 1% House Edge Dice Game - page 121. (Read 435357 times)

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?

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.

LOL   I'd love to see THAT bet.

Okay, you might be right about cut in the action.  I'm going to do some examples so we can see which one is better.

But, I do know is that by using yours or a revision it will make it a lot more computationally simple, and a lot more fairer for low bets.

I see what you mean, and I'm thinking about it. Suddenly I can't remember why I dismissed this in my head as a possibility. Also, I simply wrote down what I thought I had understood Doog say was what he was gonna implement. Though I wasn't 100% sure, that's why I asked him to comment on the post (and also on the chat, but I think he stepped out right as I asked).

One thing I can think off the top of my head is that by risking more, the investors that add up to a high max bet are drawing high risk players (players that are willing to play for higher payoffs. By giving low risk (risk averse, 0.25%er) investors a cut of these bets, they're leeching off of the business that is attracted by high risk (risk seeking, 1%er) investors. Why should they get a cut of those bets? Those bets are made for a high payoff because certain investors were willing to offer it. Does that make sense?

I don't think this is what he was referring to, but like I said in my post above, I'd like doog to confirm if it's correct or not.

In the method I described, investors at 0.25% do not profit (or lose) at all for a bet made with [profit for that bet] > [their investment] x [0.0025] x [their share of the pool]

Now that I write it out, perhaps I'm missing one piece for the calculation to be exact. But the concept I think is sound... what I meant was that what you wrote, where those with max profit at 1% profiting 4 times those at 0.25%, was incorrect. You only "profit 4 times more" than people with your same risk level with 1/4 the size of your investment. What different risk choices (max profit %s) does is segregate investors, so that only more risk-seeking investors profit (or lose) from higher max profit bets.

Really great site and overall good business decisions doog.  I think 0.5% is a pretty solid risk profile.

No its not the coward way.  You'll get less action of big bets.

Okay, I think GOB made a mistake.  I get his point of view and his goals but there are a few problems.  I'll be posting a revision.

I think there's some revisions that need to be done to GOB's method.  The problem is the risk-averse investors won't be contributing to max bet anymore for high bets which means the max bet might not even be that much higher.  I think the low risk need risk a bit to the high risk bet but only up to the 0.25%.  That way risk is still controlled , when nakowa bets big it'll be like a max bet for the risk-averse people.

The problem is that GOB used the risk-averse bankroll for the risky people, which means risky people had more exposure.  But, then the max profit might not even go up.  So I think lower risk people still need to contribute to higher risk bets, but they'll be taking less risk, variance, profit.  I need to think about it and I'll be posting some examples.

Ah man!  Yeah, we never will come to consensus!

I thought the method Gob just described was the one Doog said he wasn't even considering because it was a way for cowardly investors to profit from the brave investors. 

If the average investor sets 0.5%, then don't I just come along, set 0.1% and deposit 5 times as much, and then basically cruise along nearly risk free? 

I seem to be wrong about so many things that I think I know for sure, but isn't there just one biased random walk and, some way or another we each pick what % we want to handle?

Peter

This is what I thought at first but it doesn't actually decrease Nakowa variance (bet size variance) for risk-averse players.  It just decreases luck variance (for less profit).  And decreasing Nakowa variance will also decrease chances of profit for risk-averse players.

I actually if you're able to implement it this way it would be a lot better.

I was thinking an implementation the other way but this way makes a lot more sense.  The other way is flawed as it is just a band-aid fix.

When you lowered the max bet to 0.25% this decreased variance not because it was 1/4 kelly criterion but because the max bet was closer to a average bet size to decrease variance.  So if we did variable the 0.25% and the 1% will basically have the same variance but differently.  The 0.25% will still be affected by Nakowa's high bets, as they'll be part of the higher max bets even though they want to decrease variance.

Secondly, if you ever added leverage this problem would be a lot more pronounced.  This is because the max bet would be a lot higher and variance would be higher (even if you did 1/4 kelly criterion).  So, variance isn't really based off of kelly, its based off of where most of your bets are around compared to the max bet (I'm talking about significant bets).  It's hard to explain but I hope you understand what I mean.

So, if we solve the problem now by spending more time to implement GOB's proposal then you won't have these problems in the future (unless this is what you've been working on).

Otherwise,  it will be based off of kelly criterion.  Higher percent will take on more risk, variance, and profit.  But there is the other variance which is based off of average max bet.

Secondly, I must say that all investors are equal currently.  Even if we decrease the bet risk by 75% everyone still gets the same share of the profit.  If you implement GOB's proposal then everyone will still be on equal footing.  Which I must say is more fair.  And then when leverage is implemented then people can try to get an advantage.

But with this method it is used to control variance from bigger bets, which is the main goal.

EDIT: I think there's some revisions that need to be done to GOB's method.  The problem is the risk-averse investors won't be contributing to max bet anymore for high bets which means the max bet might not even be that much higher.  I think the low risk need risk a bit to the high risk bet but only up to the 0.25%.  That way risk is still controlled , when nakowa bets big it'll be like a max bet for the risk-averse people.

The problem is that GOB used the risk-averse bankroll for the risky people, which means risky people had more exposure.  But, then the max profit might not even go up.  So I think lower risk people still need to contribute to higher risk bets, but they'll be taking less risk, variance, profit.  I need to think about it and I'll be posting some examples.

Maybe there will be hiccups with implementation, but I can't see it.  It seems so simple to me now that I get it:

Investor A and B deposit 100 BTC each. 

Investor A selects 0.25% and Investor B selects 1%. 

A whale makes the max bet.  Investor A risks 0.25 BTC on this roll and Investor B risks 1 BTC.  Should the whale win, Investor A would be left with 99.75 BTC and Investor B would be left with only 99 BTC. 

A smaller fish comes along and makes a bet to win max_profit / 10.  Investor A now risks 1/10th * 0.25% of 99.75 and Investor B risks 1/10th * 1% of 99 BTC. 

In other words, they gain or lose in proportion to what they risk per roll. 

If each investor could hypothetically react instantly to maintain their balance at 100 BTC, then Investor A would earn an income stream identical to Investor B, just scaled by a factor of 4. 

And on and on...

I think this isn't exactly correct. This is how I think it'll work and I would love if Dooglus could let me know if this is correct or not:

If you and I are both invested at (say) 100btc (thus having the same percentage of the bankroll), then:

A) For bets that pay (profit) less than or equal to 0.25% of 100, or 0.25BTC, we both make/lose the same amount

B) For bets that pay (profit) more than 0.25% and less than or equal to 1% of 100, or 0.25BTC, you do not participate, and I do.

C) Bets that pay more than 1%, neither of us participate (if Doog allows investors to choose >1% personal max profit)

NOTE!!!! Many people continually mistake MAX BET (which doesn't exist as a concept on JD*) and MAX PROFIT. STOP MAKING THIS MISTAKE!

Max Profit = the maximum you can profit on one bet.

Example 1: Nakowa bets 210BTC at 49.5% and that pays 210BTC (under the as of now max profit of 210).

Example 2: I'm feeling lucky and bet 2BTC at 1%, which pays 196BTC. (In scenario B above, the person with their max profit set to 0.25% would NOT participate in this bet, neither upside nor downside).

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.)

Doog, could you confirm this is correct please?

EDIT: Doog did respond and the A/B/C scenario I wrote above is wrong, though it's not what Peter R wrote in the quote above it. My note about people not confusing max profit with max bet still stands, though

This sounds like one of those problems that you don't truly understand until you try to code it.  Then you throw away the first attempt and start over.

Maybe it really is that simple... but it has to be done in a way that scales so it doesn't drag down performance.  I hope dooglus will share some details after he's wrestled with the implementation.

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

The discussion is still useful. I guess I partake in this conversation, not really to sway doog, but more to get things straight in my brain so that I can hopefully make rational decisions. 

And I bet with the benefit of another 6-months of hindsight (especially after we have dynamic risk), the optimal strategy will almost seem "obvious."

I am still confused about the exact implementation of this "select your own max profit" and how it will work.

I think by now it's clear that the discussion will not converge to a consensus.  I'm looking forward to when investors can specify their max bet percentage individually.  Maybe the 1% people will end up with the lion's share of the profits over the long run.  Maybe they'll go bust, leaving the .25% people the winners.  Who knows?  (We all know, we just disagree!)

I hope that dooglus will build in some kind of statistics so we can gain some insight from other people's experience.  (Maybe the equivalent of creating a 1 BTC investment in each tier and reporting the balance once a day.  I'd love to be able to load that kind of data into a spreadsheet.)

To be quite honest, I am still trying to wrap my head around the mathematics and system dynamics of JD.  As my understanding of these concepts crystallizes, I may increase or decrease my investment, as well as my opinion on "what is best." 

But as of today, I am confidently riding the "1%-Kelly-is-optimal" train.  What further convinced me was the rapid growth in JD bankroll after the 1% -> 0.25% change.  I expect a new equilibrium point would have formed between 2 and 4 times the bankroll prior to the change (thereby increasing counter-party risk).  But I think aggregate investor profits would have actually taken a hit due to the lower max bet.     

My mind is open and I think a lot of us here [lurkers included ] are trying to learn too, so please continue to share why you believe 0.5% or 1% is too high.