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.
Topic: Just-Dice.com : Invest in 1% House Edge Dice Game - page 128. (Read 435491 times)
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 total capital and increase counterparty risk to have similar returns. So you failed in reducing your overall risk, whereas just investing less but keeping the optimal balance would actually have reduced your risk.
+1
Reducing Kelly size hurts because it increases counter-party risk at a given level of expected earnings.
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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]?
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.
sr. member
Activity: 294
Merit: 250
This bull will try to shake you off. Hold tight!
I think the biggest problem here is that the relationship between expected return and variance for the Kelly criterion is not linear.
This graph illustrates the problem well:
Cutting the max bet from 1% to 0.5% for example cuts the variance in half while it only reduces the expected return by 25%. This is another reason why full Kelly is probably not the best idea in this situation with many different investors with different risk tolerances.
I think using 0.5% for example is a lot better than full 1% because by using 0.5% max bet each individual investor have more option to regulate the variance they are willing to accept by just increasing or decreasing their investment and actually get a better risk/reward than what you would with full Kelly.
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...
This graph illustrates the problem well:
Cutting the max bet from 1% to 0.5% for example cuts the variance in half while it only reduces the expected return by 25%. This is another reason why full Kelly is probably not the best idea in this situation with many different investors with different risk tolerances.
I think using 0.5% for example is a lot better than full 1% because by using 0.5% max bet each individual investor have more option to regulate the variance they are willing to accept by just increasing or decreasing their investment and actually get a better risk/reward than what you would with full Kelly.
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...
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.
I think the biggest problem here is that the relationship between expected return and variance for the Kelly criterion is not linear.
This graph illustrates the problem well:
This graph illustrates the problem well:
Thanks for posting that!
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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...
But 1% of *what*? 1% of the amount actually deposited and in JD's control? Or 1% of the amount each investor wants to put at risk [some of which they may hold offsite].
If we take it as a given that investors in aggregate are willing to risk more than what they physically deposited with JD, then could we not argue that the max bet should be higher than 1% [of the amount actually in JD's control]?
Another Option
On another option that hasn't been explored much, perhaps we should have an option where investors can choose to be based on amount wagered instead of amount won - at say a substantial reduced amount - example would be at 40% house 'risk cut'.
On another option that hasn't been explored much, perhaps we should have an option where investors can choose to be based on amount wagered instead of amount won - at say a substantial reduced amount - example would be at 40% house 'risk cut'.
The problem with this is that those investors aren't risking anything at all. When the house needs coins to pay out a winner, these investors aren't going to give up their coins. They may as well not even bother depositing their coins, because we're just going to put them into cold storage and then give them back, with interest.
Sure, I agree, unless the capital is needed for something e.g. boosting the max bet, or for things like advertising in order to get more return on investment. However, the pot is already pretty high, even after the recent losses, so I can understand why this idea probably doesn't have much merit, unless all the investors abandon the site due to variance/losses
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I think using 0.5% for example is a lot better than full 1% because by using 0.5% max bet each individual investor have more option to regulate the variance they are willing to accept by just increasing or decreasing their investment and actually get a better risk/reward than what you would with full Kelly.
I think 0.5 would be a good compromise. I think if we can continue to get 5000 wagered a day, which we were getting without nawoka, then I'm happy with those returns. 0.5% max bet doesn't prevent 99% of gamblers from gambling on just-dice - tbh I don't think even 0.25% does
I'd really like to see a graph of number of bets placed for each % of house pot, and volume, then potentially take the 95 percentile of bets and set max bet there. My guess would be that > 95% of bets would still have been placed even with a house pot of 0.1%
Will
I think the biggest problem here is that the relationship between expected return and variance for the Kelly criterion is not linear.
This graph illustrates the problem well:
Cutting the max bet from 1% to 0.5% for example cuts the variance in half while it only reduces the expected return by 25%. This is another reason why full Kelly is probably not the best idea in this situation with many different investors with different risk tolerances.
I think using 0.5% for example is a lot better than full 1% because by using 0.5% max bet each individual investor have more option to regulate the variance they are willing to accept by just increasing or decreasing their investment and actually get a better risk/reward than what you would with full Kelly.
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...
This graph illustrates the problem well:
Cutting the max bet from 1% to 0.5% for example cuts the variance in half while it only reduces the expected return by 25%. This is another reason why full Kelly is probably not the best idea in this situation with many different investors with different risk tolerances.
I think using 0.5% for example is a lot better than full 1% because by using 0.5% max bet each individual investor have more option to regulate the variance they are willing to accept by just increasing or decreasing their investment and actually get a better risk/reward than what you would with full Kelly.
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...
Thinking more about the two "tuning parameters" GOB just described: deposit reserve ratio, and max profit %. I am wondering how many degrees of freedom this system actually has.
inputs: (D) deposit amount [edit: in JD's control], (R) deposit reserve ratio, (M) maxprofit bet %
outputs: (P) profit, (V) variance of profit, (C) counter-party risk
If I increase D, holding R and M fixed, then P, V and C go up, I think.
If I decrease R, holding D and M fixed, then P and V go up, but C stays fixed.
If I increase M, holding D and R fixed, then P and V go up, but C stays fixed.
How exactly is decreasing R different than increasing M?
inputs: (D) deposit amount [edit: in JD's control], (R) deposit reserve ratio, (M) max
outputs: (P) profit, (V) variance of profit, (C) counter-party risk
If I increase D, holding R and M fixed, then P, V and C go up, I think.
If I decrease R, holding D and M fixed, then P and V go up, but C stays fixed.
If I increase M, holding D and R fixed, then P and V go up, but C stays fixed.
How exactly is decreasing R different than increasing M?
Depends on exactly what you define D, R, P and V to be.
IF:
D= total deposit, including coins held offsite
R= deposit reserve ratio where R is % of coins held AT justice
P= expected investment growth rate
V= investment variance
THEN:
If I increase D, holding R and M fixed, then P stays constant, V stays constant (if bet sizes grow relative to it, which won't be the case, so it probably decreases) and C goes up.
If I decrease R, holding D and M fixed, then P and V stay constant (given I don't get auto-divested), but C decreases (fewer coins help at JD).
If I increase M, holding D and R fixed, then (due to Kelly Criterion):
a) if M increases and is <1%, then P and V go up, and C stays fixed.
b) if M > 1% and increases, then P goes down, V goes up and C stays fixed.
c) if M < 1% and increases to >1%, then P can increase or decrease depending on the exact numbers, V goes up, and C stays fixed.
Does that make sense? If you change the definitions of DRP&V I'll redo it.
Yes, given your way of defining D (I was defining D as what you actually sign over to JD, which is why my logic table looks a bit different). But maybe your first line is wrong:
"If I increase D, holding R and M fixed, then P stays constant, V stays constant (if bet sizes grow relative to it, which won't be the case, so it probably decreases) and C goes up."
Wouldn't increasing D lead to an increased share of the pie and thus larger values of P, V and C?
When you talk about increasing M, I noticed that you are applying the Kelly Criterion based on the sum of the reserves held at JD and those held offsite (your definition of "D"). So, I think proves that it is OK--and in fact necessary for profit maximization--to have a max bet % greater than 1% of the reserves held at JD (i.e., the number dispayed on the website). It's OK because there are other reserves that will flow into JD should the ones currently controlled by JD become depleted.
And participants who "fakes reserves" by more than a factor of 2, like you point out, would be expected to burn through the smaller amount of funds that actually possess and bust. Darwinism.
Thanks for the further info on the Kelly criterion, BTW!
Wouldn't increasing D lead to an increased share of the pie and thus larger values of P, V and C?
Going back to the first line, that's the one that gave me the most difficulty. But yeah, you're right. Sorry for the confusion.
As for your argument, I don't understand *exactly* what you're trying to say but I think I get the gist. I'll say this, for each individual person, yes, the KC requires you to think of your entire bankroll, not just what happens to be "transferred" into JD (just like if a casino is analyzing their business, they would take into account all their assets, or at least liquid assets, not just what happens to be in the cage on a given night).
However, I'll stress again what I mentioned in another one of my posts (I think on the poll thread). While (A) risking 1% of 1000 btc deposited at JD vs. (B) risking 2% of 500 btc deposited at JD and 500 btc held offsite result in the same max bet for the first bet (10 btc), that DOES NOT, hold at the investment starts to go up or down. For example, take A and B above and imagine a player comes in and loses 100 btc (site wins 100):
A) Invested goes from 1,000 to 1,100. Max profit goes from 1% * 1,000 = 10 to 1% * 1,100 = 11
B) Invested goes from 500 to 600. Max profit goes from 2% * 500 = 10 to 2% * 600 = 12
The same goes if a player wins 100 BTC (site loses 100):
A) Invested goes from 1,000 to 900. Max profit goes from 1% * 1000 = 10 to 1% * 900 = 9
B) Invested goes from 500 to 400. Max profit goes from 2% * 500 = 10 to 2% * 400 = 8
So, while they start with the same max profit, as investment evolves, they deviate. In the 2% case, it doesn't maintain the KC with relation to your whole bankroll. As your investment grows it, it overshoots the KC, and as your investment decreases, it undershoots it.
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
(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.
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.
(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.
Most of the real casino are making crazy money every month and are not in a negative profit after a couple of months
In all fairness, casinos operate on like, 5% edge or whatever. Pretty hard to lose money like that, even if you're unlucky.
Sorry but it's exactly the same as reducing the max bet, except it's pretty much lying to the gambler.
Winning big because of luck has to be possible, otherwise who would want to gamble?
Winning big because of luck has to be possible, otherwise who would want to gamble?
Will not prevent anyone to win 100 btc betting 1, with a smaller percent of chance. But it is stupid to keep a high max profit.
Imagine that the bankroll is 30k btc, and max bet is 100%. Someone will 1 million btc could easily win the 30k btc with a high probability, almost 100%....
Investissor's money should be safer.
Most of the real casino are making crazy money every month and are not in a negative profit after a couple of months
We should not limit max profit / max bet, but split huge bets into several smaller ones for reducing variance (and it should be automatic: if someone bets 5k bets at 50% win rate, he should receive anything from 0 to 10k, with all bets recorded, without doing anything).
This sort of decomposition would significantly boost the implied house edge on the decomposed bets. Yes it would reduce variance but i do not think it would be very correct towards the players.
Ugh. Let me try once again.
If you remove the liquidity aspect of JD, many other gambling investments become very attractive again.
If you remove the liquidity aspect of JD, many other gambling investments become very attractive again.
The liquidity aspect was just removed by lowering max bet and pissing off the whale. Investors who did not divest are stuck with a loss that it will take long to cover unless nakowa comes back and gambles hard.
We should not limit max profit / max bet, but split huge bets into several smaller ones for reducing variance (and it should be automatic: if someone bets 5k bets at 50% win rate, he should receive anything from 0 to 10k, with all bets recorded, without doing anything).
Gamblers want volatility. This is what they pay negative ROI for. This is the service a casino offers.
We should not limit max profit / max bet, but split huge bets into several smaller ones for reducing variance (and it should be automatic: if someone bets 5k bets at 50% win rate, he should receive anything from 0 to 10k, with all bets recorded, without doing anything).
In general: don't invest money you need to be liquid.
Nakowa copycats will want 1% max profit.
Certainly. You have to balance attracting them with not risking so much when there aren't enough big bets... I'm curious if that's possible.The only thing you have to balance is the pair you should grow.
I was against lowering the max bet. Let's try to keep the discussion devoid of emotion, like real men should do. You're just joining a circlejerk without even understanding what you are talking about.
I was (semi)-joking, but the discussion is really very simple. Take the most profitable action while avoid going bankrupt. Everything else is just people being scared. If you're scared you should lower your investment to the point were you are comfortable again.
Anyway, this isn't my business, I'm just a participant. If Dooglus wants to run this sub-optimally, he's free to do so
sr. member
Activity: 294
Merit: 250
This bull will try to shake you off. Hold tight!
Math never lies. Irrational fear is NOT your friend.
(take back the max profit 1% so he can TRY HARD to cover his losses, came on doog...)
Yes and no; you have to understand that to bet the same amount he has to make a lot more bets, and thus the variance will more easily play in our favor.(take back the max profit 1% so he can TRY HARD to cover his losses, came on doog...)
I'm not saying that as an argument for staying at 0.25% max bet though. If we had much more high bets (in number of bets) it would be safe to increase the max bet; the issue is not enough bets. I'm hoping for Nakowa copycats, especially with the news coverage.
Nakowa copycats will want 1% max profit.
Yup, since doog seems persistent to keep the max bet lower, I'd like to also request for at least 0.5% max bet for the time being.
Changing a well thought out variable to 4 times less is just out of order.
Nakowa copycats will want 1% max profit.
Certainly. You have to balance attracting them with not risking so much when there aren't enough big bets... I'm curious if that's possible.The only thing you have to balance is the pair you should grow.
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