Pay On Target: New High variance payout System Offered by Ozcoin

[organofcorti]

Personally I'd prefer a smaller a which would make the cap unnecessary.

The maximum value of a share is still effectively unbounded, even for smaller a, so a single share can still bankrupt the pool.  This seems to me to be a different type of risk from that which a PPS operator takes, for example - where the rate at which the pool can lose money is clearly bounded.

It's extremely unlikely though. If a is 0.5 and uncapped, after 1048576 shares have been submitted the pool has a probability of paying ~ < 1.03 * PPS  is 99.999999%

Edit: I just realised that figure is at beyond the limit of my accuracy. It's probably just the maximum for that calculation and the RVs I used. Still, the point stands.

[Wave]

Looking at feedback, thinking, talking with others our next experiment will be at a= 0.8 which brings back in high variance but share value will be capped at 1.5*D (5055272)
 to reduce chance of pool going broke

Thanks for persisting and all the feedback - I feel we can make this work and be fun
cheers
Graet

Excuse me for being lazy, but what would the max payout be under this potential scenario?

[organofcorti]

Looking at feedback, thinking, talking with others our next experiment will be at a= 0.8 which brings back in high variance but share value will be capped at 1.5*D (5055272)
 to reduce chance of pool going broke

Thanks for persisting and all the feedback - I feel we can make this work and be fun
cheers
Graet

Excuse me for being lazy, but what would the max payout be under this potential scenario?

I think rather than maxing the share value at 1.5*D it would be easier for miners to understand if there was a semi-permanent maximum payment - for example a 1/2 block reward.

[Meni Rosenfeld]

Personally I'd prefer a smaller a which would make the cap unnecessary.

The maximum value of a share is still effectively unbounded, even for smaller a, so a single share can still bankrupt the pool.  This seems to me to be a different type of risk from that which a PPS operator takes, for example - where the rate at which the pool can lose money is clearly bounded.

Yes, but it's a "so you're telling me there's a chance" can. With a=0.4 and wd=1, the chance that a share will cause a loss of more than a reward of a single block is about 1 in a quintillion, I think they can handle it.

[os2sam]

Personally I'd prefer a smaller a which would make the cap unnecessary.

The maximum value of a share is still effectively unbounded, even for smaller a, so a single share can still bankrupt the pool.  This seems to me to be a different type of risk from that which a PPS operator takes, for example - where the rate at which the pool can lose money is clearly bounded.

Yes, but it's a "so you're telling me there's a chance" can. With a=0.4 and wd=1, the chance that a share will cause a loss of more than a reward of a single block is about 1 in a quintillion, I think they can handle it.

There may be some wisdom in the KISS method by putting a reasonable cap on max reward as opposed to taking a "1 in a quintillion" chance of something astronomically bad happening.

Have any of us said "the chance of X happening is so remote that we don't need to worry about it?"  I have, and far too many times I've had to follow up by saying "ain't never seen that before".
Sam

[organofcorti]

Have any of us said "the chance of X happening is so remote that we don't need to worry about it?"  I have, and far too many times I've had to follow up by saying "ain't never seen that before".

Well, perhaps your analysis of the probability of X occurring was faulty? That said, I've always thought million-to-one chances happen nine time out of ten.

[os2sam]

Have any of us said "the chance of X happening is so remote that we don't need to worry about it?"  I have, and far too many times I've had to follow up by saying "ain't never seen that before".

Well, perhaps your analysis of the probability of X occurring was faulty? That said, I've always thought million-to-one chances happen nine time out of ten.

I rarely rely on my analysis of a probability of anything.  I used to rely on others analysis a little more often but have been taught by the School of Hard Knocks not to do that when the consequences are too high.

Graet will need to determine what his comfort level with the consequences are.

[abracadabra]

Have any of us said "the chance of X happening is so remote that we don't need to worry about it?"  I have, and far too many times I've had to follow up by saying "ain't never seen that before".

Well, perhaps your analysis of the probability of X occurring was faulty? That said, I've always thought million-to-one chances happen nine time out of ten.

Exactly... Like "storms of the century" seem to happen every year

oh.. and with all the math formulas being spewed here by meni and ooc, i'm beginning to think that both of them are actually wolfram alpha sock puppet accounts 

[Meni Rosenfeld]

There may be some wisdom in the KISS method

(1-a)*(wd*B/D)*(sd/wd)^a
is simpler than
[(1-a)/(1-a*wd^(1-a)*(1.5D)^(a-1))]*(wd*B/D)*(min(1.5D,sd)/wd)^a.

a^2/(1-2a) is simpler than -1+((-1 + a)^2 X (-wd^(2 a) X + 2 a wd X^(2 a)))/((-1 + 2 a) (-wd^a X + a wd X^a)^2). The expression for the variance is what you need to truly bound your risks.

by putting a reasonable cap on max reward as opposed to taking a "1 in a quintillion" chance of something astronomically bad happening.

Have any of us said "the chance of X happening is so remote that we don't need to worry about it?"  I have, and far too many times I've had to follow up by saying "ain't never seen that before".

You should distinguish
1. Hunches that something is unlikely, or derivation of probabilities based on strong assumptions of dubious truth value
from
2. Probability derivations for essentially pure random processes where there are virtually no relevant assumptions.

#1 are only as good as your process - in other words, usually not very good. #2 Really do mean something. Something that has a true probability of 1 in a billion to cause, say, my own death, is really nothing to worry about.

[hackjealousy]

I'd like to calculate the difference between what I would be making PPS (with a 4% fee) and with POT.  If S is the submitted share difficulty and T is the target difficulty, then the reward for the two methods is equal when S = T (1 / (1 - a))^(1/a).  For a = 1/2, we have S = 4 T.  A POT share at 4 times the difficulty of the target is thus worth as much as a standard PPS share at that target.

I'd like to use the "Average Share" on the "POT Statistics" page to determine if I'm doing better than PPS.  However, I have two issues:

1.  One of my miners is vardiff and I can't find an "Average Target Difficulty" in the statistics.
2.  I don't know if the "Average Share" is the true average or an average over a certain amount of time.

[GenTarkin]

1.  One of my miners is vardiff and I can't find an "Average Target Difficulty" in the statistics.
2.  I don't know if the "Average Share" is the true average or an average over a certain amount of time.

As per #2 - blak told me average share is just a rolling avg of.. last share * cur share / 2 .. so just a period in time. I would like to see an all time average too.

For #1 - there still is the question of what does valid shares actually reflect? Ive been told its shares submitted then based down to their 1diff equivilant, but in testing this seems to not mathmatically be correct. Then there is the other side, is it just a total of actual shares submitted, regardless of their vardiff. But, Im being told by developers the first one is how its figured, but it seems to actually be working more like my 2nd point.. so... /really confused.

[crazyates]

1.  One of my miners is vardiff and I can't find an "Average Target Difficulty" in the statistics.
2.  I don't know if the "Average Share" is the true average or an average over a certain amount of time.

As per #2 - blak told me average share is just a rolling avg of.. last share * cur share / 2 .. so just a period in time. I would like to see an all time average too.

This doesn't make any sense to me.

[GenTarkin]

1.  One of my miners is vardiff and I can't find an "Average Target Difficulty" in the statistics.
2.  I don't know if the "Average Share" is the true average or an average over a certain amount of time.

As per #2 - blak told me average share is just a rolling avg of.. last share * cur share / 2 .. so just a period in time. I would like to see an all time average too.

This doesn't make any sense to me.

sorry, last share diff + cur share diff / 2

[Wave]

I'm out gents, back to DGM for me.  At least for now.

-Wave

[Graet]

@all
Doing up some more user stats currently
My brain collapsed last night, had a sleep going to look at new formulae and feedback, appreciate the help, I feel we are moving in the right direction


Wave, thanks for giving it a go and the feedback, you posted just after i went to bed, the answer is
at work_difficulty diff 1 and D = 3370182 share_difficulty (1.5*D)= 5055273
( 1 * 24.25 / 3370182 ) * (( 1 - 0.8 )*( 5055273 / 1 )^0.8 )=0.331958715BTC

Thanks folks
Graet

[Roy Badami]

Yes, but it's a "so you're telling me there's a chance" can. With a=0.4 and wd=1, the chance that a share will cause a loss of more than a reward of a single block is about 1 in a quintillion, I think they can handle it.

Ok, if that's really the case then I withdraw my objection.  The probability of Ozcoin being wiped out at a=0.4 is many orders of magnitude lower than the probability of a meteor destroying all life on Earth :-)

roy

[os2sam]

Yes, but it's a "so you're telling me there's a chance" can. With a=0.4 and wd=1, the chance that a share will cause a loss of more than a reward of a single block is about 1 in a quintillion, I think they can handle it.

Ok, if that's really the case then I withdraw my objection.  The probability of Ozcoin being wiped out at a=0.4 is many orders of magnitude lower than the probability of a meteor destroying all life on Earth :-)

roy

Hmm, should I feel better now?

Just two more days to the end of the Aztec calendar you know .
Sam

[crazyates]

Ooh the Ozcoin page has updated with some cool stats, tracking your shares across rounds and comparing them to PPS. So far, over the past 15 rounds, I'm -0.0136 behind straight PPS. Right before this started, my highest was 600k, but since then I've barely gotten a single 10k share. I'll prolly keep going for another few days to see how it tracks when you do hit a really high share, and then I'll decide which method to keep using.

Oh, I'm only using a lone BFL Single, but my varr diff is manually set to 2. Would that affect my earnings much? From what I can tell, a manually set work_difficulty makes for higher-paying high-diff shares, but fewer low-paying low-diff shares. Is this correct?

[organofcorti]

Oh, I'm only using a lone BFL Single, but my varr diff is manually set to 2. Would that affect my earnings much? From what I can tell, a manually set work_difficulty makes for higher-paying high-diff shares, but fewer low-paying low-diff shares. Is this correct?

Sort of. You get paid the same as if the shares you submitted were only half the difficulty the are(since vardiff = work_difficulty =2), but multiplied by 2.

Think of it like this:

Reward per share = function(share_difficulty/work_difficulty) *  work_difficulty

[organofcorti]

Wlog we assume wd*B/D=1. The pdf of sd for sd>=wd is wd/sd^2 and the payout is (sd/wd)^a. So without a cap and without a constant factor, the expected payout is

\int_{wd}^{\infty}(wd/sd^2)(sd/wd)^a\ sd

This is 1/(1-a), and thus we need a constant factor of (1-a) to make this equal to 1.

With sd capped to X the integral becomes

\int_{wd}^{X}(wd/sd^2)(sd/wd)^a\ sd + \int_X^{\infty}(wd/sd^2)(X/wd)^a\ sd

The second term is (X/wd)^(a-1) and the first term (by subtracting the primitive function at the endpoints) is (1-wd^(1-a)*X^(a-1))/(1-a). Add to get [(1-a*wd^(1-a)*X^(a-1))/(1-a)], so the constant term should be [(1-a)/(1-a*wd^(1-a)*X^(a-1))].

Thanks for that. Nice clear way of showing how to think about the problem.