Good.  The simple form of the theorem that is suggested by the two conditions I gave is easy to prove but it would be nice to say something more along the lines of "If X is a hop-proof pool then there must exist a function f and ...".  This shouldn't be tough (kind of fun really) but as I said a while back I've not done any of the maths for pooled mining and instead am enjoying just going with rough intuition (which frequently leads to my making false assertions but that's fine).  Good luck with this, not that you'll need it.


If you've been following my posts you'll know I'm a fan of "off-topic".


Congrats!  It's a shame you don't get higher status than "Hero Member".

Yes, this is pretty much all I meant.  Most PPS pools right now pay an amount per share which depends on difficulty but not transaction fee rewards.  This is insignificant in the grand scheme of things right now, I just thought it was interesting.

Also, I've always used "hoppable" with reference to solo mining rather than the PPS reward system or as a general relative property.

Unfortunately, the profitability of merged mining over normal Bitcoin mining has fallen quite a lot since it was first rolled out but it's still a nice bonus (about 3.6% right now).  There was a period after merged mining became available that Namecoin mining was actually more profitable than Bitcoin mining (so the merged mining bonus was over 100%)!  Namecoin difficulty is still rising fast so this bonus should continue to drop.

My apologies, I had to dash while I was composing this post and didn't have time to read it.  By "interpolate" I didn't mean to suggest any particular mathematical way of calculating payouts but rather just meant to suggest that by varying one of the parameters you would obtain a continuum of reward systems from PPLNS to Geom.  I admit this was a poor choice of word but couldn't think of anything better at the time.  Spectrum is a good word for this.

As for the "decay" part I was being particularly dense when I wrote this and I'm sorry for any confusion caused (I'll edit my earlier post if I can).  I somehow managed to get the idea in my head that it would be possible to have a non-hoppable reward system where for each block the full reward is paid out according to the shares submitted in that round.  I was talking about the "decay" in value such a share submitted to such a pool must experience before the end of the round (and thought it would exist and be some kind of exponential decay).  Of course, the only reward system that satisfies these two properties is PPLNS with N=1.  I was flatly wrong, "That's not really it" was just kindness .

After a quick read of your initial post about the Geometric method I see what you are saying about Prop and PPS.

May I ask what you do for a living Meni?

Yes.  The goal of many of the reward systems is to ensure that each submitted share has the same expected value.  PPLNS does this (unless carelessly implemented), PPS does this (this too can be implemented in a way that is technically hoppable thanks to the transaction fee reward), and Geom does this.  As far as I understand it, DGM simply interpolates between PPLNS and Geom is a spectrum of different non-hoppable reward systems ranging from PPLNS to Geom and, consequently, takes an additional parameter.  If a reward system has this property and pays all rewards out in a timely manner then it simply cannot be hopped (for the time issue, compare DGM to SMPPS).

The interesting aspect is that, for a fixed difficulty and hashrate, the number of blocks generated in a certain period is very well modelled by the Poisson distribution (equivalently, the time until the next block is found is very well modelled by the exponential distribution).  Consequently there is a natural "decay", not built into Bitcoin by design, but simply a mathematical phenomenon.  If you just design a reward system with shares decaying in value at some random rate you prescribe then most likely the pool will be hoppable.  The decay must exactly match that required by the mathematics.  This is why the proportional reward system is hoppable; the decay is not the same as that required by the mathematics.  Nonsense

Good.  I would imagine that some people opting out of merged mining are specifically wanting to not support the Namecoin network.  Honestly though, knowing the mining community I would expect most people opting out mistakenly believe that doing so will boost their Bitcoin income.

If a miner at your pool opts out of merged mining and they submit a share which would generate a Namecoin block is the winning hash not broadcast?  I couldn't find anything on the "Pool Disccusion" page about it.

Cool!  With such an update I believe it could be argued that yourbtc.net is less hoppable than most existing (possibly all) PPS pools!

The simulations are really only suitable for illustrating a particular reward system, it is mathematics that establishes whether or not a reward system impacts intermittent miners.

A real data test will be difficult to perform for a number of reasons.  I fear all that could be gleaned from such a test is which pool "currently" performs the best and say nothing conclusive about future performance or about reward systems.

I've just gotten back and am glad to see that this pool is doing well (aside from the continuing server instability issue).  Reaching 200 GH/s, if only briefly, was unbelievable.  Does anyone know what caused this spike in hashing power?

@urstroyer: What's the situation with regard to the correct proportioning of share scores with respect to currently available transaction fees?  I noticed that while merged mining and the new PoolServerJ were being discussed that bitcoind 0.5 was mentioned (I forget where).  Certainly I'm not asking for such a tweak in the near future, I'm merely curious about the current state of affairs.

Awesome!  Have fun with the upgrade (it's always satisfying to work with new hardware).



I was particularly impressed to see that the pending donation is nearly 1% of the pending payout, a huge improvement (not long ago it was only 0.3%).

That seems sensible to me.  Long polling shouldn't be necessary for a local network at all (not that it hurts).  I would argue that, even with long polling, pool miners will have more of a stales problem than solo miners.

It wasn't clear to me but I did suspect we might be working from different definitions of "expect".  Thanks for clearing that up.  You might consider putting a note about that in your text for mathematicians and gamblers.


I'd argue that warning people that there's a real chance they could get no reward for a few hours mining at a PPLNS pool is far from technical.

Yes, round boundaries are done away with too and this is a little more technical and possibly could be omitted.  I agree that it is another hurdle as many miners think of a share as being part of a block rather than simply a proof-of-work packet.  It can be confusing that a share found in one round can still be generating income many rounds later.

Agreed.  This is not a place for discussing the viability of various pool systems but for helping miners select a pool which works for them.  No-fee PPS pools do exist and, even without merged mining, such a pool is a decent choice for a miner.

Scores decay exponentially if the miner is disconnected. How is that not punishing the disconnection?
[/quote]
The score for previous shares decays exponentially whether the miner disconnects or not. Remaining connected doesn't stop the decay, it just replenishes the score with the score of the new shares.
[/quote]

Yes, this seems to be a common misunderstanding and so I think is very much worth including in your work kislam.  Scores are not designed to decay to attack intermittent miners and thereby reduce pool hopping, they are there to ensure that the expected value of a submitted share is independent of the current round age.

To clarify, when you say "expect" are you referring to the concept of "expected value" from the theory of probability or something more along the lines of "a high chance of receiving at least a certain amount".

If you are concerned about the latter it would be worth pointing out that mining for a few hours at a small PPLNS pool (say N = [difficulty]) has a definite, positive, non-negligible probability of paying out 0 BTC (similar to how a lottery ticket can end up being worthless).  This is one aspect of PPLNS that many miners (even 24/7 miners) find psychologically difficult to handle and, consequently, I feel it is a fair criticism of the reward system.


Interesting.  I might also expect a large array of small PPLNS (or similar) pools.  If there were one such pool a miner may well want to send 2% of their hashing power to increase their variance and expected income so such a setup seems stable.  That's juts a knee-jerk reaction though, I think I'll give this some thought.

Thanks for this, a neat little bit of trivia.  I honestly didn't expect the tipping point to be as small as N = 0.071*[difficulty].

Try not to let the trolls bother you.  I hope you find posting on this forum entertaining.

Given how slowly and painfully the mining community is processing "reward systems" I fear auditing is very much a future concern (and one I'm somewhat interested in).  Do you have a thread where you talk about possible far future scenarios for mining?  Both the topics of possible reward systems and number/sizes of pools would make for interesting discussion.

Interesting.  I see that a proportional pool (assuming no pool hoppers) proves more of a problem for random intermittent miners versus 24/7 miners than a similar PPLNS pool (regardless of the value of N) (which in turn is more problematic than most other reward systems).  However, I don't have much of a feel for the value of N at which the share-based variance at PPLNS is similar to that of a proportional share.  Have you calculated such a value of N or merely shown that it is less than [difficulty]/2.

Also, I completely agree.  I'm not clear exactly on what the "intermittent issue" is but based only on the name I can safely say that if it's a problem for PPLNS then it's a bigger problem for proportional (certainly for N=[difficulty], arguably for all N).

Is that right?  I thought long polling was all about helping the mining software and bitcoind communicate and thereby reducing the proportion of invalid shares.  If both pieces of software are on the same private network such communication should be a non-issue.  To me, the interesting communication problem is the broadcasting of a new block to all existing bitcoind nodes.

Could someone explain long polling or give me a link?  Particularly I'd like to know whether or not it improves on bitcoind's current block broadcasting and, if so, how?

Agreed.  With an average 3 outages a day over the last week I'd expect people to be leaving this pool in droves.  Given the fierce competition out there between the pools one can't expect a near future promise of stability to last for long.