The description you quoted from Eligius is spot on; this is the basic idea behind PPLNS.  A real implementation will be slightly more complicated because it must account for changes in N and/or in difficulty and must also be careful about what happens when the pool starts and ends.

Yes, if you stop mining and none of your shares end up within the (X-N, N] range then you get no reward.  If there is one block in the range (X-N, N] you get 50/N BTC (assuming no transaction fee rewards and 0% fee), if there are two blocks in the range (X-N, N] you get 100/N BTC, and so on.

Let's suppose we have a PPLNS pool with N = difficulty/2 (and assume difficulty is fixed for simplicity).  The PPLNS pool here is a good real world example.  The average number of shares to a round here is 2*N (because share difficulty is 1 here).  Some rounds are much shorter and others are much longer but most are longer than N.  It is not possible to hop this pool in the way you describe without some kind of time machine.  To "reverse pool hop" you need to know when a round is going to end.

Lol, sorry about that.


The value of your shares changes as more information about the near future of the pool is revealed.  This has nothing to do with whether or not you continue to mine at the pool yourself.  If I submit a share it will lose value as non-block-generating shares are submitted and gain value when blocks are found; N pool shares after my submission the true value of my share will be fully revealed.  Exactly the same happens at proportional pools and, indeed, with most reward systems.  A share is behaving very much like the scratch card I described which has a 1/4 chance of being a winner ($4 prize).  The value of the scratch card is $1 (expected value) but, when it is scratched to reveal no prize its value decreases $0.  The risk of this decrease in value remains whether or not you decide to buy more cards before scratching the first.

The only two sound ways of mining I'm aware of which don't decrease the value of your share as future non-block-generating shares are submitted (i.e. have zero share variance) are PPS and PPLNS with N = 1 (effectively solo mining).  These are both completely hop-proof and don't favour 24/7 mining over intermittent mining.  PPS requires a fee to be sustainable (at 0% the pool balance will follow a random walk and will become arbitrarily large and negative at points in the future).  This problem cannot be avoided (SMPPS tries to avoid it by placing the random walk along the time axis - this is more subtle but equally flawed).


I agree that the mechanic for hopping is similar to that for a proportional pool.  However, a proportional pool can be effectively hopped with information from the past whereas, a PPLNS pool can only be exploited using information from the future.  I agree that you don't need to know exactly when the round will end but the lack-of-memory property of the distribution of future blocks w.r.t. shares tells us that the current round duration gives us absolutely no information on the expected number of blocks in the next N shares.

No I don't.  What is wrong with it?


If you start mining now then your chances of your shares being in the range (X-N, N] are exactly the same as they would be at the beginning of a round.  The expected round length for the current round is precisely 2,140,994 + 1,468,195.430 = 3,609,189.43 shares (basic corollary of the lack-of-memory property) and it gets longer with every single non-block-generating share submitted.  Suggesting that the round is close to an end because many shares have been submitted is like suggesting that a heads is due after flipping a fair coin five times and getting tails each time.

You are more than welcome to try to "reverse pool hop" the PPLNS pool here, you will be helping the miners out by lowering the variance slightly and you'll get a fair reward for your shares in the long run.

This is not a problem, it is a fact about the reward system.

This is true but completely irrelevant to the issue of pool hopping.

GoldenBoar, your recent comments betray your lack of understanding and it's clear to me that you won't comprehend the mathematics without some careful thought and study.  If you genuinely want to learn then feel free to PM me.

I'm sorry Mike for hijacking your thread, I got carried away.  I'll stop now.

Wow, I've missed a lot while I was ill.

That said, I've monitored the site from my tablet, and it's been holding stable (although the hashrate is all over the place).

Yes, in theory you can game PPLNS, however it wouldn't make sense with proportional pools available. Additionally, the short rounds of pplns would all be missed by pplns hopping, making it exceptionally unattractive to pool hoppers.

There's something wrong with the SMPPS pool. The current BTC round share is ~100,000 but no block is being listed as found. If we haven't found a block, it should be ~3,000,000.

Everything else seems to working right. Some of my rewards have been shifted from Unconfimed to Balance.

Seems like there is an issue in block reporting since I rebuilt the server. All winning blocks are being rewarded properly, but not all are being diplayed.

There WAS an SMPPS BTC block found and paid, but it is not showing.

I've made a change to the database to facilitate a fix, but it may take a few days to straighten out the old blocks.

UPDATE: Or NOT I managed to implement the new block dates very quickly. There shouldn't be any missed by stats now and the page load on stats and blocks is MUCH faster.

Now I can maybe focus on my failing headless miner.

Y2K!!!!

I would say PROP for LTC. So many crypto currencies i can't keep up.