Bitcoin Forum

so i read the paper and understand the idea but what i want to know is, given the fact you gain 28% more potential BTC with 2 pools, how long does it actually take for the variance of hopping to settle down and produce that extra 28% on average? or more likely to correlate with real world statistics, to even be within 5%, 10%, 25% of it, again on average? or better yet, if there are n number of pools, how long does it take your average BTC to be within a given range of the potential gain for n pools?

there are probably several other variables that need to be defined to answer this like pool speed, difficulty, and others i'm not sure of. but if anyone could just plug in some example values based off current conditions or values and write an equation to express this or graph it i would be really interested to see the results. if something like this has been done just point me in that direction. hopefully i expressed this clearly enough

I don't have the numbers from the top of my head, but in the bithopper thread there is quite a lot posts about theoretical/real world statistics and about variance and options how to reduce it.

https://bitcointalk.org/index.php?topic=26866

The thread is quite long and not very organized, so it might be rather time consuming to search through it. However you have a good chance of finding some answers to your questions there.

yes that thread is quite long and unorganized, but i've been through most of it and can't recall seeing anything quite along the line of what i'm looking for. and if i missed it, well, i really don't want to re read 200 pages. thank you for the advice though.

There is a lot to consider.  Consider that I have moved most of my hashing off of pools that are susceptible to hopping, and that others will too.  Right now pool hopping gives you an advantage (and takes it from others who do not know or understand that their pool is being hopped)  Read the threads below and see if your pool is mentioned (as being a good pool to take advantage of) and consider writing the owner, and if no changes are made, leaving.  If you are not hopping, and on a pool that is being used by hoppers, you are probably loosing BTC.

check out the bithopper thread:
https://bitcointalk.org/index.php?topic=26866.0

and the cherrypicking thread:
https://bitcointalk.org/index.php?topic=33031.0

while you are right about a hopper mining more BTC than a non hopper, that doesn't answer my question.

I think in the end the payout variance would be the same as with "standard" mining + depending on the block solving rate of the pool(s) you're hopping.

BULLSHIT.
They get every bit of expected value. Show me one damn person whoses shares got stolen by a hopper.

The pools say they will pay (your shares/total shares) * 50 and ABSOLUTELY everyone gets that. Hoppers and non hoppers a like. You can put in your shares and see you get every penny due to you.

THEY ARE REALLY ACTUALLY PISSED CAUSE HOPPERS LEAVE WHEN IT ISNT PROFITABLE FOR THEM TO STAY.

Almost no pool has stated rules against hoppers.

And it isnt differnt than people mining BTC when it is profitable and then stopping when the price drops to $6 and then starting again when it hits $10

It is no different than the people jumping on namecoin when it is more profitable then bitcoin and then leaving when it isnt.


it is no different than those who jump on ixcoin or i0coin when they are insanely profitable.


Tell me.. if bitcoin drops to 1 penny a coin, will you stop mining? WELL THEN YOU ARE A DIRTY HOPPER.

WE are following stated rules. NOT A GOD DAMN COIN Gets stolen from anyone. People make less value cause they stay when it is no longer profitable and then get pissed at the people who leave.

Very true, you have to watch the rules of the game, and choose wisely.. just like in ANY DAMN GAME. And people who know how to play better than you will. And in any game of profit, people will look for ways to maximize their profits. AS long as they are following the rules, they arent theives, and more than someone who challenges you for stepping across the line in bowling or complains when you clean your ball in golf.. when you would never due such a thing cause you arent that picky.



DOnt be an ignorant , be pissed at the rules and the payout methods, not the people who follow them to their maximal potential. Now I'm going to go hop back onto I0coin cause it is making more money than me than bitcoin.. sorry to all the bitcoin miners who are staying behind.. i;m not stealing shit from you guys either.

I can tell you for a fact that variance is variable!  You will never "settle down" to a steady 28%.  Your income will go up and your income will go down.  Mine has and so will yours.

i realize i will never hit that 28% mark, at least not consistently, but how long until i come with a certain percentage of it on average? surely someone on this forum has the math skills to come up with some numbers. let's say there are two pools, both are proportional payouts and mine at 100 Gh/s each. say my rig mines at 1 Gh/s. maybe i get 1.2 BTC one day and .3 BTC the next day and so on back and forth...given a constant difficulty, how many days, months or years before that daily BTC i mine will always keep my total average BTC mined within a certain percentage of that ideal 28% increased gain? i am still asking my original question, just trying to reword it and fill in some blanks.

is this simply a ridiculous question to begin with? can it even be answered? pool hopping seems to be quite a hot topic and to me this seems like one of the most logical first questions someone would ask. i know hopping makes me more BTC than not hopping, and i know the theoretical maximum is 28% more for 2 pools, but what is a real world average gain?

and as much as i am pro hopping, i would love if we could keep this thread strictly to the math and leave opinions in the ethical hopping thread.

After several days of hopped mining my efficiency for different pools are as follows: 102%, 113%, 57%, 180%, 145%, 109%, 143%, 100%.
Your number may be higher or lower, who knows. But this should give you some information.

how exactly is the efficiency calculated?

Effective share value = BTC pool balance / number of shares submitted to the pool
Expected share value = 50/difficulty

Efficiency = Effective share value / Expected share value

This formula does not take into consideration luck involved with mining.

so how would you calculate the maximum possible efficiency for a given number of pools?

Kind of a nonsense question. The maximum possible efficiency would be if one pool consistently found a block immediately when you submitted a share, and your share was the only share counted. That's for any number of pools (because you would never hop off pool 1).

You need other parameters to bound maximum possible below 100%.

that is a nonsense question. i confused myself between efficiency and potential gain from hopping. what i meant to ask was, what is the potential BTC gain of hopping among a given number of pools? 2 pools increases my gain by a possible 28% extra BTC. does each additional pool simply add another 28% potential gain? so 3 pools is 56%, 4 pools is 84% and so on?

Meni's paper on pool payout functions already has this covered (see the "Pool" subforum, somewhere on page 3 or so).

Where do those additional coins come from ? :)

this is exactly what i was looking for, thank you.

There are no "additional coins". You can earn more than expected because the payout system is flawed.

Everyone submitting shares past 100% of difficulty on a prop. pool is knowingly giving away shares for less than solo mining would earn. If someone does this because he/she likes to mine in pools or whatever other reason - fine! These people will however earn LESS than expected.  They don't "loose" coins however, as they knowingly submit these shares to a pool with a payout system that is known to be broken for half a year now. It is clearly stated how payout will look like, so anyone mining at a pool can know and estimate what to expect (unless stats are delayed...).

They lose coins compared to what they would make if there were no hoppers... It's a zero sum game.  The number of coins to go around is pretty much fixed.  If no one hopped everyone would get the same amount of coins as if everyone hopped.  Somewhere in the middle hoppers get more and non-hoppers get less. 

There's any number of convoluted rationalizations to dress it up with but the simple fact is pool-hoppers make additional profit at the cost of non-hoppers.  Sure you could argue that it's their own stupid fault.  They don't know about hopping or they do but don't know how to avoid it.  Or perhaps in rare case they just like giving coins away.  But it doesn't alter the fact that for hoppers to win there has to be non-hoppers that lose.

That's 100% true, however the only thing that changes is the distribution of existing coins - there are no additional coins whatsoever that hoppers gain just for hopping. they gain their fair rewards for mining, only that they gain more than others.

To counter-balance hoppers, all you'd need to do is to increase your hashing rate (overclocking, backup machine...) by the percentage of hoppers in your pool during the 43.5% window while not taking that additional hash rate of yours into account in calculations. Then you'd again earn 100% of expected value again also in proportional pools. this goes a bit away from the original question of the OP however, which is still unanswered as far as I see it.

Indeed it is still unanswered. There have been several helpful responses but they dont quite answer my original question. Most likely there are too many variables to fill in to get a meaningful answer. Menis paper does a great job of telling the expected percentage gain from a given number of pools. Is there a way to fill in some blanks using his equations to generate a timeline using current pool data?

You can answer this yourself with a simple excel chart (this one's for Excel 2010, Excel 2007 and earlier have a similar function):

	Number of events actually occuring in a certain timeframe
	Number of events that should occur on average in a certain timeframe
=POISSON.DIST(A1;A2;TRUE)	Cumulative probability (sum of probabilities for 0-X events)
=POISSON.DIST(A1;A2;FALSE)	Probability of just X events occuring

In A2 you'd enter for example if you'd wait for 18 million shares at difficulty 1.8 million: 10 rounds (variable, since it depends on the pool's hashing speed how long this takes)
In A1 then you'd enter how many blocks should be found during these 18 million shares, for example: 8

In A3 you then see that there's a probability of ~1/3 that 0,1,2...7 or 8 blocks are being found in the next 18 million shares at difficulty 1.8 million.
In A4 you see that the probability to have exactly 8 blocks within the next 18 million shares at difficulty 1.8 million is ~11.25%

The nice thing about poisson is however that probability = variance.

To see the variance, you can assume that you hit always X blocks in X*difficulty shares, so A1 and A2 are always the same number and represent the number of rounds you wait.
Then you take a look at A4 and increase the numbers in A1 and A2 until you have reached your amount of rounds it takes. For 5% variance in block findings (= payouts) it takes for example ~64 rounds, for 10% variance just 16 rounds and for 25% variance 3 rounds.

You can improve upon this idea by adding an average hash rate + difficulty to the equations, then you would just enter the amount of rounds and get the variance, but that would require another 10 minutes of work (actually typing this took far longer than creating it in Excel).

Hopping mutiple proprotional pools is not covered in the paper you mention, just one prop and one pps. From simulations though I can say you can expect about 200% +/- 20% after 720 rounds (currently about a month at 2Thps). After 160 rounds (about a week at 2Thps) it's up to +/- 30% (approx).

This is only if you are hopping multiple pools of the same hashrate. Add multiply different hashrates and it gets a bit more complicated. Smaller pools tend to increase variance.

The variance can be calculated, but it depends on so many factors (and even with very simplified assumptions, the resulting expressions are messy) that for this purpose, you're probably better off with empirical observations like organofcorti's.

Raulo's paper only does 1 prop + backup. My paper (http://bitcoil.co.il/pool_analysis.pdf) (work in progress) deals with multiple pools.

Ah, thought he meant Raulo's (mentioned in the OP). Your paper is really quite interesting, and validated an assumption I made in simulation but wasn't completely sure of:


I'll be keeping an eye on your work!