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Author Topic: pool hopping questions  (Read 2040 times)
Sukrim
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August 23, 2011, 01:23:48 PM
 #21

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.

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August 23, 2011, 01:57:27 PM
 #22

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?
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August 23, 2011, 02:49:41 PM
 #23

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).

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organofcorti
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August 23, 2011, 02:54:23 PM
 #24

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?


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.

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Meni Rosenfeld
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August 23, 2011, 03:41:04 PM
 #25

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.

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?

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.
Raulo's paper only does 1 prop + backup. My paper (work in progress) deals with multiple pools.

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organofcorti
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August 23, 2011, 04:06:15 PM
 #26

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.

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?

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.
Raulo's paper only does 1 prop + backup. My paper (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:

Quote
The minimum value of x among m pools, assuming they all have constant hashrate (though not necessarily equal between them), follows the exponential distribution with mean 1=m.

I'll be keeping an eye on your work!


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