Why pooled mining - Revision history

Dree12: outdated

2012-12-10T02:46:49Z

outdated

← Older revision		Revision as of 02:46, 10 December 2012
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	This page is an analysis of the costs/benefits of pooled mining.		This page is an analysis of the costs/benefits of pooled mining.

Gmaxwell: clarify

2011-07-02T15:43:51Z

clarify

← Older revision		Revision as of 15:43, 2 July 2011
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	This page is an analysis of the costs/benefits of pooled mining.		This page is an analysis of the costs/benefits of pooled mining.

	Some people say that no matter what, over the long run mining solo will provide the same return as mining in a pool. This is not true. Reality is subtly different from this: In reality, while competent solo mining has an equal _average_ return to competent, cheater-less, fee-less pooled mining the distribution of rewards is very different: Solo mining has higher odds of small no payout at all, ~~and~~ also higher odds of large payout. The bitcoin system is not stationary, so you can't be promised to average out over time, but this doesn't change that your expected return (an average against alternative yous) is the same either way.		Some people say that no matter what, over the long run mining solo will provide the same return as mining in a pool. This is not true. Reality is subtly different from this: In reality, while competent solo mining has an equal _average_ return to competent, cheater-less, fee-less pooled mining the distribution of rewards is very different: Solo mining has higher odds of small or no payout at all, but also higher odds of large payout. The bitcoin system is not stationary, so you can't be promised to average out over time, but this doesn't change that your expected return (an average against alternative yous) is the same either way.

	However, even though the combination of good and bad luck results in the same average most people value very low returns disproportionally less.		However, even though the combination of good and bad luck results in the same "average" most people value very low returns disproportionally less: Most are willing to lose most of the chance of enormous returns in exchange for getting rid of most of the chance of no returns.

	Let's start with the current conditions...		Let's start with the current conditions...
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	\|70.49%		\|70.49%
	\|}		\|}

	~~=== Conclusion ===~~
	~~500Mh/s are definitely not worth mining for a long time but chances to find at least one block are well beyond the above stated 4%.~~

	[[Category:Mining]]		[[Category:Mining]]

Gmaxwell: Don't confuses variance differences from expected return differences.

2011-07-02T15:41:21Z

Don't confuses variance differences from expected return differences.

← Older revision		Revision as of 15:41, 2 July 2011
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	This page is an analysis of the costs/benefits of pooled mining.		This page is an analysis of the costs/benefits of pooled mining.

	Some people say that no matter what, over the long run mining solo will provide the same return as mining in a pool. This is true in the ~~case~~ of ~~stable difficulty~~, ~~or in case~~ of ~~hash power being high enough that difficulty doesn~~'t ~~grow significantly in the '~~average time' ~~window to generate a block at~~ your ~~hash rate. It also assumes the solo miner has the same technological functionality as the pool~~ (~~which~~ is ~~generally not~~ the ~~case; e.g~~., ~~longpolling) Otherwise, as I will show below, it is possible that~~ the ~~probability~~ of ~~generating a block even "at infinity" will be less (far~~ less~~) than 1~~.		Some people say that no matter what, over the long run mining solo will provide the same return as mining in a pool. This is not true. Reality is subtly different from this: In reality, while competent solo mining has an equal _average_ return to competent, cheater-less, fee-less pooled mining the distribution of rewards is very different: Solo mining has higher odds of small no payout at all, and also higher odds of large payout. The bitcoin system is not stationary, so you can't be promised to average out over time, but this doesn't change that your expected return (an average against alternative yous) is the same either way.

			However, even though the combination of good and bad luck results in the same average most people value very low returns disproportionally less.

	Let's start with the current conditions...		Let's start with the current conditions...

Giszmo: /* The Maths */

2011-06-24T15:34:33Z

The Maths

← Older revision		Revision as of 15:34, 24 June 2011
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	* 202 days / 20160 blocks = 14 minutes / block		* 202 days / 20160 blocks = 14 minutes / block
	* hashrate = difficulty * 2**32 / time		* hashrate = difficulty * 2**32 / time
	* The Average hashing speed back then was (2**32 / 14 minutes) 5Mh/s		* The Average hashing speed back then was (2**32 / 14 minutes) '''5Mh/s'''
	* Today is June 24th 2011		* Today is June 24th 2011
	* Since block 20160 there have been [http://blockexplorer.com/b/133056 133056] - 20160 = 112896 blocks in 689 days.		* Since block 20160 there have been [http://blockexplorer.com/b/133056 133056] - 20160 = 112896 blocks in 689 days.
	* There were '''163''' blocks created per day.		* There were '''163''' blocks created per day.
	* Net performance increase was on average ((1+p)**112896=(11Th/s)/(5Mh/s)) ~~'''0.00013 per block'''~~		* Net performance increase was on average '''i=0.00013 per block''' using this formula: ((1+i)**112896=(11Th/s)/(5Mh/s))

	==== Assumptions ====		==== Assumptions ====

Giszmo: added figures for 1,3,6 months

2011-06-24T13:51:03Z

added figures for 1,3,6 months

← Older revision		Revision as of 13:51, 24 June 2011
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	\|-		\|-
	\|1 month		\|1 month
	\|84.83		\|84.83%
	\|-		\|-
	\|3 months		\|3 months
	\|74.25		\|74.25%
	\|-		\|-
	\|6 months		\|6 months
	\|71.04		\|71.04%
	\|-		\|-
	\|1 year		\|1 year

Giszmo: /* Results for not finding a single block in 10 years */

2011-06-24T13:50:16Z

Results for not finding a single block in 10 years

← Older revision		Revision as of 13:50, 24 June 2011
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	Probability for finding no block at all after n years are:		Probability for finding no block at all after n years are:
	{\| cellpadding="10" cellspacing="0" border="1"		{\| cellpadding="10" cellspacing="0" border="1"
	\|~~year~~		\|time
	\|probability of not finding a single block		\|cumulative probability of not finding a single block
	\|-		\|-
	\|1		\|1 month
	\|70.~~50196610996503%~~		\|84.83
	\|-		\|-
	\|2		\|3 months
	\|70.~~4899742485864%~~		\|74.25
	\|-		\|-
	\|3		\|6 months
	\|70.~~48996841288616%~~		\|71.04
	\|-		\|-
	\|4-10		\|1 year
	\|70.~~48996841004953~~%		\|70.50%
			\|-
			\|2 - 10 years
			\|70.49%
	\|}		\|}

Giszmo: removed the confusing starting condition before the first block.

2011-06-24T13:43:15Z

removed the confusing starting condition before the first block.

← Older revision		Revision as of 13:43, 24 June 2011
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	\|year		\|year
	\|probability of not finding a single block		\|probability of not finding a single block
	\|-
	\|0
	~~\|100%~~
	\|-		\|-
	\|1		\|1

Giszmo: redid the maths adjusting the priorly stated 96% odds of ever finding a block at 500Mh/s to 70%

2011-06-24T13:39:03Z

redid the maths adjusting the priorly stated 96% odds of ever finding a block at 500Mh/s to 70%

← Older revision		Revision as of 13:39, 24 June 2011
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	TODO: write in the details of calculating the probabilities, make some pretty charts?, calculate out the hash rate at which you have 25,50,75 percent chance of never generating a block solo under various assumptions.		TODO: write in the details of calculating the probabilities, make some pretty charts?, calculate out the hash rate at which you have 25,50,75 percent chance of never generating a block solo under various assumptions.

			== Alternative Perspective ==
			Mathematically the profit is the same for these conditions:
			* chance to make 10,000$ is 0.01%
			* chance to make 1$ is 100%

			=== What are the chances to not ever get a block? ===
			While a mathematician toying around with bitCoin mining might be fine with knowing it is mathematically fine to not see a BTC forever as the lucky case of getting 50 at a time will totally balance the odds of not finding it, others, especially those who want to get their hands on first bitCoins, might have a different feeling about it.

			So what are the odds of never finding a BTC?

			==== How BitCoin Works / Simplifications ====
			The bitCoin block chain readjusts its [[difficulty]] every 2016 blocks trying to make the next 2016 blocks be processed in 10 minutes each given an average performance of the past 2016 blocks.
			This process brings in some unsteadiness but to be conform with above equations time frame, we also look at periods of 2016 blocks but take difficulty only into consideration to determine the time frame for 2016 blocks and look at bitCoin as a lottery.

			==== The Maths ====
			* [[genesis block\|block 0]] was created January 3rd 2009
			* [http://blockexplorer.com/b/20160 block 2160] was created '''July 25th 2009'''
			* block 0 to 2160 took 202 days at difficulty 1.
			* 202 days / 20160 blocks = 14 minutes / block
			* hashrate = difficulty * 2**32 / time
			* The Average hashing speed back then was (2**32 / 14 minutes) 5Mh/s
			* Today is June 24th 2011
			* Since block 20160 there have been [http://blockexplorer.com/b/133056 133056] - 20160 = 112896 blocks in 689 days.
			* There were '''163''' blocks created per day.
			* Net performance increase was on average ((1+p)**112896=(11Th/s)/(5Mh/s)) '''0.00013 per block'''

			==== Assumptions ====
			* 500Mh/s
			* total net performance of 11Th/s
			* total net performance increase of i=0.013% per block over a long time
			* 163 blocks per day over a long time

			==== Results for not finding a single block in 10 years ====
			* For each block odds are o(#block)=1-500M/(11T(1+i)*#block)
			* For all blocks odds are the product of o(0) to o(3600*163)
			Until someone brings up the analytic solution to this product, here is a code snipped to calculate it:
			private double calculate() {
			double odds = 1.0d;
			for (int i = 0; i < 3600 * 163; i++) {
			if (i % (360 * 163) == 0)
			Log.d("", Double.toString(odds));
			odds *= odds(i);
			}
			return odds;
			}

			private double odds(int i) {
			return 1.0d - 5E8 / (11E12 * Math.pow(1.00013d, i));
			}
			Probability for finding no block at all after n years are:
			{\| cellpadding="10" cellspacing="0" border="1"
			\|year
			\|probability of not finding a single block
			\|-
			\|0
			\|100%
			\|-
			\|1
			\|70.50196610996503%
			\|-
			\|2
			\|70.4899742485864%
			\|-
			\|3
			\|70.48996841288616%
			\|-
			\|4-10
			\|70.48996841004953%
			\|}

			=== Conclusion ===
			500Mh/s are definitely not worth mining for a long time but chances to find at least one block are well beyond the above stated 4%.

	[[Category:Mining]]		[[Category:Mining]]

Luke-jr: Undo revision 11362 by Giszmo (talk): Quit it

2011-06-23T00:56:54Z

Undo revision 11362 by Giszmo (talk): Quit it

← Older revision		Revision as of 00:56, 23 June 2011
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	This page is an analysis of the costs/benefits of pooled mining.		This page is an analysis of the costs/benefits of pooled mining.

Giszmo: Undo revision 11344 by Luke-jr (talk) - see talk.

2011-06-22T22:47:33Z

Undo revision 11344 by Luke-jr (talk) - see talk.

← Older revision		Revision as of 22:47, 22 June 2011
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	{{stub}}		{{stub}}
			{{Delete}}

	This page is an analysis of the costs/benefits of pooled mining.		This page is an analysis of the costs/benefits of pooled mining.