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Title: [Math] Need an equation of block solving expectation Post by: pent on March 01, 2012, 01:11:04 PM Please help to draw an equation of block solving expectation (in hashes) depending on current difficulty/tarrget.
I see that one provided here is not correct: https://en.bitcoin.it/wiki/Difficulty#How_soon_might_I_expect_to_generate_a_block.3F time = difficulty * 2**32 / hashrate I suppose value expectation here is "difficulty * 2**32", but this equation provides incorrect solutions for current network values. I was about to use formula for discrete finite random value: http://en.wikipedia.org/wiki/Expected_value But the Bitcoin target is uint256, and i see no possible way to calculate it. Title: Re: [Math] Need an equation of block solving expectation Post by: pent on March 01, 2012, 03:56:02 PM Sorry guys, all is fine :)
M = D * 2**256 / (0xffff * 2**208) = D * 2**256 / 2**224 = D * 2**32 or M = MaxTarget * 2**32 / Target Title: Re: [Math] Need an equation of block solving expectation Post by: elrodvoss on June 22, 2012, 05:06:01 AM I saw this and I was hoping that someone could help me figure out the math.
What I want to do in a excel file is enter in the Difficulty and Mhash/sec and give me the coins per day. from that I should be able to add on any other figure, just need the basic math for difficulty/mhash. Thanks in advance Title: Re: [Math] Need an equation of block solving expectation Post by: elrodvoss on June 22, 2012, 05:13:18 AM Think I answered my own question:
time = difficulty * 2**32 / hashrate But what does 2**32 stand for? i understand that when I enter it into excel it would be =sum difficulty *2??32/hashrate I don't understand what the 2**32 equals, but I assume that number is times the difficulty and then divided by the hashrate Title: Re: [Math] Need an equation of block solving expectation Post by: nave on June 22, 2012, 05:32:10 AM Think I answered my own question: time = difficulty * 2**32 / hashrate But what does 2**32 stand for? i understand that when I enter it into excel it would be =sum difficulty *2??32/hashrate I don't understand what the 2**32 equals, but I assume that number is times the difficulty and then divided by the hashrate It's 2 raised to the 32nd power. Or in excel 2^32, equal to 4 294 967 296. Title: Re: [Math] Need an equation of block solving expectation Post by: Pieter Wuille on June 22, 2012, 11:42:39 AM Difficulty 1 corresponds to a maxtarget 0x00000000FFFF0000000000000000000000000000000000000000000000000000, or a probability of 65535/2**48. Difficulty D corresponds to a probability of 65535/(D * 2^48).
Title: Re: [Math] Need an equation of block solving expectation Post by: Sukrim on June 22, 2012, 12:14:02 PM Difficulty 1 corresponds to a maxtarget 0x00000000FFFF0000000000000000000000000000000000000000000000000000, or a probability of 65535/2**48. Difficulty D corresponds to a probability of 65535/(D * 2^48). And 2^32 is a number very close to 65535/2^48, so it is often used in calculations that don't need to be 100% exact or where a few Satoshis more or less don't matter. |