From mboxrd@z Thu Jan 1 00:00:00 1970 Received: from sog-mx-2.v43.ch3.sourceforge.com ([172.29.43.192] helo=mx.sourceforge.net) by sfs-ml-2.v29.ch3.sourceforge.com with esmtp (Exim 4.76) (envelope-from ) id 1YrZIf-0007YI-8A for bitcoin-development@lists.sourceforge.net; Sun, 10 May 2015 22:02:17 +0000 X-ACL-Warn: Received: from slow1-d.mail.gandi.net ([217.70.178.86]) by sog-mx-2.v43.ch3.sourceforge.com with esmtp (Exim 4.76) id 1YrZIe-00056g-0z for bitcoin-development@lists.sourceforge.net; Sun, 10 May 2015 22:02:17 +0000 Received: from relay6-d.mail.gandi.net (relay6-d.mail.gandi.net [217.70.183.198]) by slow1-d.mail.gandi.net (Postfix) with ESMTP id 9CDFB47B8BC for ; Sun, 10 May 2015 23:48:49 +0200 (CEST) Received: from mfilter8-d.gandi.net (mfilter8-d.gandi.net [217.70.178.137]) by relay6-d.mail.gandi.net (Postfix) with ESMTP id 13749FB86F for ; Sun, 10 May 2015 23:48:41 +0200 (CEST) X-Virus-Scanned: Debian amavisd-new at mfilter8-d.gandi.net Received: from relay6-d.mail.gandi.net ([217.70.183.198]) by mfilter8-d.gandi.net (mfilter8-d.gandi.net [10.0.15.180]) (amavisd-new, port 10024) with ESMTP id E8pGbEpph-84 for ; Sun, 10 May 2015 23:48:39 +0200 (CEST) X-Originating-IP: 92.229.161.198 Received: from [192.168.1.2] (x5ce5a1c6.dyn.telefonica.de [92.229.161.198]) (Authenticated sender: thomasv@electrum.org) by relay6-d.mail.gandi.net (Postfix) with ESMTPSA id 9FCECFB8A0 for ; Sun, 10 May 2015 23:48:39 +0200 (CEST) Message-ID: <554FD237.2020009@electrum.org> Date: Sun, 10 May 2015 23:48:39 +0200 From: Thomas Voegtlin User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:31.0) Gecko/20100101 Thunderbird/31.6.0 MIME-Version: 1.0 To: bitcoin-development@lists.sourceforge.net References: <16096345.A1MpJQQkRW@crushinator> In-Reply-To: Content-Type: text/plain; charset=windows-1252 Content-Transfer-Encoding: quoted-printable X-Spam-Score: 0.0 (/) X-Spam-Report: Spam Filtering performed by mx.sourceforge.net. See http://spamassassin.org/tag/ for more details. X-Headers-End: 1YrZIe-00056g-0z Subject: Re: [Bitcoin-development] Proposed alternatives to the 20MB step function X-BeenThere: bitcoin-development@lists.sourceforge.net X-Mailman-Version: 2.1.9 Precedence: list List-Id: List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Sun, 10 May 2015 22:02:17 -0000 Le 08/05/2015 22:33, Mark Friedenbach a =E9crit : > * For each block, the miner is allowed to select a different difficul= ty > (nBits) within a certain range, e.g. +/- 25% of the expected difficulty= , > and this miner-selected difficulty is used for the proof of work check.= In > addition to adjusting the hashcash target, selecting a different diffic= ulty > also raises or lowers the maximum block size for that block by a functi= on > of the difference in difficulty. So increasing the difficulty of the bl= ock > by an additional 25% raises the block limit for that block from 100% of= the > current limit to 125%, and lowering the difficulty by 10% would also lo= wer > the maximum block size for that block from 100% to 90% of the current > limit. For simplicity I will assume a linear identity transform as the > function, but a quadratic or other function with compounding marginal c= ost > may be preferred. >=20 Sorry but I fail to see how a linear identity transform between block size and difficulty would work. The miner's reward for finding a block is the sum of subsidy and fees: R =3D S + F The probability that the miner will find a block over a time interval is inversely proportional to the difficulty D: P =3D K / D where K is a constant that depends on the miner's hashrate. The expected reward of the miner is: E =3D P * R Consider that the miner chooses a new difficulty: D' =3D D(1 + x). With a linear identity transform between block size and difficulty, the miner will be allowed to collect fees from a block of size: S'=3DS(1+x) In the best case, collected will be proportional to block size: F' =3D F(1+x) Thus we get: E' =3D P' * R' =3D K/(D(1+x)) * (S + F(1+x)) E' =3D E - x/(1+x) * S * K / D So with this linear identity transform, increasing block size never increases the miners gain. As long as the subsidy exists, the best strategy for miners is to reduce block size (i.e. to choose x<0).