From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: <pete@petertodd.org> Received: from smtp1.linuxfoundation.org (smtp1.linux-foundation.org [172.17.192.35]) by mail.linuxfoundation.org (Postfix) with ESMTPS id 34715122A for <bitcoin-dev@lists.linuxfoundation.org>; Tue, 1 Sep 2015 07:56:22 +0000 (UTC) X-Greylist: from auto-whitelisted by SQLgrey-1.7.6 Received: from outmail149077.authsmtp.com (outmail149077.authsmtp.com [62.13.149.77]) by smtp1.linuxfoundation.org (Postfix) with ESMTP id 62BC0A8 for <bitcoin-dev@lists.linuxfoundation.org>; Tue, 1 Sep 2015 07:56:21 +0000 (UTC) Received: from mail-c237.authsmtp.com (mail-c237.authsmtp.com [62.13.128.237]) by punt15.authsmtp.com (8.14.2/8.14.2/) with ESMTP id t817uIGx074688; Tue, 1 Sep 2015 08:56:18 +0100 (BST) Received: from muck (030-098.web.ny.np1.net [64.61.30.98] (may be forged)) (authenticated bits=128) by mail.authsmtp.com (8.14.2/8.14.2/) with ESMTP id t817uEQ9072497 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES128-SHA bits=128 verify=NO); Tue, 1 Sep 2015 08:56:16 +0100 (BST) Date: Tue, 1 Sep 2015 03:56:14 -0400 From: Peter Todd <pete@petertodd.org> To: Daniele Pinna <daniele.pinna@gmail.com> Message-ID: <20150901075613.GD17380@muck> References: <CAEgR2PE35K6kt1sZ0iDu2Y9vv+6+Omgg_n4n3gtMggYuE3YD-g@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/signed; micalg=pgp-sha256; protocol="application/pgp-signature"; boundary="GyRA7555PLgSTuth" Content-Disposition: inline In-Reply-To: <CAEgR2PE35K6kt1sZ0iDu2Y9vv+6+Omgg_n4n3gtMggYuE3YD-g@mail.gmail.com> X-Server-Quench: ecb0aaa1-507e-11e5-9f76-002590a135d3 X-AuthReport-Spam: If SPAM / abuse - report it at: http://www.authsmtp.com/abuse X-AuthRoute: OCd2Yg0TA1ZNQRgX IjsJECJaVQIpKltL GxAVKBZePFsRUQkR aAdMdgMUC1AEAgsB AmMbW1xeVVt7WGQ7 bQ5PawRDYUpQVg11 VUBOXVMcUA1pBll0 ZxceVRt2fgIIf3l5 bQg3DSJbDRUrdFt4 QkkBCGwHMGJ9YTYY Vl1YdwFReQMbfxxA PlMxNiYHcQ5VPz4z GA41ejw8IwAXBR5v az0kZXk1e3wqMRN0 BFg5HTI1AQU5Ryg0 NREjQl4B X-Authentic-SMTP: 61633532353630.1024:706 X-AuthFastPath: 0 (Was 255) X-AuthSMTP-Origin: 64.61.30.98/587 X-AuthVirus-Status: No virus detected - but ensure you scan with your own anti-virus system. X-Spam-Status: No, score=-2.6 required=5.0 tests=BAYES_00,RCVD_IN_DNSWL_LOW autolearn=ham version=3.3.1 X-Spam-Checker-Version: SpamAssassin 3.3.1 (2010-03-16) on smtp1.linux-foundation.org Cc: bitcoin-dev@lists.linuxfoundation.org Subject: Re: [bitcoin-dev] ERRATA CORRIGE + Short Theorem X-BeenThere: bitcoin-dev@lists.linuxfoundation.org X-Mailman-Version: 2.1.12 Precedence: list List-Id: Bitcoin Development Discussion <bitcoin-dev.lists.linuxfoundation.org> List-Unsubscribe: <https://lists.linuxfoundation.org/mailman/options/bitcoin-dev>, <mailto:bitcoin-dev-request@lists.linuxfoundation.org?subject=unsubscribe> List-Archive: <http://lists.linuxfoundation.org/pipermail/bitcoin-dev/> List-Post: <mailto:bitcoin-dev@lists.linuxfoundation.org> List-Help: <mailto:bitcoin-dev-request@lists.linuxfoundation.org?subject=help> List-Subscribe: <https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev>, <mailto:bitcoin-dev-request@lists.linuxfoundation.org?subject=subscribe> X-List-Received-Date: Tue, 01 Sep 2015 07:56:22 -0000 --GyRA7555PLgSTuth Content-Type: text/plain; charset=us-ascii Content-Disposition: inline Content-Transfer-Encoding: quoted-printable On Sun, Aug 30, 2015 at 10:01:00PM +0200, Daniele Pinna via bitcoin-dev wro= te: > Since my longer post seems to be caught in moderator purgatory I will > rehash its results into this much smaller message. I apologize for the > spamming. >=20 > I present a theorem whose thesis is obvious to many. >=20 > *THESIS: All hashrates* *h' > h generate a revenue per unit of hash v' > > v. * >=20 > Let us absurdly[1] assume that an optimal hashrate *h* exists where the > average revenue for each hash in service is maximized. This will result > from perpetually mining blocks of size *q,* is *v. *All larger hashrates = *h' > > h* will generate an average revenue per hash *v' < v*(effectively the > conclusion of my paper) due to the higher orphan risk carried from having > to mine blocks of size *q' > q*. Leading from Peter's model and my > analysis, the origin of this balance lies in the fact that larger miners > must somehow be forced to mine larger blocks which in turn carry a larger > orphan risk. >=20 > What happens if a large miner *h'* chooses not to mine his optimal block > size *q' *in favor of a seemingly "sub-optimal" block size* q*? > Since he mines a block of identical size as the smaller miner, they will > both carry identical orphan risks[2], and win identical > amounts*R+M(q)* whenever > they successfully mine a block. Since the larger miner can statistically > expect to win *h'/h* more blocks than the smaller miner, they will each > earn an identical revenue per unit of hash *R+M(q)/h*. >=20 > This however directly contradicts the assumption that an optimal hashrate > exists beyond which the revenue per unit of hash *v' < v*if *h' > h. * > *Q.E.D * >=20 > This theorem in turn implies the following corollary: >=20 > *COROLLARY: **The marginal profit curve is a monotonically increasing of > miner hashrate.* >=20 > This simple theorem, suggested implicitly by Gmaxwell disproves any and a= ll > conclusions of my work. Most importantly, centralization pressures will > always be present. FWIW I did a quick math proof along those lines awhile back too using some basic first-year math, again proving that larger miners earn more money per unit hashing power: http://www.mail-archive.com/bitcoin-development@lists.sourceforge.net/msg03= 272.html --=20 'peter'[:-1]@petertodd.org 000000000000000010b552c5f5c18705ccb1b21c550c08872089f89076840d6d --GyRA7555PLgSTuth Content-Type: application/pgp-signature; name="signature.asc" Content-Description: Digital signature -----BEGIN PGP SIGNATURE----- iQGrBAEBCACVBQJV5VobXhSAAAAAABUAQGJsb2NraGFzaEBiaXRjb2luLm9yZzAw MDAwMDAwMDAwMDAwMDAxMGI1NTJjNWY1YzE4NzA1Y2NiMWIyMWM1NTBjMDg4NzIw ODlmODkwNzY4NDBkNmQvFIAAAAAAFQARcGthLWFkZHJlc3NAZ251cGcub3JncGV0 ZUBwZXRlcnRvZC5vcmcACgkQwIXyHOf0udySCgf/ZbUHT7dN5kD1eQZylSWvj2ql OIkGpKcf5HZcH9knYn/C4uY6TU7/X5dYN2vpOtmMQWw3FaNXkBzhp/3KunFuO7+R e5SWILWjEeyE4mAKJAvxjv3Yf4r1YBd6judA5KYpHrcbbgjQl5daln1Df+1+iZxf AgIHIkM+JvZ3obXC4ixCtAmAijIIFBTcaY9qOnb+DbADi3Uiyrsvh5LPQpoPl2wk 7pHz1rjFCsYmh/nrUl0zVXabnQiwT4HhrnyLxF1y7VvgSfJT9OYDUMRtC6Q9EXfn yA2saU0LgpxslbGnszyOeCo2GEJsLFS7vMaQXaexXIe5xBizgdjNDI0MmLfavg== =SUjN -----END PGP SIGNATURE----- --GyRA7555PLgSTuth--