My paper did show that the advantage decreased with the block reward. However, in that limit, it also seemed to imply that a network state would appear where the revenue per unit hash decreased with increasing hashrate which should be impossible as just discussed.

In a followup email, I showed how the origin of this effect stems from the orphaning factor used which doesn't preserve the full network revenue per unit block. This led me to correct my assertions by pointing out that our miner profit equations seemed to be just lower bounds to the miner's true expected profit. As such, just because the lower bound on the revenue per unit hash advantage decreases with the block reward, this doesn't necessarily imply that the real revenue per unit hash advantage does also.

I suspect that the orphaning factor used, independently of the specific form of the block relay time, is incorrect or incomplete as stated.

Best,
Daniele

Daniele Pinna, Ph.D

On Tue, Sep 1, 2015 at 10:06 AM, Peter R <peter_r@gmx.com> wrote:
On 2015-09-01, at 12:56 AM, Peter Todd via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> wrote

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/msg03272.html

I don't believe anyone is arguing otherwise.  Miners with a larger fraction of the network hash rate, h/H, have a theoretical advantage, all other variables in the miner's profitability equation held constant.  

Dpinna originally claimed (unless I'm mistaken) that his paper showed that this advantage decreased as the block reward diminished or as the total fees increased.  This didn't seem unreasonable to me, although I never checked the math.  

Best regards,
Peter