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
>
>
>
>
>