Post
Topic
Board Pools
Re: Optimal pool abuse strategy. Proofs and countermeasures
by
Meni Rosenfeld
on 01/05/2013, 06:49:29 UTC
I have written a description of the optimal pool abuse strategy (for a single pool) with proofs and calculations. Available here:
http://bitcoin.atspace.com/poolcheating.pdf

Raulo, you have a mathematical error on page 1, in equation (4).

Your \xi depends on n. Consequently, you cannot pass to limit only in part of the expression.

The expression q:=1- (1/2^32* D)  is a real number < 1. Consequently, Q(n)=q^n -->0 as n --> \infty.

This makes perfect sense, because the probability that you will "almost surely" (in the sense of probability theory) find a block if you wait long enough (infinitely long).
It's not an error, though tricky and somewhat unclear.

He is assuming that \xi is constant while n and D are variable. For \xi=2, for example, he is considering a case that the hashes calculated are twice the average needed; he then considers what happens when D, and correspondingly n, go to infinity (continuous case). In this case the chance of not finding a block is indeed exp(-2).