Nope, it's one extra hop. To make it two extra hops, you need to increase the chance of not decrementing to 66.67%.Update of /cvsroot/freenet/freenet/src/freenet In directory sc8-pr-cvs1:/tmp/cvs-serv25429/src/freenet
Modified Files:
Version.java Log Message:
6295:
If HTL == maxHTL, 50% chance of not decrementing. I believe this
converges to an extra 2 hops, somebody please check my math. This
provides some plausible deniability when you send a request at max
HTL (perturb runs only on client level...).
EXPLANATION:
Given a request at HTL==25, there's a 50% chance that it will immediately decrement. There's a 25% chance that it will decrement after 1 hop. There's a 12.5% chance that it will decrement after 2 hops. 6.25% ... 3 hops, etc.
So, in terms of expected # of extra hops, E:
E=0.5*0 + 0.25*1 + 0.125*2 + 0.0625*3 + ... =0.5*Sum[k=0 to infintiy,k*(0.5^k)] =0.5*0.5/(1-0.5)^2 =1
To derive that, I used the formula:
Sum[k=0 to infinity,k*q^k] = q/(1-q)^2, (for |q|<1)
So, if we want it to converge to 2 extra nodes, and q is the chance that we don't decrement, we have to solve:
2=(1-q)*0 + q*(1-q)*1 + q^2*(1-q)*2 + ... =(1-q)*Sum[k=0 to infinity,k*q^k] =(1-q)*q/(1-q)^2 =q/(1-q)
Solving for q: q=2/3. So, make the chance of not decrementing=2/3.
-Martin
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