A lot of people aren't satisfied with theoretical equations. So I created a simulation. I wrote a script in python...
Thanks liquidfire, for your simulation. Good idea. It's the next best thing to me actually making the change in my pool, to test it out.
There is a problem with it though. Block solve times, and share solve times, are not between 0.5 and 1.5 of their average. Nor are they uniformly distributed. They are between 0 and infinity, and some kind of inverse square distribution maybe.
I believe that bug is what's producing your results, showing that slow miners are disadvantaged. Because if a share cannot be solved in 0.5, and a block comes before then, then his work is wasted.
You are absolutely correct, that they are not between 0.5 and 1.5. But if i did between 0.25, and 1.75, 0.1 and 1.9, etc i'd get the same results long-term. And so on and so forth.
Accounting for the infinite right edge would be very, very difficult (not impossible) to simulate. In the end, it doesn't matter... because if I did, all that would do would shift the average somewhat to the right. But, the same thing would happen to the block time as well. They cancel each other out. At that point I am dealing with a different average. It doesn't matter what the average is that you use, the effect will still be there.
I am sure someone smarter than me can replace that small part of the code with a formula to simulate the real range. Its beyond my math knowledge. But know I am aware it is a flaw. I am almost certain the result would be very very similar if you did simulate that. I will attempt to do some research and see if I can figure it out. If i can, I'll re-run the simulations and see what happens. If anyone knows the right distribution for this, I can certainly convert it to python. H20 might be onto something about the inverse square distribution.
Again, I am picking arbitrary numbers to be the average. It doesn't matter what I pick. the point is the relationship between the two workers.
The block find time, and the share find time of the miner are going to be equally effected by any changes to the calculation of the times.