Quote from: mikaelh on November 05, 2013, 10:13:27 AM

Quote from: mhps on November 05, 2013, 09:43:05 AM

Quote from: Trillium on November 05, 2013, 03:50:51 AM

If my understanding is correct, when we hit 10.000 diff, then the chainsperday value will change to a much lower number since its related directly to the whole integer value of the difficulty.

If you only have one (or a small few) machines then you probably wont see a block each day anymore.

I think it is mistake, because longer (>9) length chains are ignored when the block-found probability is calculated. See http://www.peercointalk.org/index.php?topic=695.msg6311#msg6311
If the longer chains are included, there is no jump in block-found difficulty when the network difficulty goes over an integer limit.

Yes, my original formula here actually wasn't accurate for high fractional difficulties. The issue boils down to the probability of the 10th number being prime. I thought that the probability would be negligible but actually it is about 3.5% according to my estimates (this number depends on the primorial used during mining). That means that about 3.5% of 9+-chains turn out to be 10-chains (9+-chains refers to chains at least of length 9). As the fractional difficulty increases, the number of accepted 9-chains diminishes while the 10-chains remain unaffected. Eventually there will be more 10-chains qualifying for blocks than 9-chains.

So my latest estimate for the amount of blocks found is:
blocks/day = chains/day * (1 - fracDiff + 0.035)

There will be a jump in the difficulty when difficulty goes to 10.0. That's because none of the 9-chains will qualify for blocks and we have to start looking for 10+-chains. I've actually been working on a paper related to this. Right now it looks like 10.0 will be more difficult than 9.996 will be which means we could get stuck between 9.996 and 10.0 for a while.

You can actually see that happening before in my charts:
http://xpm.muuttuja.org/charts/

If you look closely enough, the network block rate seems to have dropped when we went from 8.996 to 9.0. Of course we were using an older version of the mining algorithm back then which probably behaved slightly different.

I actually think 10.0 will be a bit 'easier' than 9.99. The reason is the stock miner will have finally switched to searching for 10-chains in the sieve and it will find a few more 10 chains than when it was searching for 9-chains. Once the diff passes .96 I think it is better to search for 1-higher chains. The biggest factor is just the nature of division though.. going from 9.0 to 9.5 cuts in half the number of 9-chain-blocks you will find (from 100% to 50%). But so does going from 9.98 to 9.99 (from 2% to 1%)