Quote from: Luke-Jr on June 23, 2011, 06:08:07 PM

Tonal is a superior number system originally devised in 1862. The equivalent in the newer hexadecimal format is 0.ffff

and why didn't it prevail?

and where do u get the 0.ffff from, which should be 65535/16^4 right? and the "diff" is the difficulty(http://blockexplorer.com/q/getdifficulty) in ton/hex?

Quote from: HanSolo on June 23, 2011, 08:05:09 PM

Your analysis seems to assume there's some benefit under PPLNS from hopping in and out, so a lot of people will do it. There's no benefit, so it will only be a small group of superstitious people.

There's no benefit? what makes u believe that? just a statement, but no verification isn't enough.

lets examine a few examples.

Code:

expanation:
y-axis(up): reward paid per quarter round in halfs each digit
x-axis(right): relative time(not time! that depends on the pools h/s) in average quarter round shares(877226/4) each digit
after a block is solved the numbers start counting up again: 23Solved123456Solved1234Solved1....

average round lenght: 1234
fast round: 12 (half the shares needed)
long round: 123456 (1,5 times the shares needed)
even longer: 12345678 (double the shares needed)

normal miner/hopper getting paid a half: #
hopper getting paid a half, but not normal miner: W
the hopper hops from the end of the pplns round to a normal pps-server, and when the round is on average halfway through the hopper joins the pplns again:
12hopper joins34hopper leaves12hopperjoins34hopper leaves12hopperjoins34...

#
#
2 for this segment(~220k submited shares) the miner/hopper got paid two halfs(average) normal pps payout

#
3 for this segment(~220k submited shares) the miner/hopper got paid 1 half(50% of average)

#
#
#
4 for this segment the miner/hopper got paid 3 halfs(150% of average)

W
#
1 for this segment the miner got paid 1 half(#) and the hopper got paid 2 halfs(#+W)

i hope u get what i mean, lets look at the corresponding graphs:

just average rounds: normals and hoppers get paid the same, except the miner gets all his money from the pplns-server, where as the hopper gets 50% from the pplns (34), and the other(12) paid from the pps-server. hopping gives neither an advantage nor a disadvantage:

Code:

########
########
########
########
12341234123412341234

now a longer round appears(123456), and the hopper gets more(all W's) than the normals. so it averages out for the hopper, but the normals have a net loss:

Code:

########
WW########
WW########
########
####
1234123412345612341234

now an even longer round occurs(12345678). the normals get two average rounds(12341234) just halfs, where as the hopper just gets 1 normal round of halfs(3434), so he gets less of the deficit from hopping:

Code:

########
WW ########
WW ########
########
####
123412341234567812341234

now an even longer round occurs(123456789abc, triple size of average). even the hopper gets hit by lots of "just halfs" and even a part nothing, which can be minimized by joining even later. but despite that, his balance is again better than of the normals:

Code:

########
########
WW #########
####WW
1234123456789abc12341234

a shorter than average round(12).hopper gets paid the averages on 12 from the pps, and is there to gain the triplepay from the (34) parts from the pplns. hopping gives again neither an advantes nor a disadvantage:

Code:

########
########
########
########
####
123412341212341234

as u can see hopping on prop as on pplns has some advantages and not as much disadvantages of joining said pool.

Quote from: HanSolo on June 23, 2011, 08:05:09 PM

If irrational superstitious hoppers make a PPLNS pool larger when there has been a long period without a generated block, that just makes the pool more attractive to rational variance-minimizers and fuss-minimizers, seeking a fair pool requiring minimum attention.

the pool gets more attractive? again just a statement, proof is needed too! can only be, because of the faster but smaller payouts(increased h/s).
but with lots of hoppers there also much risk for the normal miners mining very long for nearly nothing(relative time as pointed out above). the 12 parts take more time because only the normals mine and the hoppers are gone, additionally those parts have a good chance of being paid just once or even nothing at all(wich should be clear looking at the graphs above). it's the oppotise from prop! on prop u dont want to mine the last shares of a block and on pplns u dont want to mine the first shares.

Quote from: HanSolo on June 23, 2011, 08:05:09 PM

So lets say the hoppers leave after a generation in a futile search for higher returns elsewhere. Note that they are then increasing the variance of their still-alive PPLNS shares so this hop is even worse than neutral for one possible goal.

Some of the variance-minimizers and fuss-minimizers who joined during the hopper inrush are likely to stay. Each seasonal cycle of irrational hoppers should leave the pool with a larger base. And slowly train the hoppers to stop wasting their effort.

variance? i'm not quite sure what u want to point out. but i guess: the worth of their already mined shares is not affected if the keep mining or not.