📅 Original date posted:2015-05-10
📝 Original message:Le 08/05/2015 22:33, Mark Friedenbach a écrit :
> * For each block, the miner is allowed to select a different difficulty
> (nBits) within a certain range, e.g. +/- 25% of the expected difficulty,
> and this miner-selected difficulty is used for the proof of work check. In
> addition to adjusting the hashcash target, selecting a different difficulty
> also raises or lowers the maximum block size for that block by a function
> of the difference in difficulty. So increasing the difficulty of the block
> by an additional 25% raises the block limit for that block from 100% of the
> current limit to 125%, and lowering the difficulty by 10% would also lower
> the maximum block size for that block from 100% to 90% of the current
> limit. For simplicity I will assume a linear identity transform as the
> function, but a quadratic or other function with compounding marginal cost
> may be preferred.
>
Sorry but I fail to see how a linear identity transform between block
size and difficulty would work.
The miner's reward for finding a block is the sum of subsidy and fees:
R = S + F
The probability that the miner will find a block over a time interval is
inversely proportional to the difficulty D:
P = K / D
where K is a constant that depends on the miner's hashrate. The expected
reward of the miner is:
E = P * R
Consider that the miner chooses a new difficulty:
D' = D(1 + x).
With a linear identity transform between block size and difficulty, the
miner will be allowed to collect fees from a block of size: S'=S(1+x)
In the best case, collected will be proportional to block size:
F' = F(1+x)
Thus we get:
E' = P' * R' = K/(D(1+x)) * (S + F(1+x))
E' = E - x/(1+x) * S * K / D
So with this linear identity transform, increasing block size never
increases the miners gain. As long as the subsidy exists, the best
strategy for miners is to reduce block size (i.e. to choose x<0).
Thomas Voegtlin [ARCHIVE] /
npub10f…7ej47
2023-06-07 15:34:03
in reply to nevent1q…a3ve
Author Public Key
npub10f96gqrsu4qpygfgvuvzce47aavjvql703egfde0l2hua8dzpszs67ej47Published at
2023-06-07 15:34:03Event JSON
{
"id": "853953a7134b081c7fbade7aa2bd4417bf8c1f94b29f57afe320adda4cdc7c29",
"pubkey": "7a4ba40070e54012212867182c66beef592603fe7c7284b72ffaafce9da20c05",
"created_at": 1686152043,
"kind": 1,
"tags": [
[
"e",
"aec396df7693e37c124fbd2891fe6c4a3b28f46e7fbc3f304a7b1d78d2f5ffbe",
"",
"root"
],
[
"e",
"46ddd0da13588b59dffbd4e3aada586b1f8ddcc2d6d7b31fe18de1ba02b81ce6",
"",
"reply"
],
[
"p",
"46986f86b97cc97829a031b03209644d134b939d0163375467f0b1363e0d875e"
]
],
"content": "📅 Original date posted:2015-05-10\n📝 Original message:Le 08/05/2015 22:33, Mark Friedenbach a écrit :\n\n\u003e * For each block, the miner is allowed to select a different difficulty\n\u003e (nBits) within a certain range, e.g. +/- 25% of the expected difficulty,\n\u003e and this miner-selected difficulty is used for the proof of work check. In\n\u003e addition to adjusting the hashcash target, selecting a different difficulty\n\u003e also raises or lowers the maximum block size for that block by a function\n\u003e of the difference in difficulty. So increasing the difficulty of the block\n\u003e by an additional 25% raises the block limit for that block from 100% of the\n\u003e current limit to 125%, and lowering the difficulty by 10% would also lower\n\u003e the maximum block size for that block from 100% to 90% of the current\n\u003e limit. For simplicity I will assume a linear identity transform as the\n\u003e function, but a quadratic or other function with compounding marginal cost\n\u003e may be preferred.\n\u003e \n\nSorry but I fail to see how a linear identity transform between block\nsize and difficulty would work.\n\nThe miner's reward for finding a block is the sum of subsidy and fees:\n\n R = S + F\n\nThe probability that the miner will find a block over a time interval is\ninversely proportional to the difficulty D:\n\n P = K / D\n\nwhere K is a constant that depends on the miner's hashrate. The expected\nreward of the miner is:\n\n E = P * R\n\nConsider that the miner chooses a new difficulty:\n\n D' = D(1 + x).\n\nWith a linear identity transform between block size and difficulty, the\nminer will be allowed to collect fees from a block of size: S'=S(1+x)\n\nIn the best case, collected will be proportional to block size:\n\n F' = F(1+x)\n\nThus we get:\n\n E' = P' * R' = K/(D(1+x)) * (S + F(1+x))\n\n E' = E - x/(1+x) * S * K / D\n\nSo with this linear identity transform, increasing block size never\nincreases the miners gain. As long as the subsidy exists, the best\nstrategy for miners is to reduce block size (i.e. to choose x\u003c0).",
"sig": "8b20ec6be953e6a3ec2f5fce16caedf879de9263cccdb6b5daacb4ee1cb9d4bcfe47cb9883dac8fc0bb6b0f3bbd637b2346f49d22806ddb6d4aa1dbb5bb14690"
}