On Wed, Nov 06, 2013 at 01:06:47PM -0500, Christophe Biocca wrote: > I might try building this sometime soon. I think it may also serve an > educational purpose when trying to understand the whole network's behaviour. > > What level of accuracy are we looking for though? Obviously we need to > fully emulate the steps of the network protocol, and we need to be able to > specify time taken for transmission/processing for each node. Do we care > about the actual contents of the messages (to be able to simulate double > spend attempts, invalid transactions and blocks, SPV node communication), > and their validation (actual signatures and proof of work)? > > I imagine the latter is pretty useless, beyond specifying that the > signature/proof of work is valid/invalid. > > If we could build up a set of experiments we'd like to run on it, it would > help clarify what's needed. > > Off the top of my head: > > - Peter Todd's miner strategy of sending blocks to only 51% of the > hashpower.
Speaking of, I hadn't gotten around to doing up the math behind that strategy properly; turns out 51% I was overly optimistic and the actual threshold is 29.3% Suppose I find a block. I have Q hashing power, and the rest of the network 1-Q. Should I tell the rest of the network, or withhold that block and hope I find a second one? Now in a purely inflation subsidy environment, where I don't care about the other miners success, of course I should publish. However, if my goals are to find *more* blocks than the other miners for whatever reason, maybe because transaction fees matter or I'm trying to get nLockTime'd announce/commit fee sacrifices, it gets more complicated. There are three possible outcomes: 1) I find the next block, probability Q 2) They find the next block, probability 1-Q 2.1) I find the next block, probability Q, or (1-Q)*Q in total. 2.2) They find the next block, probability (1-Q)^2 in total. Note how only in the last option do I lose. So how much hashing power do I need before it is just as likely that the other miners will find two blocks before I find either one block, or two blocks? Easy enough: Q + (1-Q)*Q = (1-Q)^2 -> Q^2 - Q + 1/2 -> Q = (1 - \sqrt(2))/2 Q ~= 29.2% So basically, if I'm trying to beat other miners, once I have >29.3% of the hashing power I have no incentive to publish the blocks I mine! But hang on, does it matter if I'm the one who actually has that hashing power? What if I just make sure that only >29.3% of the hashing power has that block? If my goal is to make sure that someone does useless work, and/or they are working on a lower height block than me, then no, I don't care, which means my original "send blocks to >51% of the hashing power" analysis was actually wrong, and the strategy is even more crazy: "send blocks to >29.3% of the hashing power" (!) Lets suppose I know that I'm two blocks ahead: 1) I find the next block: Q (3:0) 2) They find the next block: (1-Q) (2:1) 2.1) I find the next block: (1-Q)*Q (3:1) 2.2) They find the next block: (1-Q)^2 (2:2) 2.2.1) I find the next block: (1-Q)^2 * Q (3:2) 2.2.2) They find the next block: (1-Q)^3 (2:3) At what hashing power should I release my blocks? So remember, I win this round on outcomes 1, 2.1, 2.2.1 and they only win on 2.2.2: Q + (1-Q)*Q + (1-Q)^2*Q = (1-Q)^3 -> Q = 1 - 2^-3 Q ~= 20.6% Interesting... so as I get further ahead, or to be exact the group of miners who have a given block gets further ahead, I need less hashing power for my incentives to be to *not* publish the block I just found. Conversely this means I should try to make my blocks propagate to less of the hashing power, by whatever means necessary. Now remember, none of the above strategy requires me to have a special low-latency network or anything fancy. I don't even have to have a lot of hashing power - the strategy still works if I'm, say, a 5% pool. It just means I don't have the incentives people thought I did to propagate my blocks widely. The other nasty thing about this, is suppose I'm a miner and recently got a block from another miner: should I forward that block, or not bother? Well, it depends: if I have no idea how much of the hashing power has that block, I should forward the block. But again, if my goal is to be most likely to get the next block, I should only forward in such a way that >30% of the hashing power has the block. This means that if I have some information about what % already has that block, I have less incentive to forward! For instance, suppose that every major miner has been publishing their node addresses in their blocks - I'll have a pretty good idea of who probably has that most recent block, so I can easily make a well-optimized decision not to forward. Similarly because the 30% hashing power figure is the *integral* of time * hashes/second, if miners are forwarding near-target-headers, I might as well wait a few seconds and see if I see any near-target-headers; if I do for this block then I have evidence that hashing power does have it, and I shouldn't forward. So yeah, we're fucked and have got to fix this awful incentive structure somehow before the inflation subsidy gets any smaller. Also, raising the blocksize, especially by just removing the limit, is utter madness given it can be used to slow down block propagation selectively, so the hashing power that gets a given block is limited repeatably to the same group. P.S: If any large pools want to try this stuff out, give me a shout. You have my PGP key - confidentiality assured. P.P.S: If you're mining on a pool with more than, like, 1% hashing power, do the math on varience... Seriously, stop it and go mine on a smaller pool, or better yet, p2pool. -- 'peter'[:-1]@petertodd.org 00000000000000078b970f5134bae96da021744f80e04aa9dc2e2d2c2bcb07c2
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