{"type":"rich","version":"1.0","author_name":"npub1swfeusu3ua9trup00qcnrgc2yndksyvgku4epk5tec7u4fmrez6qxpul5t","author_url":"https://nostr.ae/npub1swfeusu3ua9trup00qcnrgc2yndksyvgku4epk5tec7u4fmrez6qxpul5t","provider_name":"njump","provider_url":"https://nostr.ae","html":"📅 Original date posted:2014-10-25\n📝 Original message:# Death by halving\n\n## Summary\n\nIf miner's income margin are less than 50% (which is a healthy situation\nwhen mining hardware is readily available), we might experience\ncatastrophic loss of hashpower (and, more importantly, catastrophic loss of\nsecurity) after reward halving.\n\n## A simple model\n\nLet's define miner's income margin as `MIM = (R-C_e)/R`, where R is the\ntotal revenue miner receives over a period of time, and C_e is the cost of\nelectricity spent on mining over the same period of time. (Note that for\nthe sake of simplicity we do not take into account equipment costs,\namortization and other costs mining might incur.)\n\nAlso we will assume that transaction fees collected by miner are negligible\nas compared to the subsidy.\n\nTheorem 1. If for a certain miner MIM is less than 0.5 before subsidy\nhalving and bitcoin and electricity prices stay the same, then mining is no\nlonger profitable after the halving.\n\nIndeed, suppose the revenue after the halving is R' = R/2.\n   MIM = (R-C_e)/R \u003c 0.5\n   R/2 \u003c C_e.\n\n   R' = R/2 \u003c C_e.\n\nIf revenue after halving R' doesn't cover electricity cost, a rational\nminer should stop mining, as it's cheaper to acquire bitcoins from the\nmarket.\n\n~~~\n\nUnder these assumptions, if the majority of miners have MIM less than 0.5,\nBitcoin is going to experience a significant loss of hashing power.\nBut are these assumptions reasonable? We need a study a more complex model\nwhich takes into account changes in bitcoin price and difficulty changes\nover time.\nBut, first, let's analyze significance of 'loss of hashpower'.\n\n## Catastrophic loss of hashpower\n\nBitcoin security model relies on assumption that a malicious actor cannot\nacquire more than 50% of network's current hashpower.\nE.g. there is a table in Rosenfeld's _Analysis of Hashrate-Based Double\nSpending_ paper which shows that as long as the malicious actor controls\nonly a small fraction of total hashpower, attacks have well-define costs.\nBut if the attacker-controlled hashrate is higher than 50%, attacks become\nvirtually costless, as the attacker receives double-spending revenue on top\nof his mining revenue, and his risk is close to zero.\n\nNote that the simple model described in the aforementioned paper doesn't\ntake into account attack's effect on the bitcoin price and the price of the\nBitcoin mining equipment. I hope that one day we'll see more elaborate\nattack models, but in the meantime, we'll have to resort to hand-waving.\n\nConsider a situation where almost all available hashpower is available for\na lease to the highest bidder on the open market. In this case someone who\nowns sufficient capital could easily pull off an attack.\n\nBut why is hashpower not available on the market? Quite likely equipment\nowners are aware of the fact that such an attack would make Bitcoin\nuseless, and thus worthless, which would also make their equipment\nworthless. Thus they prefer to do mining for a known mining pools with good\ntrack record.\n(Although hashpower marketplaces exist: https://nicehash.com/ they aren't\nparticularly popular.)\n\nNow let's consider a situation where mining bitcoins is no longer\nprofitable and the majority of hashpower became dormant, i.e. miners turned\noff their equipment or went to mine something else. In this case equipment\nis already nearly worthless, so people might as well lease it to the\nhighest bidder, thus enabling aforementioned attacks.\n\nAlternatively, the attacker might buy obsolete mining equipment from people\nwho are no longer interested in mining.\n\n## Taking into account the Bitcoin price\n\nThis is largely trivial, and thus is left as an exercise for the reader.\nLet's just note that the Bitcoin subsidy halving is an event which is known\nto market participants in advance, and thus it shouldn't result in\nsignificant changes of the Bitcoin price,\n\n## Changes in difficulty\n\nDifferent mining devices have different efficiency. After the reward\nhalving mining on some of these devices becomes unprofitable, thus they\nwill drop out, which will result in a drop of mining difficulty.\n\nWe can greatly simplify calculations if we sum costs and rewards across all\nminers, thus calculating average MIM before the halving: `MIM = 1 - C_e/R`.\n\nLet's consider an equilibrium break-even situation where unprofitable\nmining devices were turned off, thus resulting in the change in electricity\nexpenditures: `C_e' = r * C_e`. and average MIM after the halving `MIM' =\n0`. In this case:\n\n    r * C_e = R/2\n    C_e / R = 1/2r\n    (1 - MIM) = 1/2r\n    r = 1/(2*(1-MIM))\n\nLet's evaluate this formulate for different before-halving MIM:\n\n1. If `MIM = 0.5`, then `r = 1/(2*0.5) = 1`, that is, all miners can remain\nmining.\n2. If `MIM = 0.25`, then `r = 1/(2*0.75) = 0.66`, the least efficient\nminers consuming 33% of total electricity costs will drop out.\n3. If `MIM = 0.1`, then `r = 1/(2*0.9) = 0.55`, total electricity costs\ndrop by 45%.\n\nWe can note that for the before-halving MIM\u003e0, r is higher than 1/2, thus\nless than half of total hashpower will drop out.\n\nThe worst-case situation is when before-halving MIM is close to zero and\nmining devices, as well as cost of electricity in different places, are\nnearly identical, in that case approximately a half of all hashpower will\ndrop out.\n\n## MIM estimation\n\nOK, what MIM do we expect in the long run? Is it going to be less than 50%\nanyway?\n\nWe can expect that people will keep buying mining devices as long as it is\nprofitable.\n\nBreak-even condition: `R - C_e - P = 0`, where P is the price of a mining\ndevice, R is the revenue it generates over its lifetime, and C_e is the\ntotal cost of required electricity over its lifetime. In this case, `R =\nC_e + P`, and thus:\n\n    MIM = 1 - C_e / (C_e + P)\n\n`f = C_e / P` is a ratio of the cost of electricity to the cost of\nhardware, `C_e = f * P`, and thus\n\n    MIM = 1 - f * P / (f * P + P) = 1 - f / (f + 1) = 1 / (1 + f)\n\nMIM is less than 0.5 when f \u003e 1.\n\nComputing f is somewhat challenging even for a concrete device, as it's\nuseful lifetime is unknown.\n\nLet's do some guesstimation:\n\nSpondoolies Tech's SP35 Yukon unit consumes 3.5 KW and costs $4000. If it's\nuseful lifetime is more than 2 years and a cost of KWh is $0.1, the total\nexpenditures on electricity will be at least $6135, thus for this device we\nhave `f \u003e 6135/4000 \u003e 1.5`.\n\nIf other devices which will be sold on the market will have similar specs,\nwe will have MIM lower than 0.5. (Well, no shit.)\n\n## Conclusions\n\nReward halving is a deficiency in Bitcoin's design, but there is some hope\nit won't be critical: in the equilibrium break-even situation hashpower\ndrop is less than 50%.\nHashrate might drop by more than 50% immediately after the halving (and\nbefore difficulty is updated), thus a combination of the halving and slow\ndifficulty update pose a real threat.\n-------------- next part --------------\nAn HTML attachment was scrubbed...\nURL: \u003chttp://lists.linuxfoundation.org/pipermail/bitcoin-dev/attachments/20141025/00dbaebf/attachment.html\u003e"}