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Date: Sat, 25 Oct 2014 23:10:02 +0100
From: Ross Nicoll <jrn@jrn.me.uk>
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Subject: Re: [Bitcoin-development] death by halving
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I'd suggest looking at how Dogecoin's mining schedule has worked out, 
for how halvings tend to actually affect the market. Part of Dogecoin's 
design was that it would halve very quickly (around every 75 days, in 
fact), so it's essentially illustrating worst case scenario.

Firstly, miners do not all move/shut down as a batch. Some will stay out 
of loyalty/apathy/optimism, so there's a jolt to hashrate when the 
rewards drop, and then a drift towards a steady-state. In most cases, 
the hardware costs vastly exceed the running costs, so while they may 
never see ROI due to the reward change, there's no benefit in stopping 
mining either.

On the other side, mining hardware update cycles are extremely 
aggressive, and newer hardware runs much faster. Further, those with 
newer hardware are likely to have the best hashrate to power ratio, and 
be less likely to turn off or rent out their hardware.

So, in theory there may be an uncomfortable period where the hashrate 
drops, but I would expect that drop to be much less than 50%, that most 
hardware that's turned off is not cost-effective to rent out, and that 
newer hardware being launched would push the hashrate back up again 
within a sensible timeframe.

Ross


On 25/10/2014 19:06, Alex Mizrahi wrote:
> # Death by halving
>
> ## Summary
>
> If miner's income margin are less than 50% (which is a healthy 
> situation when mining hardware is readily available), we might 
> experience catastrophic loss of hashpower (and, more importantly, 
> catastrophic loss of security) after reward halving.
>
> ## A simple model
>
> Let's define miner's income margin as `MIM = (R-C_e)/R`, where R is 
> the total revenue miner receives over a period of time, and C_e is the 
> cost of electricity spent on mining over the same period of time. 
> (Note that for the sake of simplicity we do not take into account 
> equipment costs, amortization and other costs mining might incur.)
>
> Also we will assume that transaction fees collected by miner are 
> negligible as compared to the subsidy.
>
> Theorem 1. If for a certain miner MIM is less than 0.5 before subsidy 
> halving and bitcoin and electricity prices stay the same, then mining 
> is no longer profitable after the halving.
>
> Indeed, suppose the revenue after the halving is R' = R/2.
>    MIM = (R-C_e)/R < 0.5
>    R/2 < C_e.
>
>    R' = R/2 < C_e.
>
> If revenue after halving R' doesn't cover electricity cost, a rational 
> miner should stop mining, as it's cheaper to acquire bitcoins from the 
> market.
>
> ~~~
>
> Under these assumptions, if the majority of miners have MIM less than 
> 0.5, Bitcoin is going to experience a significant loss of hashing power.
> But are these assumptions reasonable? We need a study a more complex 
> model which takes into account changes in bitcoin price and difficulty 
> changes over time.
> But, first, let's analyze significance of 'loss of hashpower'.
>
> ## Catastrophic loss of hashpower
>
> Bitcoin security model relies on assumption that a malicious actor 
> cannot acquire more than 50% of network's current hashpower.
> E.g. there is a table in Rosenfeld's _Analysis of Hashrate-Based 
> Double Spending_ paper which shows that as long as the malicious actor 
> controls only a small fraction of total hashpower, attacks have 
> well-define costs. But if the attacker-controlled hashrate is higher 
> than 50%, attacks become virtually costless, as the attacker receives 
> double-spending revenue on top of his mining revenue, and his risk is 
> close to zero.
>
> Note that the simple model described in the aforementioned paper 
> doesn't take into account attack's effect on the bitcoin price and the 
> price of the Bitcoin mining equipment. I hope that one day we'll see 
> more elaborate attack models, but in the meantime, we'll have to 
> resort to hand-waving.
>
> Consider a situation where almost all available hashpower is available 
> for a lease to the highest bidder on the open market. In this case 
> someone who owns sufficient capital could easily pull off an attack.
>
> But why is hashpower not available on the market? Quite likely 
> equipment owners are aware of the fact that such an attack would make 
> Bitcoin useless, and thus worthless, which would also make their 
> equipment worthless. Thus they prefer to do mining for a known mining 
> pools with good track record.
> (Although hashpower marketplaces exist: https://nicehash.com/ they 
> aren't particularly popular.)
>
> Now let's consider a situation where mining bitcoins is no longer 
> profitable and the majority of hashpower became dormant, i.e. miners 
> turned off their equipment or went to mine something else. In this 
> case equipment is already nearly worthless, so people might as well 
> lease it to the highest bidder, thus enabling aforementioned attacks.
>
> Alternatively, the attacker might buy obsolete mining equipment from 
> people who are no longer interested in mining.
>
> ## Taking into account the Bitcoin price
>
> This is largely trivial, and thus is left as an exercise for the 
> reader. Let's just note that the Bitcoin subsidy halving is an event 
> which is known to market participants in advance, and thus it 
> shouldn't result in significant changes of the Bitcoin price,
>
> ## Changes in difficulty
>
> Different mining devices have different efficiency. After the reward 
> halving mining on some of these devices becomes unprofitable, thus 
> they will drop out, which will result in a drop of mining difficulty.
>
> We can greatly simplify calculations if we sum costs and rewards 
> across all miners, thus calculating average MIM before the halving: 
> `MIM = 1 - C_e/R`.
>
> Let's consider an equilibrium break-even situation where unprofitable 
> mining devices were turned off, thus resulting in the change in 
> electricity expenditures: `C_e' = r * C_e`. and average MIM after the 
> halving `MIM' = 0`. In this case:
>
>     r * C_e = R/2
>     C_e / R = 1/2r
>     (1 - MIM) = 1/2r
>     r = 1/(2*(1-MIM))
>
> Let's evaluate this formulate for different before-halving MIM:
>
> 1. If `MIM = 0.5`, then `r = 1/(2*0.5) = 1`, that is, all miners can 
> remain mining.
> 2. If `MIM = 0.25`, then `r = 1/(2*0.75) = 0.66`, the least efficient 
> miners consuming 33% of total electricity costs will drop out.
> 3. If `MIM = 0.1`, then `r = 1/(2*0.9) = 0.55`, total electricity 
> costs drop by 45%.
>
> We can note that for the before-halving MIM>0, r is higher than 1/2, 
> thus less than half of total hashpower will drop out.
>
> The worst-case situation is when before-halving MIM is close to zero 
> and mining devices, as well as cost of electricity in different 
> places, are nearly identical, in that case approximately a half of all 
> hashpower will drop out.
>
> ## MIM estimation
>
> OK, what MIM do we expect in the long run? Is it going to be less than 
> 50% anyway?
>
> We can expect that people will keep buying mining devices as long as 
> it is profitable.
>
> Break-even condition: `R - C_e - P = 0`, where P is the price of a 
> mining device, R is the revenue it generates over its lifetime, and 
> C_e is the total cost of required electricity over its lifetime. In 
> this case, `R = C_e + P`, and thus:
>
>     MIM = 1 - C_e / (C_e + P)
>
> `f = C_e / P` is a ratio of the cost of electricity to the cost of 
> hardware, `C_e = f * P`, and thus
>
>     MIM = 1 - f * P / (f * P + P) = 1 - f / (f + 1) = 1 / (1 + f)
>
> MIM is less than 0.5 when f > 1.
>
> Computing f is somewhat challenging even for a concrete device, as 
> it's useful lifetime is unknown.
>
> Let's do some guesstimation:
>
> Spondoolies Tech's SP35 Yukon unit consumes 3.5 KW and costs $4000. If 
> it's useful lifetime is more than 2 years and a cost of KWh is $0.1, 
> the total expenditures on electricity will be at least $6135, thus for 
> this device we have `f > 6135/4000 > 1.5`.
>
> If other devices which will be sold on the market will have similar 
> specs, we will have MIM lower than 0.5. (Well, no shit.)
>
> ## Conclusions
>
> Reward halving is a deficiency in Bitcoin's design, but there is some 
> hope it won't be critical: in the equilibrium break-even situation 
> hashpower drop is less than 50%.
> Hashrate might drop by more than 50% immediately after the halving 
> (and before difficulty is updated), thus a combination of the halving 
> and slow difficulty update pose a real threat.
>
>
> ------------------------------------------------------------------------------
>
>
> _______________________________________________
> Bitcoin-development mailing list
> Bitcoin-development@lists.sourceforge.net
> https://lists.sourceforge.net/lists/listinfo/bitcoin-development


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    I'd suggest looking at how Dogecoin's mining schedule has worked
    out, for how halvings tend to actually affect the market. Part of
    Dogecoin's design was that it would halve very quickly (around every
    75 days, in fact), so it's essentially illustrating worst case
    scenario.<br>
    <br>
    Firstly, miners do not all move/shut down as a batch. Some will stay
    out of loyalty/apathy/optimism, so there's a jolt to hashrate when
    the rewards drop, and then a drift towards a steady-state. In most
    cases, the hardware costs vastly exceed the running costs, so while
    they may never see ROI due to the reward change, there's no benefit
    in stopping mining either.<br>
    <br>
    On the other side, mining hardware update cycles are extremely
    aggressive, and newer hardware runs much faster. Further, those with
    newer hardware are likely to have the best hashrate to power ratio,
    and be less likely to turn off or rent out their hardware.<br>
    <br>
    So, in theory there may be an uncomfortable period where the
    hashrate drops, but I would expect that drop to be much less than
    50%, that most hardware that's turned off is not cost-effective to
    rent out, and that newer hardware being launched would push the
    hashrate back up again within a sensible timeframe.<br>
    <br>
    Ross<br>
    <br>
    <br>
    <div class="moz-cite-prefix">On 25/10/2014 19:06, Alex Mizrahi
      wrote:<br>
    </div>
    <blockquote
cite="mid:CAE28kUS-uDbd_Br3H5BxwRm1PZFpOwLhcyyZT9b1_VfRaBC9jw@mail.gmail.com"
      type="cite">
      <div dir="ltr">
        <div># Death by halving</div>
        <div><br>
        </div>
        <div>## Summary<br>
        </div>
        <div><br>
        </div>
        <div>If miner's income margin are less than 50% (which is a
          healthy situation when mining hardware is readily available),
          we might experience catastrophic loss of hashpower (and, more
          importantly, catastrophic loss of security) after reward
          halving.</div>
        <div><br>
        </div>
        <div>## A simple model</div>
        <div><br>
        </div>
        <div>Let's define miner's income margin as `MIM = (R-C_e)/R`,
          where R is the total revenue miner receives over a period of
          time, and C_e is the cost of electricity spent on mining over
          the same period of time. (Note that for the sake of simplicity
          we do not take into account equipment costs, amortization and
          other costs mining might incur.)</div>
        <div><br>
        </div>
        <div>Also we will assume that transaction fees collected by
          miner are negligible as compared to the subsidy.</div>
        <div><br>
        </div>
        <div>Theorem 1. If for a certain miner MIM is less than 0.5
          before subsidy halving and bitcoin and electricity prices stay
          the same, then mining is no longer profitable after the
          halving.</div>
        <div><br>
        </div>
        <div>Indeed, suppose the revenue after the halving is R' = R/2.</div>
        <div>&nbsp; &nbsp;MIM = (R-C_e)/R &lt; 0.5</div>
        <div>&nbsp; &nbsp;R/2 &lt; C_e.</div>
        <div><br>
        </div>
        <div>&nbsp; &nbsp;R' = R/2 &lt; C_e.</div>
        <div><br>
        </div>
        <div>If revenue after halving R' doesn't cover electricity cost,
          a rational miner should stop mining, as it's cheaper to
          acquire bitcoins from the market.</div>
        <div><br>
        </div>
        <div>~~~</div>
        <div><br>
        </div>
        <div>Under these assumptions, if the majority of miners have MIM
          less than 0.5, Bitcoin is going to experience a significant
          loss of hashing power.&nbsp;</div>
        <div>But are these assumptions reasonable? We need a study a
          more complex model which takes into account changes in bitcoin
          price and difficulty changes over time.</div>
        <div>But, first, let's analyze significance of 'loss of
          hashpower'.</div>
        <div><br>
        </div>
        <div>## Catastrophic loss of hashpower</div>
        <div><br>
        </div>
        <div>Bitcoin security model relies on assumption that a
          malicious actor cannot acquire more than 50% of network's
          current hashpower.</div>
        E.g. there is a table in Rosenfeld's _Analysis of Hashrate-Based
        Double Spending_ paper which shows that as long as the malicious
        actor controls only a small fraction of total hashpower, attacks
        have well-define costs. But if the attacker-controlled hashrate
        is higher than 50%, attacks become virtually costless, as the
        attacker receives double-spending revenue on top of his mining
        revenue, and his risk is close to zero.
        <div>
          <div><br>
          </div>
          <div>Note that the simple model described in the
            aforementioned paper doesn't take into account attack's
            effect on the bitcoin price and the price of the Bitcoin
            mining equipment. I hope that one day we'll see more
            elaborate attack models, but in the meantime, we'll have to
            resort to hand-waving.</div>
          <div><br>
          </div>
          <div>Consider a situation where almost all available hashpower
            is available for a lease to the highest bidder on the open
            market. In this case someone who owns sufficient capital
            could easily pull off an attack.</div>
          <div><br>
          </div>
          <div>But why is hashpower not available on the market? Quite
            likely equipment owners are aware of the fact that such an
            attack would make Bitcoin useless, and thus worthless, which
            would also make their equipment worthless. Thus they prefer
            to do mining for a known mining pools with good track
            record.</div>
          <div>(Although hashpower marketplaces exist:&nbsp;<a
              moz-do-not-send="true" href="https://nicehash.com/"
              target="_blank">https://nicehash.com/</a> they aren't
            particularly popular.)</div>
          <div><br>
          </div>
          <div>Now let's consider a situation where mining bitcoins is
            no longer profitable and the majority of hashpower became
            dormant, i.e. miners turned off their equipment or went to
            mine something else. In this case equipment is already
            nearly worthless, so people might as well lease it to the
            highest bidder, thus enabling aforementioned attacks.</div>
          <div><br>
          </div>
          <div>Alternatively, the attacker might buy obsolete mining
            equipment from people who are no longer interested in
            mining.</div>
          <div><br>
          </div>
          <div>## Taking into account the Bitcoin price</div>
          <div><br>
          </div>
          <div>This is largely trivial, and thus is left as an exercise
            for the reader. Let's just note that the Bitcoin subsidy
            halving is an event which is known to market participants in
            advance, and thus it shouldn't result in significant changes
            of the Bitcoin price,</div>
          <div><br>
          </div>
          <div>## Changes in difficulty</div>
          <div><br>
          </div>
          <div>Different mining devices have different efficiency. After
            the reward halving mining on some of these devices becomes
            unprofitable, thus they will drop out, which will result in
            a drop of mining difficulty.</div>
          <div><br>
          </div>
          <div>We can greatly simplify calculations if we sum costs and
            rewards across all miners, thus calculating average MIM
            before the halving: `MIM = 1 - C_e/R`.</div>
        </div>
        <div><br>
        </div>
        <div>Let's consider an equilibrium break-even situation where
          unprofitable mining devices were turned off, thus resulting in
          the change in electricity expenditures: `C_e' = r * C_e`. and
          average MIM after the halving `MIM' = 0`. In this case:</div>
        <div><br>
        </div>
        <div>&nbsp; &nbsp; r * C_e = R/2</div>
        <div>&nbsp; &nbsp; C_e / R = 1/2r</div>
        <div>&nbsp; &nbsp; (1 - MIM) = 1/2r</div>
        <div>&nbsp; &nbsp; r = 1/(2*(1-MIM))</div>
        <div><br>
        </div>
        <div>Let's evaluate this formulate for different before-halving
          MIM:</div>
        <div><br>
        </div>
        <div>1. If `MIM = 0.5`, then `r = 1/(2*0.5) = 1`, that is, all
          miners can remain mining.</div>
        <div>2. If `MIM = 0.25`, then `r = 1/(2*0.75) = 0.66`, the least
          efficient miners consuming 33% of total electricity costs will
          drop out.</div>
        <div>3. If `MIM = 0.1`, then `r = 1/(2*0.9) = 0.55`, total
          electricity costs drop by 45%.</div>
        <div><br>
        </div>
        <div>We can note that for the before-halving MIM&gt;0, r is
          higher than 1/2, thus less than half of total hashpower will
          drop out.</div>
        <div><br>
        </div>
        <div>The worst-case situation is when before-halving MIM is
          close to zero and mining devices, as well as cost of
          electricity in different places, are nearly identical, in that
          case approximately a half of all hashpower will drop out.</div>
        <div><br>
        </div>
        <div>## MIM estimation</div>
        <div><br>
        </div>
        <div>OK, what MIM do we expect in the long run? Is it going to
          be less than 50% anyway?</div>
        <div><br>
        </div>
        <div>We can expect that people will keep buying mining devices
          as long as it is profitable.</div>
        <div><br>
        </div>
        <div>Break-even condition: `R - C_e - P = 0`, where P is the
          price of a mining device, R is the revenue it generates over
          its lifetime, and C_e is the total cost of required
          electricity over its lifetime. In this case, `R = C_e + P`,
          and thus:</div>
        <div><br>
        </div>
        <div>&nbsp; &nbsp; MIM = 1 - C_e / (C_e + P)</div>
        <div><br>
        </div>
        <div>`f = C_e / P` is a ratio of the cost of electricity to the
          cost of hardware, `C_e = f * P`, and thus</div>
        <div><br>
        </div>
        <div>&nbsp; &nbsp; MIM = 1 - f * P / (f * P + P) = 1 - f / (f + 1) = 1 /
          (1 + f)</div>
        <div><br>
        </div>
        <div>MIM is less than 0.5 when f &gt; 1.</div>
        <div><br>
        </div>
        <div>Computing f is somewhat challenging even for a concrete
          device, as it's useful lifetime is unknown.</div>
        <div><br>
        </div>
        <div>Let's do some guesstimation:</div>
        <div><br>
        </div>
        <div>Spondoolies Tech's SP35 Yukon unit consumes 3.5 KW and
          costs $4000. If it's useful lifetime is more than 2 years and
          a cost of KWh is $0.1, the total expenditures on electricity
          will be at least $6135, thus for this device we have `f &gt;
          6135/4000 &gt; 1.5`.</div>
        <div><br>
        </div>
        <div>If other devices which will be sold on the market will have
          similar specs, we will have MIM lower than 0.5. (Well, no
          shit.)</div>
        <div><br>
        </div>
        <div>## Conclusions</div>
        <div><br>
        </div>
        <div>Reward halving is a deficiency in Bitcoin's design, but
          there is some hope it won't be critical: in the equilibrium
          break-even situation hashpower drop is less than 50%.</div>
        <div>Hashrate might drop by more than 50% immediately after the
          halving (and before difficulty is updated), thus a combination
          of the halving and slow difficulty update pose a real threat.</div>
      </div>
      <br>
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