<p>The math is clearly absurdly unrealistic because as there are fewer Bitcoins available, it becomes harder to lose them. So the rate of loss has to decay as the availability of Bitcoins goes down.</p>

CC BY-SA 3.0
2017-01-03T21:20:33.090Z
Although the quantity lost per iteration will fall, as the total supply decreases the RATE of loss be it half a percent, one percent, etc. per year would not change, as the circumstances leading to loss would be unchanged; death, drive failure, natural disaster, etc. The rate of loss will always be n^T where n is less than one; ie 0.99 and T is time.  It would seem to me that it is you that fails to understand logarithmic decay; half-life.
litepresence
CC BY-SA 3.0
2013-12-30T00:30:23.050Z
2013-12-30T00:30:23.050Z
David Schwartz
<p>Are you suggesting that 0.5% relative to the still available bitcoins are lost every year or 0.5% of the absolute amount of bitcoins? Anyway, either my math is lying or each would turn out to be about 10% loss in 20 years, which doesn't translate to "all" in my opinion.</p>

<p>Additionally, should the value of Bitcoin sufficiently increase (which would happen if as many Bitcoins were lost as you suggest), the protocol could be hard-forked to allow for another eight digits divisibility. While the distribution would remain the same, a fraction of a bitcoin would then still be enough to fuel a global economy. </p>

<p>Finally, since this question was first asked, wallets with deterministic key derivation have become more commonplace. As it is sufficient to transfer the master seed for such wallets, it is almost trivial to bequeath such wallets.</p>

CC BY-SA 3.0
2013-12-30T18:54:38.417Z
Excelent analysis! A loss of 0.5% of each year's existing money supply means that, over 20 years we get 1.005^20 = 1.1049 i.e. 10.49%  If it's rather 0.5% of all possible Bitcoins (that is, off the max. possible 21 million) then in 20 years we get exactly 10% . Per your 2nd definition, bitcoins would evaporate in 200 years, as per the first, in ln(2)/ln(1.005) = 138.9757 years :)
Joe Pineda
CC BY-SA 3.0
2014-01-03T02:31:51.383Z
Thanks! However, in the relative loss scenario, the loss should be `1 - 0.995^20 = 9.54%`. Otherwise one would calculate a 0.5%/a growth, not a 0.5%/a loss.
Murch
CC BY-SA 3.0
2013-12-30T00:41:06.380Z
2017-01-03T22:01:57.003Z
2017-01-03T22:01:57.003Z
Murch
<p>There is currently a bounty offered on BitcoinTalk for implementing a method that would add bitcoins back to the mining reward in the case that an address had no activity for over 50 years which would completely resolve this concern.</p>

<p>The post can be found here and is located at #3 on the list <a href="https://bitcointalk.org/index.php?topic=371601.0" rel="nofollow">https://bitcointalk.org/index.php?topic=371601.0</a></p>

CC BY-SA 3.0
2013-12-30T05:10:36.863Z
2014-01-03T04:12:04.743Z
2014-01-03T04:12:04.743Z
michael.schuett
<p>The math associated with this question is simply wrong! Conceptually, it is very simple to apply the <a href="http://en.wikipedia.org/wiki/Rule_of_72" rel="nofollow">rule of 72</a> in reverse. By applying the rule of 72, known by most bankers,  knowledgeable investors, and knowledgeable consumers of loans, it indicates half of all Bitcoins will disappear after 144 years, assuming 0.5% are lost each year. (No PHD in mathematics is required, very simple math: 144 = 72/0.5)</p>

CC BY-SA 3.0
2014-01-03T12:04:37.980Z
2014-01-03T12:04:37.980Z
skaht
<p>Every year 1% of people die.</p>

<p>If every year 1% of bitcoin is lost, every 70 years:</p>

<p>HALF the coins in circulation remain.</p>

<p>if all coins were accounted for and all were already mined:</p>

<pre><code>2086 0.99^70  = 50% remain
2156 0.99^140 = 25% remain
2226 0.99^210 = 12.5% remain 
2296 0.99^280 = 6.25% remain
</code></pre>

<p><a href="https://i.sstatic.net/k50ez.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/k50ez.png" alt="enter image description here"></a></p>

CC BY-SA 3.0
2017-01-03T11:00:22.913Z
-1 This calculation makes weird assumptions because it seems extremely unlikely that 1% of the population dying that translates to 1% of the Bitcoin users dying. Also, 1% of the Bitcoin users dying doesn't necessarily translate to 1% of the Bitcoins lost. Thus, I'm not sure what we're supposed to learn from this answer.
Murch
CC BY-SA 3.0
2017-01-03T20:45:31.340Z
so you're proposing that even though 1% of all people die every year... bitcoin holders have found the fountain of youth and therefore 1% of bitcoin holders don't die like normal people?
litepresence
CC BY-SA 3.0
2017-01-03T21:00:44.170Z
Further, besides death and failure to will; there is house fire and paper wallets, and coins lost on hard drives that fail every 10 years unlike humans which tend to make it 70+ years, then there are coins lost because sent to invalid addy, and myriad of other failures.  I suspect 1% annual loss of supply is conservative.  http://i.imgur.com/6C238Pp.png
litepresence
CC BY-SA 3.0
2017-01-03T21:57:33.417Z
No, I merely suggest that since Bitcoin is a young technology, it is adopted first mostly by 20-40 year olds, and that those age groups have a smaller portion of the dying population for decades to come. Also it seems rather absurd that with gaining importance and value people would continue to lose Bitcoin at the same rate, especially since backups of deterministic wallets (that have become more common since this question was asked) don't outdate and are thus are perfectly inheritable.
Murch
CC BY-SA 3.0
2017-01-01T01:10:57.387Z
2017-01-03T21:02:37.053Z
2017-01-03T21:02:37.053Z
litepresence
<p>In theory, yes, they will all disappear eventually. However, as the money supply decreases due to their being less Bitcoin in circulation, the price will increase due to the scarcity of the existing coins so it will become more and mor expensive to misplace your bitcoins :)</p>

CC BY-SA 3.0
2017-01-03T11:01:29.313Z
-1 Not useful to me: Repeats information from the previous answers and doesn't add any new insights.
Murch
CC BY-SA 3.0
2017-01-02T03:12:31.580Z
2017-01-02T03:12:31.580Z
k26dr
<p>During <a href="http://media.ccc.de/browse/congress/2011/28c3-4746-en-bitcoin_an_analysis.html" rel="nofollow noreferrer">this CCC conference</a> from 2011, starting from 00:18:55, the presenter suggests that as bitcoins can be lost (lost private key, dead owner, sending to an &quot;eater&quot; address that nobody possesses, etc.), and as the total amount of bitcoins has a known threshold (21 millions), <strong>there is a possibility that given enough time, most bitcoins, if not all, will actually vanish</strong> (be unusable).</p>
<p>The questions is <strong>when</strong>?</p>
<p>Actually, according to him:</p>
<ul>
<li>if 0.5% of bitcoins are getting lost per year, &quot;all&quot; bitcoins will be gone by approx. 2032;</li>
<li>if the losing rate is 0.1% per year, it will probably last for a century, but will ultimately be doomed.</li>
</ul>
<p>And if we <em>suppose</em> that inactive wallets (2 years with no transaction) are in fact lost wallets, we reach that 0.1%/year threshold...</p>

CC BY-SA 3.0
2013-12-30T00:17:35.137Z
It could happen but I'd say it's highly unlikely. Perhaps as time approaches infinity, number of bitcoins approaches 0.
Loourr
CC BY-SA 3.0
2013-12-30T00:31:58.747Z
related: http://bitcoin.stackexchange.com/q/484/5406  http://bitcoin.stackexchange.com/q/9923/5406
Murch
CC BY-SA 3.0
2013-12-30T00:44:50.973Z
possible duplicate of [What could be the consequences of many bitcoins being lost out of circulation if people lose their wallets?](http://bitcoin.stackexchange.com/questions/1638/what-could-be-the-consequences-of-many-bitcoins-being-lost-out-of-circulation-if)
Murch
CC BY-SA 3.0
2013-12-31T07:40:49.693Z
Talking about the loss rate as any percentage of total bitcoins is nonsense. It should be the percentage of wallets that are lost per time unit. As bitcoins gain use and value surely the number of wallets will increase with smaller and smaller amounts in each.
Jannes
CC BY-SA 3.0
2014-01-03T14:51:08.353Z
Just watched the video: Kay Hamacher's scenario assumes that 5% per year disappear. His chart shows an absolute decline, i.e. 5% of the total amount of Bitcoins that ever existed are lost per year. (Which is absurd for the reasons discussed below).
Murch
<shrinking-money-supply>
Will "all" bitcoins ultimately vanish? (be unusable)
Totor
# Will "all" bitcoins ultimately vanish? (be unusable)

(Asked by: username_0 on 2013-12-30)

During [this CCC conference](http://media.ccc.de/browse/congress/2011/28c3-4746-en-bitcoin_an_analysis.html) from 2011, starting from 00:18:55, the presenter suggests that as bitcoins can be lost (lost private key, dead owner, sending to an "eater" address that nobody possesses, etc.), and as the total amount of bitcoins has a known threshold (21 millions), **there is a possibility that given enough time, most bitcoins, if not all, will actually vanish** (be unusable).

The questions is **when**?

Actually, according to him:

* if 0.5% of bitcoins are getting lost per year, "all" bitcoins will be gone by approx. 2032;
* if the losing rate is 0.1% per year, it will probably last for a century, but will ultimately be doomed.

And if we *suppose* that inactive wallets (2 years with no transaction) are in fact lost wallets, we reach that 0.1%/year threshold...

**Tags:** shrinking-money-supply

> **Comments:**
> **username_1**: It could happen but I'd say it's highly unlikely. Perhaps as time approaches infinity, number of bitcoins approaches 0.  
> **username_2**: related: http://bitcoin.stackexchange.com/q/484/5406  http://bitcoin.stackexchange.com/q/9923/5406  
> **username_2**: possible duplicate of [What could be the consequences of many bitcoins being lost out of circulation if people lose their wallets?](http://bitcoin.stackexchange.com/questions/1638/what-could-be-the-consequences-of-many-bitcoins-being-lost-out-of-circulation-if)  
> **username_3**: Talking about the loss rate as any percentage of total bitcoins is nonsense. It should be the percentage of wallets that are lost per time unit. As bitcoins gain use and value surely the number of wallets will increase with smaller and smaller amounts in each.  
> **username_2**: Just watched the video: Kay Hamacher's scenario assumes that 5% per year disappear. His chart shows an absolute decline, i.e. 5% of the total amount of Bitcoins that ever existed are lost per year. (Which is absurd for the reasons discussed below).  

---

## 6 answers

### Answer by username_4 on 2013-12-30. Score: 7

The math is clearly absurdly unrealistic because as there are fewer Bitcoins available, it becomes harder to lose them. So the rate of loss has to decay as the availability of Bitcoins goes down.

> **Comments:**
> **username_5**: Although the quantity lost per iteration will fall, as the total supply decreases the RATE of loss be it half a percent, one percent, etc. per year would not change, as the circumstances leading to loss would be unchanged; death, drive failure, natural disaster, etc. The rate of loss will always be n^T where n is less than one; ie 0.99 and T is time.  It would seem to me that it is you that fails to understand logarithmic decay; half-life.  

---

### Answer by username_2 on 2013-12-30. Score: 5

Are you suggesting that 0.5% relative to the still available bitcoins are lost every year or 0.5% of the absolute amount of bitcoins? Anyway, either my math is lying or each would turn out to be about 10% loss in 20 years, which doesn't translate to "all" in my opinion.

Additionally, should the value of Bitcoin sufficiently increase (which would happen if as many Bitcoins were lost as you suggest), the protocol could be hard-forked to allow for another eight digits divisibility. While the distribution would remain the same, a fraction of a bitcoin would then still be enough to fuel a global economy.

Finally, since this question was first asked, wallets with deterministic key derivation have become more commonplace. As it is sufficient to transfer the master seed for such wallets, it is almost trivial to bequeath such wallets.

> **Comments:**
> **username_6**: Excelent analysis! A loss of 0.5% of each year's existing money supply means that, over 20 years we get 1.005^20 = 1.1049 i.e. 10.49%  If it's rather 0.5% of all possible Bitcoins (that is, off the max. possible 21 million) then in 20 years we get exactly 10% . Per your 2nd definition, bitcoins would evaporate in 200 years, as per the first, in ln(2)/ln(1.005) = 138.9757 years :)  
> **username_2**: Thanks! However, in the relative loss scenario, the loss should be `1 - 0.995^20 = 9.54%`. Otherwise one would calculate a 0.5%/a growth, not a 0.5%/a loss.  

---

### Answer by username_7 on 2013-12-30. Score: 1

There is currently a bounty offered on BitcoinTalk for implementing a method that would add bitcoins back to the mining reward in the case that an address had no activity for over 50 years which would completely resolve this concern.

The post can be found here and is located at #3 on the list <https://bitcointalk.org/index.php?topic=371601.0>


---

### Answer by username_8 on 2014-01-03. Score: 0

The math associated with this question is simply wrong! Conceptually, it is very simple to apply the [rule of 72](http://en.wikipedia.org/wiki/Rule_of_72) in reverse. By applying the rule of 72, known by most bankers, knowledgeable investors, and knowledgeable consumers of loans, it indicates half of all Bitcoins will disappear after 144 years, assuming 0.5% are lost each year. (No PHD in mathematics is required, very simple math: 144 = 72/0.5)


---

### Answer by username_5 on 2017-01-01. Score: -2

Every year 1% of people die.
If every year 1% of bitcoin is lost, every 70 years:
HALF the coins in circulation remain.
if all coins were accounted for and all were already mined:
2086 0.99^70  = 50% remain
2156 0.99^140 = 25% remain
2226 0.99^210 = 12.5% remain 
2296 0.99^280 = 6.25% remain

> **Comments:**
> **username_2**: -1 This calculation makes weird assumptions because it seems extremely unlikely that 1% of the population dying that translates to 1% of the Bitcoin users dying. Also, 1% of the Bitcoin users dying doesn't necessarily translate to 1% of the Bitcoins lost. Thus, I'm not sure what we're supposed to learn from this answer.  
> **username_5**: so you're proposing that even though 1% of all people die every year... bitcoin holders have found the fountain of youth and therefore 1% of bitcoin holders don't die like normal people?  
> **username_5**: Further, besides death and failure to will; there is house fire and paper wallets, and coins lost on hard drives that fail every 10 years unlike humans which tend to make it 70+ years, then there are coins lost because sent to invalid addy, and myriad of other failures.  I suspect 1% annual loss of supply is conservative.  http://i.imgur.com/6C238Pp.png  
> **username_2**: No, I merely suggest that since Bitcoin is a young technology, it is adopted first mostly by 20-40 year olds, and that those age groups have a smaller portion of the dying population for decades to come. Also it seems rather absurd that with gaining importance and value people would continue to lose Bitcoin at the same rate, especially since backups of deterministic wallets (that have become more common since this question was asked) don't outdate and are thus are perfectly inheritable.  

---

### Answer by username_9 on 2017-01-02. Score: -2

In theory, yes, they will all disappear eventually. However, as the money supply decreases due to their being less Bitcoin in circulation, the price will increase due to the scarcity of the existing coins so it will become more and mor expensive to misplace your bitcoins :)

> **Comments:**
> **username_2**: -1 Not useful to me: Repeats information from the previous answers and doesn't add any new insights.  

---

