Zero-Coupon Bonds / Catastrophe Bonds Based Mining Pool

[mikeywith]

I sent a PM to Theymos asking if he would be interested in using the forum funds to fund a PPS pool that is owned and operated by the community as sort of more decentralization to the mining side of Bitcoin.

My thoughts are that by next halving all small non-PPS pools would be gone, the profit margin in the mining industry is getting smaller and smaller every day and it's only a matter of time till we end up with 2-3 major pools which is a bit of concern.

Theymos did seem interested in the idea but from what I understood the forum funds aren't large enough to run a PPS pool at reasonable "very low risk" according to Meni Rosenfeld's formula.

What Theymos suggested was:

From what you said in your last PM, it seems that the bankruptcy risk can be mathematically modeled. If this is the case, then it should be possible for a pool operator to run without significant reserves itself, but buy insurance against the risk of bankruptcy. For example, a pool structured to have a 10% bankruptcy risk could run with "in-pocket" operating reserves of 288 BTC, but sell "pool catastrophe bonds" in several tranches:
 - Bond D: Bondholders pay a total of 288 BTC. This BTC goes into an escrow fund, and the bondholders get bonds in return. 90% of the time the bondholders get back 320 BTC on expiration, but 10% of the time the bond expires worthless (ie. when the pool "goes bankrupt").
 - Bond C: Bondholders also pay a total of 288 BTC. 99% of the time the bondholder gets back 290.9 BTC on expiration, but 1% of the time the bond expires worthless (ie. when the pool "goes bankrupt" and the 288 BTC from bond D isn't sufficient to cover the loss).
- Bond B: 99.9% of the time the bondholder gets back 288.3 BTC on expiration, but 0.1% of the time the bond expires worthless.
- Bond A: 99.99% of the time the bondholder gets back 288.03 BTC on expiration, but 0.01% of the time the bond expires worthless.

Note that each bond has ~zero expected value (eg. 320*0.9=288 BTC), so the bondholder isn't losing anything at infinity. In practice you'd also add a premium to the payout to account for the value of time and risk, probably by selling the bonds at auction. In practice you'd also have to do some different math, since Meni's math is based on the pool ever going bankrupt, whereas these bonds would need to expire after some finite period of time.

There a few mathematical errors in this but the idea seem interesting and I do like it.

The main issues about running anything catastrophe bond-related is that the bondholders need:

1- Assurance that the whole thing is not a scam:

Bitcointalk.org has been the center of the bitcoin evolution, it won't be hard for the community to come up with a perfect business model to attract investors, it isn't easy by any means but it could be done.

2- Very low-risk bonds since the rewards are also pretty low:

The different bond ratings solve the issue.

3- A well-maintained project.

The bitcointalk community does have some very smart devs who can probably maintain and operate a large scale pool, the two names I can think of are -ck and Kano as pool operators, although it's near impossible to get these two to work together, I guess we could figure something out.

* I have spoken about this with Phill, he has some interesting thoughts which I didn't quote here just in case he wants them to be private, so I hope him and everyone else can chime in with some thoughts on the project, and whether you think this business model could work or not, and of course, why and why not.

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[philipma1957]

I will sleep on this and try to poke some holes at it on Friday.

Not that I dislike the idea, but there are risks I will lay out as best I can.

A pps pool paying part of the tx fees

643512   6.25 + 0.60411003
643511   6.25 + 0.84270221
643510   6.25 + 0.84175771
643509   6.25 + 0.71806923
643508   6.25 + 1.34322915

in the case of viabtc they pay 96% of the 6.25 and 98% of the tx fee

so

.96 x 6.25000000 = 6.0000000000
.98 x 0.60411003 = 0.5920278294

total is 6.49202782 for block 643512

viabtc then bases % using block reward or

6.49202782/6.25 = 103.87% BASED ON A 6.25 BLOCK REWARD

SO times with high fees means. 100% or more if the pool hits a block with tx fees over 0.3 btc
and times with low fees could mean as low as 96% If the pool hit a zero fee block it would come to 96%

That is viabtc pay out numbers.  to be competitive with them means this pool would need to match that rate or better it.

It would be possible that 96% of reward and 98.5% of tx fees could work as it is better then the major pps pools payout plans.

Risk for the miner is close to none. But Pool operators could run off. Always a risk. And bad miners could point bad gear that withholds blocks which would eventually bankrupt the pool.

Risk for the pool is more complex. Meni's Rosenfeld's Formula is a guide stick to preventing bankruptcy >. His white paper states the larger the pps pool the greater the risk for the pool.

So if the pool has .7% of the network it should hit a block a day or about 6.25 btc a day along with the average tx fee number for the day which had been .6 btc

This means it would need to pay just about 6.49 to 6.5 coins a day.
If the same pool has 3.5% of the network roughly 32.5 coins a day.
If the same pool has 7.0% of the network roughly 65.0 coins a day would be paid out.

So it is something to think about as we need more then 3 or 4 pools.
A good pps+ pool with 0.7 to 7.0% of the network would be nice. A lot of math needs to be done. Math that is above my pay grade. But based on % share the coins needed to pay are as follows

% Share.   Daily coins paid.  Monthly payout--- Yearly payout

0.7               6.5 ___________ 195___________ 2,372.50
3.5             32.5 ___________ 975___________11,862.50
7.0             65.0 ___________1950__________ 23,725.00

Obviously the pool earns by block hits.
So 1 year at 90% luck would be very costly

237.250 BTC out of pocket with a 0.7% network share. pool fees are about   36.50 coins
1,186.250 BTC out of pocket with a 3.5% network share. pool fees are about 182.50

So the loss is
200 coins at 1 year of 90% luck and 0.7% of the network
1000 coins at 1 year of 90% luck and 3.5% of  the network

I will add a bit more later today.

[minefarmbuy]

As something we evaluated ourselves the risk/reward didn't line up along with a number of other factors we wanted to achieve. Leaving out the bulk of the latter. .. 

You're going to want 3-5 years of operational cost to effectively protect the venture and investors. 300 BTC was maybe 6% of what we calculated for a small op pps pool (maybe 300 BTC is just an example given for context but none the less helps gives relevance/perspective). All of which comes as a sacrifice to the users of the pool as with smaller pool hashrate your going to have a higher op fee with pps to absorb the risk/loss and will need to adjust accordingly. And so won't attract miners long term.

Bonds are an interesting idea but in this scenario any investment strategy would be very high risk to the investors. Then you need to consider who might be interested in investing in a pool, which the bulk of the investment from our analysis (and even irl) comes from the players you're looking to diversify from. Those who are invested in multiple pools already. So to say three to four pool future is more likely double that amount. Which already is basically the pooled mining environment we currently have.

I tried to elaborate more but it just keeps turning more and more into an LP shill, so this is all that's left from my edits. 

[mikeywith]

Thanks for your input, but please bear with me here because I can't seem to understand the "logic" behind the risk you talked about, as far as I know, the only way for the investor to lose money is IF the pool goes bankrupt if the pool doesn't do well or fails to attract miners the only loss is the operational cost.

Remember that these bonds are not interest-based but rather Zero-Coupon Bonds where bondholders don't get any interest for their bonds, and given enough funds to cover the reserve of keeping chances of bankruptcy at 0.01% to the investor it's a very low risk.

The only real problem I can see is not having enough hahrate to find blocks on regular bases, of course, this means you need to pay less to miners but let's assume your hahrate is too small that you have to pay 1 btc per day and yet don't find blocks for a whole year whereby you have already spent 365 btc, also the fact that miners have no motive to stick to the pool should they find another can make things worse.

An example:

You have 3 miners and their hashrate is subject to find a block in 30 days (at 100% luck), so you pay them (block/30) - fees for say 29 days at current numbers it's (6.25/30) 2.5% fees = 0.203125 BTC daily or 5.89 BTC paid for 29 days, and before the pool hits a block, those guys are gone and you have simply lost 5.89 BTC.

[minefarmbuy]

The risk I refer to is in relation to achieving successful enterprise, which you touch on just operation loss from a payout perspective a little further in your post.

Without getting into a debate on PPS scoring and why it's a net negative for miners and bitcoin's ecosystem, and assuming you want to operate a successful pool you'll want to look at securing hashrate either owned or contracted long term to mine a/your pps pool to guarantee revenue. Otherwise you're going to struggle to reach the level of investment to sustain operation at a loss for pps scoring before your able to garner a healthy market share in hashrate organically.

Of course bonds coupled with bankruptcy insurance protects the investors well, if that's just the focus here there's no real discussion besides how quickly you might expect to burn through funding, which anyone can excel at.

Also the speculation on the pooled environment is wrong imo, as pps pools will die off as op risk increases as more players exit mining, consolidating hashrate to these larger pools. Considering the abundance of pps pools currently, will be majority to die off. Essentially lean, well operated pools will survive, likely those that offer higher margins to their user base so they're able to thrive, compete, grow before another halving, as well the pools well funded with a hashrate base that is locked in.

But what do I know, I don't have a crystal ball, am biased, and already went through all these pooled scenarios in detail and is exhausting for me to rehash at for the moment, pun intended.

Still I'd be interested to see what others think, find, critique. but regardless of funding scenario if pps is the goal then you want to get a foundation of hashrate contracted to plug into your P&L model as a pool op to present to potential investors.

[kano]

...
Risk for the pool is more complex. Meni's Rosenfeld's Formula is a guide stick to preventing bankruptcy >. His white paper states the larger the pps pool the greater the risk for the pool.
...

Where does it say this?
I'm curious

The whole point of the equation is to NOT say this.
Time is not part of the equation.
A larger pool finds block faster, thus is expected to get closer to expected results faster.
What I guess you may be misusing is the term 'variance'

The issue you are having is you are missing the relevant important statistics as is shown below:

...
So 1 year at 90% luck would be very costly

237.250 BTC out of pocket with a 0.7% network share. pool fees are about   36.50 coins
1,186.250 BTC out of pocket with a 3.5% network share. pool fees are about 182.50
...

I got the impression, that last time you did take note of the fact that I have a CDF[Erl] on my pool stats (that NO other pool has)
This follows on to this exactly.
FYI it's actually called the Erlang CDF, but I abbreviate it to CDF[Erl]
https://en.wikipedia.org/wiki/Erlang_distribution#Cumulative_distribution_function_(CDF)

It is the whole point of why you need to understand that linear math does not give you the answers you need.

At 3.5% of the network, a pool is 'expected' to find, of course, 3.5% of the blocks.
Over 1 year, or 365.25 days, at 10 minutes per block, there's expected to be, on average, about 52,596 blocks a year.
It won't be exactly that, and of course more/less miners with more hash rate will affect this during each diff change.
But going with an 'expected' 52,596 blocks a year, a 3.5% pool is 'expected' to find just under 1841 blocks a year.

Now subtracting 10% (90% luck) from that gives 1657 blocks.
What's the chance that a pool will get 1657 blocks with a mean of 1.1111 difficulty or worse (90% luck or worse)
That's what the CDF[Erl] will tell you.
gsl_cdf_gamma_Q(1657,1657,0.9)=6.11077e-06 (0.000611%)
So the chance of getting 90% luck or worse for a year of 1657 blocks, is one in 163645 years
Yeah not very likely, so not worth considering.

What Meni's equation does, is take probabilities into consideration.
Since, what should you be asking? What's the chance (probability) of a pool going bankrupt.
(NOT what's the chance of a pool failing in one day or one month or one year)

You have no idea what the pool hash rate will be, nor how long it will take to get to a large % of the network.

No pool other than mine has ever stated a clear limit on what their network hash rate will be.
Most people are greedy, and do anything for more money, thus the pool OP will easily change their mind when they see a way to make more money.

So ... what is the current BTC backing value using the equation of Meni's that I keep quoting:
δ = the chance of going bankrupt
R = the amount of BTC a PPS pool must keep in reserve in it's pool wallet
B = the block BTC reward (currently 6.25 BTC)
f = the pool fee

Probability of failing - lets go with 0.1%
Pool fee - lets go with 3% - better than everyone else

R = B x (ln (1/δ)) / (2 x f) = 6.25 x 6.9078 / (2 x 0.03) = 719.6 BTC

Yes if they are a tiny pool they 'could' consider gaining that backing over time since they may take a long time to find even 100 blocks.
But who is going to actually guarantee they can and will do that?
They could have terrible luck and the first block be 1000% ... so they need around 60 BTC just for the first 10 'expected' blocks no matter how big they are ...
Yes everyone may see the pool is going down hill and run before they 'lose much'
... assuming the pool is clear about what blocks they find and how much they pay out ... oh wait ... what PPS pool that exists does that?

[mikeywith]

Without getting into a debate on PPS scoring and why it's a net negative for miners and bitcoin's ecosystem...

Since this is a proposal for a community project, then this particular point does matter, mind explaining how PPS is a net negative for BTC?

I do understand that you as someone who owns a PPLNS pool could be biased but that doesn't change the fact that your inputs are highly valuable.

The way I see it is that the investors/bondholders will have a very low-risk investment, I also don't think it's mandatory to have pre-hash contracts before you launch, I think it all boils down to the fact that the hashrate is irrelevant as long as the reserves of the pool are large enough to keep a low probability of bankruptcy, we have living proofs of small PPS pools such as Sigmapool.

Also, another factor that this whole idea revolves around the fact that this pool is going to be owned and operated by the Bitcointalk community, maybe my hopes are set too high but I am pretty confident that everyone who cares about bitcoin would pick this pool over Bitmain's or any other large cooperation's pool ESPECIALLY when they have to pay the same fees on both pools.

Pool fee - lets go with 3% - better than everyone else...

3% isn't better then everyone anymore, F2pool and BinancePool have 2.5% fees, which is very likely the bare minimum any pool can have to be sustainable long term which means the following reserves are needed to keep a 0.1% chance of going bankrupt.

(6.25  *ln 1000) / (2*0.025) = 863.46 BTC

[philipma1957]

Where does it say this?
I'm curious

If I quote that from his white paper can we end the feud?

My definition of larger pool is larger network share.

Here is why I say size matters

2.2 Pay-per-share (PPS)
In the PPS system, the operator is not a passive middleman between the participants, coordinating the joint effort to reduce individual variance. Rather, he actively absorbs all of the variance each miner is facing. When a participant submits a share, he is immediately rewarded with (1 − f )pB, corresponding to the expected value of this share’s contribution, minus fees – no matter how many blocks are eventually found. The operator gets to keep all the rewards for found blocks.
The payment per share is thus a deterministic value known in advance. This has several advantages for miners:
• Zero variance in the reward per share. There is still some variance in the number of shares found by the miner in unit time, but this is mostly insignificant.
• No waiting time until a block is found to obtain payment.
• Easy to describe the exact payment that will be received.
• Easy to verify that the promised reward is given, and that there are no losses due to dishonesty on the part of the operator or other parties.
• No losses due to pool-hopping, which is ineffective against this method.
However, this is the riskiest reward system for the pool operator – to be able to offer zero variance to participants, he must take all the variance himself. He can make a nice profit on short rounds – where he gains the entire block reward but only has to give payment for less than the average number of shares – but can lose substantially on long rounds. His variance is the same as the solo variance of mining with the capacity of the entire pool (in absolute terms, the variance increases proportionally to the hashrate). To compensate for his risk, the operator will charge a higher fee than with other methods, and this is the disadvantage of PPS for miners.
If the operator doesn’t correctly balance the pool’s fee with his financial reserves, the pool has a good chance of eventually going bankrupt. As derived in Appendix C, to keep the bankruptcy probability below δ, the operator should keep a reserve of at least
B ln 1δ R= 2f .
The required reserves are higher than most people anticipate. Operating such a pool is thus best left for those who know how to manage their risks responsibly, and miners who appreciate stability should shy away from improperly managed PPS pools which could shut down at any minute.

the pool owners variance risk increase with size of the hash rate.

So that practically speaking a 100ph pool needs a smaller reserve then a 1000 ph pool or a 10000ph sized pool

the formula for bankruptcy is absolute and is unchanging

but size matters since in the long run we are all dead and no cares about a pool 1000 years from now.

but for
1 year
2 years
3 years
4 years
5 years

the risk of bankrupcty is tied into the pools size.

     100 ph pool will earn  100 x 0.00000793 x 365        289.445 coins in a year.    or     46.3 blocks
   1000 ph pool ...............................................       2894.450 coins in a year     or   463.0 blocks
10,000 ph pool ...............................................     28944.500  coins in a year.    or 4630.0 blocks

the formula is absolute and will come up with the same number or reserve size  for all 3 pools above.

Meni simply says the 100 ph pool is carrying less variance risk

than the 10,000 ph pool is.

kano has good math skills better then mine

I am simply saying the bigger the pool the more coins it can lose quickly.

Lets say pool a should do 100 blocks in a years and its has 98% luck they are 2 blocks short.

Lets say pool b should do 10000 blocks in a year and it has 98% luck. they are 200 blocks short.

equal luck but more of a loss.

now in the case of 98% luck both pools would turn some profit since i mention earlier that fee structure would be 96% of the rewards and 98.5 % of the prior days tx fee average

A pool with this fee structure gets into trouble if it has an extended down turn achieving 94% luck means reserves get eaten into.

now if the pool should earn 100 blocks in a year it is down 6 blocks and fees paid were around 5 blocks

the pool loses 1 block worth of its reserve.

here is the tricky part. and this is why kano and I are disagreeing  about application of the bankruptcy formula

if the pool earns 10000 blocks a year it is down 600 blocks and fees paid of 500 blocks mean the larger pool is off 100 blocks.

now the idea of a 100  stretch of blocks doing 95% luck creates a cdf of (let kano do this math)

and the idea of a 10000 block   of blocks doing 95% luck creates a cdf of (let kano do this math)

the math will say it is less likely for the 10,000 block stretch at  95% luck this is true and why i agree the formula is set in stone.

but practical application of the formula is not set in stone.

for example kanos last 1000 blocks were 96.12% luck this would lose some  money for a pps pool owner

that pays 96% of reward and 98.5 % of tx fees.

the likely hood of it happening is of some importance thus meni’s formula

the  practicality of applying the formula is more difficult.

we are  doing a 1 year bond. on a 100 block a year pool going broke and crashing the bond of 10 blocks is less likely

then crashing a 10block bond on a 1000 block a year pool or worse yet on a 10,000 block a year pool

the bond having a 1 year life  would need to be larger with a large pool.

even though meni’s formula never changes.

personally I think the risk for the pool owner and for the bond holders is too high.

Plain and simple if the pps pool does really well it is subject to a with holding attack.
I would think this can not be fixed very easily.

[kano]

...
I am simply saying the bigger the pool the more coins it can lose quickly.
...

Again, time is not included anywhere in the equations.
That's why I highlighted that word you put there on the end.

and as I said:

You have no idea what the pool hash rate will be, nor how long it will take to get to a large % of the network.

... and everything else I've said related to that.

You keep going on about how much a certain size pool can lose.

But you are actually wrong.

It wont lose 10% of it's earnings over even 1657 blocks.
... as I point out above already.

It's not linear.
e.g. at 10,000 blocks you won't get a CDF[Erl] of 95%

Read what I actually posted above.

You like to throw out random numbers and say "hey this is big"
But size DOESN'T matter to determine the limit.

Read this line VERY carefully, since you wont read everything I've said above:
Fact: If a pool is 10 times larger it wont lose 10 times as much.

[philipma1957]

 kano  lets try this the last 1000 blocks made by your pool your luck was 96.12%

can we agree on this?

it says so on your pool luck chart.

so I will use that number.

get back to me so we can start with an agreement. With 1 fact.


all pools have a luck rate they may not publish but they have one. can we agree on this?


and in theory if a pool was to have only your gear with good block making firmware.
no coding errors .
a good connection to internet it could be said to trend towards 99-100% luck  but as we all know variance can have it drift away.

your pool first  1400 blocks about 104% luck
 luck next 1000 blocks 96.12 blocks.

if i own a pps pool and choose to ignore meni rosenfeld formula when i go for bond support i would need to have a basis of something to show my idea.

I could study pool luck of major pools and observational study would show most pools range from

94 to  106% luck when studied in 1000 block time periods.

but that when studied in 100 block time periods the range can be 90 to 110 blocks

so i set a time limit on a bond a year the bond is for 10 blocks.

if the pools payouts are 96% for rewards And 98.5% for tx fees

i eat into the bond at the 95-96% luck rate.

and i wipe the bond out at the 86-87% luck rate.

but as i said  all the math assumes no,one attacks the pool with bad gear/firmware.

which is why i am poking holes in the poolS founding concept.

[kano]

kano  lets try this the last 1000 blocks made by your pool your luck was 96.12%

can we agree on this?

it says so on your pool luck chart.

so I will use that number.

get back to me so we can start with an agreement. With 1 fact.
...

Firstly, don't forget that the last 1000 blocks made on my pool paid ... drum roll ... 103.99% PAPPS ... wow sucks to be on all those other pools

Anyway:
You're still not understanding these three words:
It's not linear.

Re-read my last post as many times as it takes until you understand what it says.

Simple calculation I've already done:

...
Now subtracting 10% (90% luck) from that gives 1657 blocks.
What's the chance that a pool will get 1657 blocks with a mean of 1.1111 difficulty or worse (90% luck or worse)
That's what the CDF[Erl] will tell you.
gsl_cdf_gamma_Q(1657,1657,0.9)=6.11077e-06 (0.000611%)
So the chance of getting 90% luck or worse for a year of 1657 blocks, is one in 163645 years
Yeah not very likely, so not worth considering.
...

Which says, a pool wont get 90% luck for 1657 blocks.

But to see that it isn't linear, that I keep saying.

Let's try 16570 blocks a year at 90% luck:

gsl_cdf_gamma_Q(16570,16570,0.9)=1.14938e-43 = never gonna fucking happen in the life of the universe
or one in 8.7 million billion billion billion billion years
(and by billion billion I mean 10^9 times 10^9)

See, just simply multiplying the pool hash rate by 10 goes from 'not gonna happen' 1 in 163645 years to 'wont even happen in the life of a billion consecutive universes'

You can pick 95% or 96% or even 97%
But you can't apply those numbers to a larger pool and ignore the CDF[Erl]
You have to consider the CDF[Erl] for each pool size.
... and you have no idea what the pool size is or will be.

In cases like the 90% example above, it VERY QUICKLY becomes invalid to even consider.

[philipma1957]

Yes, but you are assuming a lot one that the setup is not under attack from withholding. The gear is all good.

You once said 100% luck is a bit unrealistic 99.5% luck is more likely in the long long long run.

The range of your pool. was 104% for 1400 blocks then 96% for 1000 blocks.

We both agree that a 10000 block stretch is more likely to get closer to 99.5-100.00%

And we both agree that a 100 block stretch will show 90 to 110 luck

more easily then a 10000 block stretch will do.

Simply because a longer run lets the leveling of luck happen.

So I am not disagreeing that a larger pool is supposed to level closer to 99.5-100%

And that a 10000 block a year pool is less likely to do 96% or 104%

then a 100 block pool is to do 96% to 104%

I am simply saying that the 100 block pool is more easily cover with a 10 block bond for a year then the 10,000 block pool is covered by the same size bond.

You are insisting that both pools need the same reserve (bond) because of Meni's formula

If I make this pool and have to pay 27 blocks a day 1 bad day the first day of the pool and the bond will suffer.
If I make this pool and have to pay .27 blocks a day 1 bad day the first day of the pool and the bond will survive it.
If you look at bigger pools such as ant pool they do have bad days.

If I was funding the bond for the pool I would think that I am more likely to lose money then make it.
If I were the pool owner I would think I am likely to fail.

I know that after 1 year my 100 block a year pool needs to have made 98 blocks for the pool owner and the bond owner to both profit. Not only they do 98 blocks but they space them fairly well.

I know after 1 year my 10000 block a year pool need to have made 9800 blocks to profit.

In both cases they made 98% of why they should make and fees are 4% and 1.5% which cover  the short fall in luck.

I know that after 1 year my 100 block a year pool needs to have made 97 blocks to pay the bond back or ask for a renewal.
As my fee structure will cover that

At the 96 block level I am most likely losing money and dipping into the bond.

So the bond owner would have a small loss.

to give an example using your pool numbers here are your last 100 blocks
--------------------------Time------------------------------CDF[Erl]----Luck%--------------
"Last 100 Blocks   100.3wks   106.41%   102.35%   0.7458   93.97%   95.31%"

93.97%. which is a cdf of 0.7458

So 1 in four times this can happen.

So if I build this pool  sell a 1 year  bond and it does 100 blocks when it should have done around 106 blocks in a years time.

what are my results the fees on 100 blocks are around

4 blocks and 1 coin   but I need to pay 106 blocks I am down 1 block and 5.25 coins of my bond.

So by simply looking at your pools stats

it is about 25% chance of losing around 11.5 coins. of the 62.5 or 10 block bond. In 1 year of a 100 block pool
based on the cdf of 0.7458

I don't want to start a pool or fund a bond with a 25% chance of losing some money

So basically with a fee structure of 4% on the block reward and 1.5% on the tx fees

a 100 block a year pool has a 25% chance of losing 11.6 coins out of 62.5 coins.

now if I pull your 500 block stats from kano.is I get this

----------------------Time------------------------------CDF-------Luck%--------------
Last 500 Blocks   163.2wks   107.53%   108.84%   0.9513   93.00%   100.31%

So 500 blocks made should have been 537 blocks made

my fees on 500 blocks based on 4% and 1.5% = 20 blocks and 5 coins

so 537-500 = 37 blocks - 20 blocks and 5 coins = 16 blocks and 1.25 coins loss which wipes out a 10 block bond.

the chance of that happening is about 5 percent based on your cdf of 0.9513

I don't want to start a pool with a 5% chance of failing at the 500 block point

1 last set of numbers lets say I do a 50 block a year pool and have a 10 block bond.

here are your 50 block numbers

"----------------------Time------------------------------CDF-------Luck%--------------
Last 50 Blocks   88.6wks   115.94%   103.57%   0.8684   86.25%   88.52%"

so 50 blocks my fees are 2 blocks and .5 coins

I should have made 58 blocks

so 58-50 =  8 blocks short.   my fees reduce it to 6 blocks -.5 coins. which once again heavily dents the 10 block bond.

with a 0.8684 cdf the chance is 13.16% that it  CAN HAPPEN.

I do not use Meni's formula as a guide stick I simply used  observation of stats that show

a   50 block cdf gives a 14% chance of a loss some of the bond.
a 100 block cdf gives a 25% chance of a loss some of the bond.
a 500 block cdf gives a  5% chance of losing more then the bond.

So how do I sell this idea to an investor?

The answer is binance is willing to lose some coins to support its trading platform
The answer is bitmain is willing to lose some coins to support bitdeer and gear sales

The answer is any one with a btc based platform that is raking in heavy coins may want to run a pps pool to keep miners around.

Could I honest tell my bond holder it is a good idea.

No unless he is running coinbase or hiabtc  or bittrex since it helps to keep his trading business around.

To kano thank you for your clear and precise stats.

and as one can see a 500 block luck rate of 93% is  more unlikely then a  86% luck rate at 50 blocks

which is going towards kano's arguementnt that it is not linear

but more coins were lost by the 500 block luck rate of 93% which is what I have been trying to say for 2 years. That in the case of pps the pool size matter for the amount of  coin losses.

It does not matter that the 50 block event was 1 in 7 shot to happen this reduces the bond from 10 blocks to just under 6 blocks
and the 500 block event was 1 in 20 shot to happen this equals loss of bond and 7 blocks of coins into debt beyond the bond.

Both cases suck and are not a good selling point for a bond investor.

the block stats are from kano.is
see where most are

Code:

Block Statistics

Description-------	Time	Mean Diff%	MeanTx%	CDF[Erl]	Luck%	?PAPPS%
Last 5 Blocks----	39.7wks	107.55%	110.05%	0.6231	92.98%	101.40%
Last 10 Blocks---	52.9wks	91.84%	106.28%	0.4368	108.88%	114.68%
Last 25 Blocks---	72.3wks	105.95%	105.40%	0.6398	94.39%	98.59%
Last 50 Blocks---	88.6wks	115.94%	103.57%	0.8684	86.25%	88.52%
Last 100 Blocks-	100.3wks	106.41%	102.35%	0.7458	93.97%	95.31%
Last 250 Blocks-	139.4wks	103.80%	104.22%	0.7307	96.34%	99.49%
Last 500 Blocks-	163.2wks	107.53%	108.84%	0.9513	93.00%	100.31%
Last 1000 Blocks	201.3wks	104.01%	109.15%	0.8968	96.14%	103.99%
All - Last 2432 Blocks	305.4wks	98.76%	104.67%	0.2721	101.25%	105.03%
Monthly Statistics

UTC Month	Pool Avg	Blocks	Expected	Mean Diff%	MeanTx%	CDF[Erl]	Luck%	PAPPS%
2020 July	10.32PHs	2	0.37	18.44%	107.57%	0.0534	542.36%	578.16%
2020 June	11.04PHs	1	0.51	51.25%	101.60%	0.4010	195.14%	196.49%
2020 May	13.85PHs	1	2.86	286.12%	133.03%	0.9428	34.95%	46.08%
2019 December	18.86PHs	1	1.63	163.50%	100.46%	0.8050	61.16%	60.89%
2019 October	19.14PHs	1	0.86	85.67%	101.07%	0.5754	116.73%	116.92%
2019 September	20.91PHs	2	1.45	72.34%	101.71%	0.4242	138.23%	139.33%
2019 August	33.05PHs	2	1.50	75.17%	104.04%	0.4433	133.04%	137.17%
2019 July	27.12PHs	1	1.37	136.96%	101.02%	0.7458	73.01%	73.10%
2019 June	51.03PHs	5	5.24	104.71%	105.93%	0.5998	95.50%	100.26%
2019 May	49.18PHs	4	6.99	174.83%	106.42%	0.9179	57.20%	60.32%
2019 April	40.40PHs	3	2.56	85.33%	104.77%	0.4714	117.20%	121.69%
2019 March	63.41PHs	6	4.03	67.21%	103.00%	0.2200	148.78%	151.87%
2019 February	62.33PHs	7	5.78	82.54%	101.71%	0.3581	121.15%	122.12%
2019 January	87.37PHs	7	10.00	142.80%	101.03%	0.8696	70.03%	70.11%
2018 December	54.43PHs	4	6.33	158.27%	101.53%	0.8760	63.18%	63.57%
2018 November	204.05PHs	10	18.52	185.22%	100.78%	0.9884	53.99%	53.92%