I don't really have any context, but it doesn't seem like this is a hard problem.  Given the following assumptions:
1. The PT was denominated in LTC
2. The PT owner had (and still has) the actual shares
3. The ownership of PT shares is known to the PT owner

The most equitable thing to do is for the PT owner to transfer those shares to people on the new exchange.  If the new exchange does not support LTC, they can liquidate at a fair market value and convert those BTC to LTC.

It sucks for the owner because it's a lot of work - it sucks for the users because until that time they have no liquidity, but I can't think of a solution that doesn't have those drawbacks.  It doesn't really impact other holders of COG at all, unless there is a major sell-off on the new exchange, but a sudden increase in volume is likely after the new exchange goes live anyways.

Are any of my assumptions wrong?  Why would a forced-buyback be better for anyone? What alternatives would be more fair to any of the involved parties?

Let's rerun some maths with current numbers:

According to Garr's message here:
https://bitcointalk.org/index.php?topic=67547.msg3226890#msg3226890

We are expecting 14x2TH/s boxes, bringing our total to nearly 29TH/s.  Both Garr and CoinTerra have confirmed that they are on schedule for January recently.

The last difficulty increase was 41%, which is higher than anticipated.  It is unlikely that the diff will continue to increase 41% every 2 weeks between now and January, but I'll use it as an example.

Echoing my previous comments, time to find a block on average T = diff * (2**32) / rate.  Expected blocks per unit time B = 1/T, expected BTC per unit time P = B * 25BTC/block

P = 25.0 * 1.0 / ( diff * (2**32) / rate ) => BTC/second (multiply by 60*60*24*7 for weekly profits)

It is the middle of october, so say there is 2 weeks in october, 4 in november, 4 in december, and 4 in january.  This means 7 difficulty adjustments.  Call it 8 to fudge for growth reducing the cycle time.

Difficulty at the end of January (projected) => 268mil * ( 1.41**8 ) => 4187mil

P = 24.38 BTC/week

At 26420 shares, that is 0.000923 BTC per week, or an annualized return of 0.048 BTC per share, or 20% @ 0.25BTC per share.  (of course, the annualized return is instantaneously measured as of january, the actual return over the year will depend greatly on the difficulty leveling off, cognitive continuing to grow exponentially, or both).

Long story short, the maths look ok, even with this "back of the envelope" calculation, but we certainly hope the difficulty will not increase by 41% every 2 weeks between now and January.  If the difficulty increases by less than 41%, we receive our mining hardware before the very last day of January, or other beneficial opportunities arise, we stand to make even more profit.  The equations are all up there, so feel free to plug in your own estimates.

Let's also remember that mining in general is a poor investment at this time, but if you are going to invest in mining, the way to do it is via a company like cognitive where you benefit from the economy of scale (and Garr's bulk pricing deals).  Buying a single share of cognitive today is, as long as cointerra comes through, like buying 1.08GH/s to be delivered in January, meaning at 0.25BTC/share you are paying 0.23BTC/GH in January.  Evaluated on the BTC/GH alone this doesn't look like a particularly good deal, except not a lot of people can drop 6k on buying hardware direct from cointerra, but pretty much anyone can afford a few shares of COG (also, it beats the USB block eruptors event at their most recent pricecut, and has way better power/scaling perf).  If you look at the future projections of 1 petahash by Q2 2014 it is the long-term value of cognitive which justifies this price IMO (we all hope! =D ).

EDIT: it is worth noting that my previous maths used assumptions about difficulty growth being around 65% per month.  This one assumes 41% growth per adjustment period, which is roughly the network DOUBLING every month.  Whether this estimate or the other is more accurate remains to be determined (and is probably up to KNC and cointerra's delivery schedule).

This is a fair point and completely valid criticism of my maths.  I used just one possible value for the network growth rate.  The reason why I am still ok with sinking money into the mining market is because I believe exponential growth is short-term, not long-term.  Whether the network grows 60% a month or 120% a month during the next 6 months, it must eventually level off.  My reasoning follows.

I don't think anyone will produce chips better than 28nm any time soon.  My understanding is the top-of-the-line CPUs are 14nm but to produce chips at that size costs billions of dollars of setup, and is very unlikely until the entire bitcoin economy exceeds a couple trillion dollars at least. (see: http://en.wikipedia.org/wiki/Semiconductor_device_fabrication).  Similarly, 22nm only became practical for CPUs this year (according to that wiki page, though I kinda thought they had them in 2011 or 2012).  22nm is also very very expensive still.  For that reason, 28nm is probably the last die size we will see bitcoin asics in for some time.

Now don't get me wrong, there will still probably be "second gen 28nm" chips which are more optimized than the first gen (by spending more time optimizing the layout / gate logic / etc) but the gains are going to be bounded, and we aren't going to see "many orders of magnitude power improvements" like we have in the past.  When Hash per Watt stops growing exponentially, after a short lag, so will the network because people will turn off old hardware, and keep the new gen hardware, and hardware will take longer to pay for itself (but become less likely to be obsolete).  Your device makes 1btc per unit power which costs 1btc to buy.  btc increases in value 10%.  Your device is profitable.  You buy more devices, the diff increases, your device now only makes 0.7btc in the same amount of time, and costs 0.7btc to run - it isn't making profit anymore.  This is the "steady state" the network should eventually reach (probably not at break-even, but at a small profit, whatever profit the market is wiling to bear for running hardware).  Mining companies like COG will make the most profit because of their already-sunk-hardware costs, their economy of scale, and (related) lower power costs.

I would like to hear alternate opinions, especially with the reasoning behind them - I am a computer engineer but I do not have expertise in markets or financial stuffs.  But it seems to me like when network goes linear (or flat) and the steady state I have described above is achieved, the value of cog will be in the hardware they own (that is new enough to continue to turn a profit), and the steps Garr is taking now are going to secure that value.

To rehash some numbers I threw around earlier... The current projected difficulty change (in about 18 hours) is a 33.2% increase.  33.2% increase twice a month (roughly) yields 77% increase per month.  The difficulty will be about 150mil on October 1st.  Between then and Feb 1st, we have 4 months.  Since the diff changes slightly faster than twice a month let's actually call that 10 diff increases instead of 8, at 33.2% per increase.  The diff on Feb 1st is thus projected to be (150mil * (1.332**10)) => 2,637mil.

The equation I am using again is: ((diff_in_millions*1000*1000)*(2**32) / (28.0*1000*1000*1000*1000) / (60*60)) => X hours to find block, divide 24 by X to get blocks per day, mult by 25 to get BTC/day

Assuming 200*20 + 10240 shares => 14420 shares (as the extra 600 contracts have not been released yet, once they have they will roughly cut the numbers in half)

For the first 2 weeks of February, we can expect to make: 5.34 BTC/day => 0.00259 BTC per share each week
For the second 2 weeks of Februrary (diff 3513mil) we can expect to make : 4.008425 BTC/day  => 0.00195 BTC per share each week
For the first 2 weeks of March (diff 4678mil) we expect: 3.01BTC/day => 0.00146 BTC per share per week
For the second 2 weeks of March (diff 6232mil) we expect: 2.259BTC/day => 0.00110BTC per share per week

This means in the first 2 months after we receive the hardware (even if we get it on Jan 31st) we project 0.0208 BTC/share return.  If additional hashing power arrives in the next month or two on the order of 1048TH as Garr implied, cog can capture significant hash share before the craze dies down and people stop buying hardware (due to diminishing returns), If cog is over a petahash when the network growth flips from exponential to linear, it could be a great long-term investment, but even if it isn't it should sustain growth at least until then.

Perhaps we can fill out this table and add columns/rows as people think of more things that are important, or have other suggestions?

Name	hosted in US?	Trading Fee	Easy to use / solid website	distributed
Impossible perfect exchange	NO	0%	YES	YES
BTCT	YES	0.25%/0.20%	YES	NO
BitFunder	YES	1.0%/0.5%	YES	NO
Havelock	?	0.4% sell only	YES	NO
Others?

havelock has *much* better (lower) fees, but I see bitfunder's shareholdings are all public making the event of a seizure recoverable.  Does anyone advocating havelock have a link / info about their closure procedures?  I'd love to end up with the better fees but in the end, safety is paramount IMO.

as I posted on some threads for other assets I own - when choosing a new home, having a plan in event of sudden seizure of the exchange is paramount.  BTCT always had the best plan on this account - if they poofed overnight, the assets holders would be able to (read: have no excuse not to) continue paying dividends, etc. because BTCT emailed out a list of share ownership daily.

It is certainly preferrable that BTCT is shutting down slowly and responsibly, allowing us to make plans, but we should take this into account in looking at bitfunder.  If they do not currently take some of the same measures BTCT did, why not?  Can we pressure them to do so?

the bids are pretty sparse, but I don't see a ton of people panic selling either.  Most people who held through these low share prices will hold through this, IMO.

Between havelock, bitfunder, others I don't know about, etc. I hope Garr will pick then one with the best shutdown strategy.  BTCT always went to great lengths to ensure if the worst happened, operators would be able to continue running their assets (and have no excuse to 'get lost'), which bolstered confidence in general.  Now that the worst is happening, when selecting a new home we should look for similar assurances (list of investors emails / BTC addresses / etc mailed out regularly, etc).

Yeah, 750 GH/s is definitely one lone kid with 10 shill accounts. Definitely not a valuable mining cooperative.  Thanks for adding your astute observations to the intellectual discussion

I hope Garr can post an update with more details early this week.  Maybe the NDA will have lifted? Or, maybe he can at least tell us when the NDA will lift?  I suspect what people really want to see is evidence that the hardware cog is buying is actually a much better deal than is available to your average direct buyer, as well as other competing mining companies.

If our current hashrate is 750HG/s, our projected december hashrate is 10TH/s, and our project Q2 2014 hashrate is 1048TH/s, then:

Assuming COG.F1 converts to COG.F2 and both mature in December and the additional 600 contracts are sold and mature (they would only mature when we start receiving CT hardware) that means currently 800 contracts or 16000 additional shares

(using today's 24-avg of 0.192BTC/share)
Total hash rate | Total shares | GH/share | BTC/GH
750GH | 10420 | .0720 GH/share | 0.138BTC/GH
10TH | 26420 | 0.381GH/share | 0.5BTC/GH
1048TH | 26420 | 39.9GH/share | 0.0048BTC/GH

So today we have a share price indicating 0.138BTC/GH, but if our future plans pan out we can expect to have 0.38GH/share by December/January and buying today and holding until we have 1048TH would mean getting 0.0048BTC/GH, IMO this is a risky but high-reward investment (since there is the risk of CT plus the risk of network difficulty going crazy), but historically COG has been well-managed so I am not worried about risk from there.

If you instead use 0.25 as the share price (the share price when you buy COG.F2 at 5btc) you get 0.00626BTC/GH, still a very good deal.

The waiting calculation is super straight forward.  Regardless of what the diff is at, the coins we earn is inversely proportional to the diff.

According to http://mining.thegenesisblock.com/ the historical diff increase is:

Over the last 30 days: 125% (1.25 per month)
Over the last 60 days: 323% (1.8 per month)
Over the last 90 days: 457% (1.65 per month)

So the last 30 days have leveled off a bit, but last month it was crazy and it was pretty high even the month before that.

Presuming back-of-the-envelope 80% monthly growth (not unlikely due to cointerrra shitting a ton of hash power onto the network) we see:

First batch = 100 units
Second batch = 100 * (1/1.8 ) = 55 units

Using units to avoid talking about exactly how many coins, because it doesn't matter, we are making a comparison, the units are unimportant.

The lifetime sum of units made by the hardware for first batch are:

limit[x->0,inf] sum(100/(1.8**X)) => sum(100, 55.55, 30.86, 17.15, 9.53, 5.29, 2.94, 1.63, ...) which is approximately 225 units

The lifetime sum of units made by the same hardware starting one month later, with the same 80% monthly diff increase, is:

limit[x->1,inf] sum(100/(1.8**X)) => sum(55.55, 30.86, 17.15, 9.53, 5.29, 2.94, 1.63, ...) which is approximately 125 units

225 / 125 is exactly 1.8, of course, the very constant we used.  So, long story short, whatever the average difficulty increase is during that month, as long as the difficulty increase remains close to it in the future too, we can estimate waiting 1 month will cost us 1/(1+%) coins, or 55% for a difficulty increase of 80%

Diff increase during first month (assuming future difficulty increases are fairly consistent for at least some time):  % fewer coins gained during lifetime
95%: 49% fewer coins
80%: 45% fewer coins
65%: 39% fewer coins
55%: 35% fewer coins
45%: 31% fewer coins
30%: 23% fewer coins

In summary, if we get a 50% discount or more to wait, it is worth waiting, even if the difficulty *doubles* that month.  If we get a 20% discount or less, even the lowest difficulty increase we have seen in months would still make it worthwhile to pay the extra money (also, assuming our hardware makes enough coin to be profitable, which we hope will happen either way).  If it is somewhere in the middle, it comes down to what we expect the difficulty to be - and if CT delivers, I would bet it is going to be closer to the high side.

Thoughts?

EDIT: no sunglasses in my formulae!

I seem to recall reading somewhere that something other than a strict majority is needed... am I smoking something?  What are the reqs for a motion to pass?

Since the maths are annoying and helpful, I will run them for people.

Assumptions:

1. The minimum diff increase will be 50% per month from now until december.  The expected diff increase will be 65% per month from now until december.  The high-end (hopefully worst-case) diff increase will be 85% per month from now until december.
2. Cointerra will deliver 10TH/s to cog, all at once, which will begin hashing in december.
3. These will take the form of 5 2TH/s units which each draw 1200W (what I used for my maths earlier)

regardless of 1 and 2, using only assumption 3 we can analyze power draw:
5units * 1.2kW * $0.02/(kW*h) = $0.12/h = $2.88 per day to run the hardware.  That's pretty good.

Using all three assumptions now:

current difficulty is looking to be about 110mil by Sept 15th.  December 15th is 3 months away, yielding our three difficulty numbers:

(110mil*(X**3)) where X is 1.5, 1.65, and 1.85=> 371mil, 494mil, 696mil

The expected time to find a block is

difficulty to find block * 2**32 / hash rate(per second) / (60s/m * 60m/h * 24h/day) = X days

If diff were 110 mil (so, today), 10TH/s would produce:

expected coins per week = 24hours / day * (7days/week)  * (diff * 2**32 * / (10 * 1000000000000) / (60*60)) * 25BTC/block => 320BTC/week

at diff 371mil, 94.9 BTC/week
at diff 494mil, 71.3 BTC/week
at diff 696mil, 50.6 BTC/week

So even at the most pessimistic network estimates, COG would be making 50BTC/week in december if cointerra comes through for us - which, at ~26000 shares (say COG.F1 and COG.F2 both mature) is a dividend of 0.0019 per share per week, or an annualized return of 0.10 BTC/year (31% of current price).  Of course, that's just on the 10TH/s. 

Finally, we can make one more assumption, which is that given the risk of BTC and mining, most mining companies adjust to a share price such that annualized returns are between 10 and 20%.  IF we assume that, it implies a target price of 0.5 BTC/share (yielding 20% annualized return) on this 10TH/s purchase alone (and future hashing may raise that).

Of course, there are a lot of assumptions going on here.  This math is all just for demonstrative purposes.  Each investor needs to carefully consider all the assumptions, and the ways those assumptions could be wrong, before investing.

Cointerra isn't the weekly trend, Garr has been working on that deal for a long time, according to his posts.  He hinted at the existence of this deal a long time ago, when he originally proposed the first 100 shares of COG.F2.

Jumping on the "dump avalon" bandwagon, on the other hand, I agree, was a decision made much more quickly, I recognize your concerns there.

The thing is, math is math.  The best argument for dumping avalon at this point is "if cointerra fails, having ~1TH/s of avalons starting in a month or two aren't going to drasticaly change our outcome", because as my calculations show, we can't even run them for very long. at best we shut them off after just 4-5 months of running.  It'd literally be better to bank the BTC and invest in some other opportunity at that time - or just do it now (via labcoin, bitfury, whatever else we can get).

One can diversify by buying shares of different mining companies - so if you don't like the low-basket ratio of cog, sell just a few shares and buy some of something else as well.  I hope you would agree even if cog had nothing but cointerra orders, if Garr can support his claims in the near future, that alone makes cog an extremely valuable investment and thus a strong part of any well-balanced mining company portfolio.  If cog has the best deal with cointerra, far better than *any* other mining company (which again, Garr has implied but not yet provided solid evidence of) then cog absolutely should spend most if not all of their funds on cointerra because it is the best bang for their BTC.

Possibly relevant: http://thegenesisblock.com/avalon-refunds-22000-btc-2-9m-to-asic-miner-customers/

Maybe we could change our order to 2nd gen chips instead?  projected 10x higher hashrate, and almost assuredly lower power usage too (though still not quite as good as cointerra, should be a good hedge against cointerra failing).  Another possibility to raise a motion for?

I agree, discussion is key.  Also, I agree generally with more-eggs-in-more-baskets.  I think the value of the avalon basket is pretty low even if it does come through, and if cointerra "pulls a BFL" there are still many other companies delivering hashing power to the network.

Garr seems to have put most of our eggs in the cointerra basket because we are getting "a very good price" with them (though exact numbers are still pretty hazy).  If the sense folks have is that we want COG.F to be "a different basket" than COG.F2, then maybe we should ask garr to try to get one of the cointerra competitors (like labcoin? I dunno, I'm not up on the options) with those funds.  Or even BFL monarchs?  I wouldn't be supprised if Garr doesn't ever want to buy from BFL again, but we're talking a small % of COG's funds, right?  Also, we might have chip discounts, etc.?

So what do you guys think, do you want to see a motion to diversify into more than just cointerra, even if it is just 10% of our funds or whatever?

Fair enough.  According to TGB again, Cointerra's chips do 2TH/s on 1200W.  (1200W * ($0.02/1000W*h)) => $0.024/h,  $0.024/h / (2000GH/s * 60s/m * 60m/h) => $0.00000000333/GH.

Compared to the previous number, we have 5.299e-7 versus 3.33e-9, or ~160 times more efficient.

6 months out, 1678 mil diff, => 1678mil * 2**32 * $0.00000000333/GH * (1/1bil GH) => $23.999.

So at a difficulty of 1678 mil, doing the number of hashes needed to discover a block on 110nm chips will cost $3817 and doing it on 28nm chips will cost $24.  3817/24 => ~160, so our numbers match expectations.

Of course, this assumes cointerra hits their power/hash goals, etc, since we don't know if they have a working proof of concept yet, and we know from BFL companies have failed to reach predictions before.

EDIT: if we assume 60% growth over the next year - so 12 months out - we would be at 28147mil diff.  This is VERY unlikely - exponential growth cannot continue forever.  Nonetheless, if it happened, we'd have $402.56 per block.  Of course, as I argued above, discovering blocks would still be very very slow, but even at insane exponential growth, we wouldn't be turning our miners off even after 12 months from now (9months from getting them).

EDIT2: how slow?  at 1TH/s (for fair comparison) and 12-month diff (28147mil) we expect 0.000714 BTC/day, but a single cointerra device is 2TH/s, which would make 0.0014BTC/day, and if we get the full 1048TH/s garr has predicted, we'd be at 0.749BTC/day even 12 months from now.  You can do the math yourself to fill in the gaps if you want.

According to http://mining.thegenesisblock.com/, avalon batch 3 (which, if I understand correctly, are based upon the same chips), produce 65GH/s at 620W, or 105MH/w.

At best, electricity costs $0.02/kW*h, or 0.02/1000W*h, so (620W*($0.02/1000W*h)) => $0.0124/h to run 65GH/s, or 0.0124$/h / (65GH/s * 60s/m * 60m/h) =>$0.0000005299/GH.  At a difficulty of 100mil, the average number of hashes to solve a block are 100mil * 2**32 => 429496729600000000H => 429496729GH, which means a block "costs" $0.0000005299 *429496729GH => $227.59 but is worth ($130/BTC * 25BTC) => $3250.  If the diff increases 60% per month (currently it is increasing at 77% per month according to TGB) then in 3 months it will be 100*(1.6**3) = 410mil, and so on, so I made this table:

If profit is value - electric cost:
today 100mil => (3250 - 228) => $3022 per block found
3 months 410mil => (3250 - 933) => $2317 per block found
4 months 655mil => (3250 - 1491) => $1759 per block found
5 months 1048mil => (3250 - 2385) => $865 per block found
6 months 1678mil => (3250 - 3817) => turn it off, dawg.

Not only does each block net less profit, but we also expect to find blocks slower.
Time to find a block => diff * 2**32 / (hash per s) = time
At 1TH/s, we find:

Today 100mil => 100mil * 2**32 / (1TH/s) *(1m/60s*1h/60m) => 119h to find a block => 0.20 blocks per day => 5.02 BTC/day
3 months 410mil => 0.049block/day => 1.22BTC/day
4 months 655mil => 0.030block/day => 0.7692BTC/day
5 months 1048mil => 0.0192block/day => 0.48BTC/day

So the point is, even 3 months from now, we'd be lucky to be making 2BTC/day, even though it is profitable it'd be better for garr to spend his time deploying hundreds of TH in hardware that won't have to be turned off in just 2 months later.  I am unconvinced avalon hardware will be actually hashing in less than 1-2 months from now if we don't cancel the order.

Summary:  I was wrong - the avalon chips will probably be profitable to run for 4-7 months, depending on network growth.  However, the returns will be so small, I'd still rather bet on future tech, as exponential growth cannot be sustained after 28nm, but we are already seeing 110nm stuff get left in the dust.

The decision is less clear cut, but I still feel like avalon refund is the way to go.  We already have a few batch 2/3 devices, right?  It's not like we have no avalon hardware, it just seems silly to keep putting money into the old stuff when we could instead put it into the better stuff.

Please correct any errors you find.

EDIT: typos

The other aspect to consider is the avalon chips aren't just slower, they are higher-power-usage as well, which means it will literally cost more electricity to run them than they produce in BTC very soon, if the network growth continues or even if it just grows linearly (it is currently exponential).  The avalon chips are not worth it because Garr would have to turn them off in a few months anyways, because they are not economical to run anymore.