Quote from: EskimoBob on June 22, 2013, 08:46:11 PM

Write this down - ALL perpetual mining "bonds" that pay based on FIXED Mh are turds and are guaranteed to lose their value.
Buy "turds" ONLY if you believe that difficulty is going to drop.

EskimoBob, you can't just say they are turds, and leave it at that. You have to explain or nobody will listen to you.

Anyone that wants to mine or wants to buy a PMB (which is not really a bond, btw) must understand the following. The value of a PMB depends on the dividends that it pays and the dividends depend on the difficulty.

Here is how the dividends are computed:

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dividend per block = hashes per second * 25* 600 * 65535/2⁴⁸ / difficulty

The dividend per block for 1Mh/s at the current difficulty is 0.00000018 BTC.

The total dividend for 2016 blocks (the number of blocks at each difficulty) at the current difficulty is 2016 times that, or 0.00036406 BTC. I'm going to call this D. The total amount of dividends received (D_T) is simply the sum of all the dividends paid forever:

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D_T = D + D₁ + D₂ + D₃ + ...

Now, we know that the difficulty continues to rise because more people are mining and technology advances. Every time the difficulty rises, the dividend falls by the same amount. In other words, if the new difficulty is 20% higher, then the new dividend about 20% lower (actually it is multiplied by 1/1.2, or 0.83).

Let's pretend that the difficulty rises 20% every change. That is,

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D₁ = D / 1.2
D₂ = D₁ / 1.2
D₃ = D₂ / 1.2
...

So,

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D_T = D + D/1.2 + D/1.2² + D/1.2³ + ...

Luckily, Gauss (at the age of 4, believe it or not) figured out a simple formula for computing this value:

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D_T = D * (1 + 1/0.2), or 0.00218436 BTC

So there you have it. If the difficulty increases by 20% every time, a 1 Mh/s PMB will pay up to 0.00218436 BTC in dividends, and you will lose money if you pay more than 0.00218436 BTC for it.

The general equation for determining how much a PMB is going to pay is this:

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D_T = H * D * (1 + 1/R)

H is the hashing rate in Mh/s
D is the amount of dividends paid for 2016 blocks (approximately 14 days) at the current difficulty and a 1 Mh/s hash rate
R is the expected increase in difficulty every 2016 blocks (if the increase is 20%, R is 0.2)