Organofcorti work is awesome, so are his tables.
But, if nothing more than a raw indication is needed, one could use Chebyshev alone:
http://en.wikipedia.org/wiki/Chebyshev%27s_inequalityWith as little as about 1.35GH/s mining power, I mine with a share-difficulty of 169.
So this is the math.
In one day I find about 1.35GH/s * 24h * 60m * 60s = 116,640,000,000,000 hashes.
In one day, in average, only 116,640,000,000,000 / ( 169 * 2^32 ) = 161 will be accepted. About one share every 9 minutes.
So my Poisson distribution (for a day) will have a mean λ = 161 and also a variance σ² = 161 (of course, in Poisson distribution mean and variance are equal:
http://en.wikipedia.org/wiki/Poisson_distribution).
Chebyshev says that:
Pr{ |X-λ| < kσ } >= 1 - 1/k²
Let's choose k=2, so that we can have 75%:
Pr{ |X-161| < 25 } >= 75%
that is:
Pr{ 136 < X < 186 } >= 75%
that is:
Pr{ 0.85λ < X < 1.15λ } >= 75%
So there's and extremely good chance (at least 75%) that my daily earnings will be not less than 85% of my average
- and not more than 115% of my average.
For me it's enough: I didn't know about organofcorti tables, I didn't want to go back to my old statistics books, and so I chose an easy way to know that yes, I can afford 169 difficulty.
