You can answer this yourself with a simple excel chart (this one's for Excel 2010, Excel 2007 and earlier have a similar function):
| Number of events actually occuring in a certain timeframe |
| Number of events that should occur on average in a certain timeframe |
| =POISSON.DIST(A1;A2;TRUE) | Cumulative probability (sum of probabilities for 0-X events) |
| =POISSON.DIST(A1;A2;FALSE) | Probability of just X events occuring |
In A2 you'd enter for example if you'd wait for 18 million shares at difficulty 1.8 million:
10 rounds (variable, since it depends on the pool's hashing speed how long this takes)
In A1 then you'd enter how many blocks should be found during these 18 million shares, for example:
8In A3 you then see that there's a probability of ~1/3 that 0,1,2...7 or 8 blocks are being found in the next 18 million shares at difficulty 1.8 million.
In A4 you see that the probability to have exactly 8 blocks within the next 18 million shares at difficulty 1.8 million is ~11.25%
The nice thing about poisson is however that probability = variance.
To see the variance, you can assume that you hit always X blocks in X*difficulty shares, so A1 and A2 are always the same number and represent the number of rounds you wait.
Then you take a look at A4 and increase the numbers in A1 and A2 until you have reached your amount of rounds it takes. For 5% variance in block findings (= payouts) it takes for example ~64 rounds, for 10% variance just 16 rounds and for 25% variance 3 rounds.
You can improve upon this idea by adding an average hash rate + difficulty to the equations, then you would just enter the amount of rounds and get the variance, but that would require another 10 minutes of work (actually typing this took far longer than creating it in Excel).
