The thing is, while variance may average out over the long term, that only matters if difficulty remains the same. If you think that I'm wrong, let me offer you a scenario. Hypothetically, let's say that based on current pool hashrate and network difficulty, we can expect one block per day. I'll offer you a choice. You can get three months of double the expected block success (two blocks per day initially), followed by three months of zero payouts. OR, you can get three months of zero payouts, followed by three months of double the expected success rate.
The naive answer is that both will average out to the same thing - and that answer is correct so long as the pool maintains the same hashrate and block difficulty throughout the six months. In reality, even if we hold the pool hashrate constant over six months, your total payouts with the two options will be radically different due to the increasing difficulty rate. The double payouts followed by a dry spell will earn much more than a dry spell followed by double payouts, simply because you're getting paid when difficulty is lower - thus more blocks are found during a given time period.
Sigh. I'm getting so tired of arguing with math fallacies. So I won't.
My statement is that while things may average out over the long term, I don't live or mine in the long term - only in the short term. If in the short term I get better results on another pool then I'm more inclined to stay with the other pool. It's exactly the same logic as saying that if I go to Las Vegas casino A and lose, then go to casino B, play the same games, and win, I'm more inclined to play at casino B the next day. Long term, on average, most players will lose at both casinos, which is why the casino business can be so profitable - but individuals can and do win big in the short term. It's pure gambler's fallacy, but it's the way many people think - both in terms of casinos and in terms of pools.
Here's the math basis I used to come to this conclusion I stated in the quote above. For simplicity, I made the following assumptions:
- Difficulty adjusts every 10 days exactly, and each increase is exactly 5%.
- All months have 30 days.
- A starting difficulty of six billion (expressed in millions below, so 6000 = 6000MM).
- Both overall pool hash rate and your share of that hash rate remain constant (which means your p2pool shares per period of time is also assumed to be constant).
- The pool always find blocks at the expected rate.
Here's the part I'm not 100% on. I'm assuming that if the difficulty exactly doubles, then your chance of finding a block is exactly halved. I suspect this isn't correct, but regardless, it's certain that as difficulty increases, the chance of finding a block decreases. So while the block probability numbers below may be slightly off, the overall trend would be the same.
Here's what the block-finding probabilities would look like (note that the table lists number of blocks found per 10-day period, not amount of BTC earned).
| Period # | Starting month | Starting day | Starting difficulty | Chance of block/day | Blocks found |
| 1 | 1 | 1 | 6,000 | 1.000 | 10.000 |
| 2 | 1 | 11 | 6,300 | 0.952 | 9.524 |
| 3 | 1 | 21 | 6,615 | 0.907 | 9.070 |
| 4 | 2 | 1 | 6,946 | 0.864 | 8.638 |
| 5 | 2 | 11 | 7,293 | 0.823 | 8.227 |
| 6 | 2 | 21 | 7,658 | 0.784 | 7.835 |
| 7 | 3 | 1 | 8,041 | 0.746 | 7.462 |
| 8 | 3 | 11 | 8,443 | 0.711 | 7.107 |
| 9 | 3 | 21 | 8,865 | 0.677 | 6.768 |
| 10 | 4 | 1 | 9,308 | 0.645 | 6.446 |
| 11 | 4 | 11 | 9,773 | 0.614 | 6.139 |
| 12 | 4 | 21 | 10,262 | 0.585 | 5.847 |
| 13 | 5 | 1 | 10,775 | 0.557 | 5.568 |
| 14 | 5 | 11 | 11,314 | 0.530 | 5.303 |
| 15 | 5 | 21 | 11,880 | 0.505 | 5.051 |
| 16 | 6 | 1 | 12,474 | 0.481 | 4.810 |
| 17 | 6 | 11 | 13,097 | 0.458 | 4.581 |
| 18 | 6 | 21 | 13,752 | 0.436 | 4.363 |
So, how does that look like in terms of blocks?
Option 1: double blocks for first three months, zero for next three months. Total blocks found: about 150 (with rounding).
Option 2: zero blocks for first three months, double for next three months. Total blocks found: about 96 (with rounding).
Option 0: no scenario, just straight mining for six months: Total blocks found: about 123.
Which would you pick? Given that your BTC payout per block is constant (as per our assumptions), I'd much rather have the first option. If I buy mining gear with a useful lifespan of a few months to a year, it very much matters to me which option I pick.