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Now, if we increase the shift size or the number of shifts while holding the other value constant, the number of shares paid will be greater than the average number of shares to find a block and the amount paid per share will be less. You appear to be advocating for this type of change.
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It's best to explain that statement since the way you've written it implies that you'd be rewarded less, which is false.
The way I have written it is correct. I was explaining from the pool's point of view not the miner's.
If we hold the number of shifts constant and increase the shift size, the payout for each shift will remain the same. If the payout remains the same for each shift, an increase in the number of shares paid per shift will result in a decrease in the amount paid per share.
I will admit that I can see how a change in point of view could lead someone to falsely assume that they would be rewarded less.
You left out the point that each share will, on average, be paid more than once ... so result, on average, with the same reward.
I think the first part of your clarification may still be confusing for some folks.
The number of shares contributed by the miner will increase proportionally with the number of shares paid during a shift because the percentage of contributed shares by the miner should remain the same, pool variance over a different sampling window of a different sampling size notwithstanding.
Increasing the N reduces variance, not reward.
Agreed