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Four short essays on mining

Difficulty, shares, near misses and luck, with the mathematics left in and figures you can play with. Read them in order, slowly, with something warm to drink.

I

On Difficulty

A lottery that sets its own price

The odds of a single hash, the Poisson clock, ECX's damped retarget and the equilibrium behind the number.

II

On Shares

Receipts for invisible work

How a pool measures hashrate from shares, why their difficulty follows a Pareto law, and why every block is a share.

III

On Coming Close

The view from just below

The closeness score, how close you should expect to come before a block, and why a near miss predicts nothing.

IV

On Luck and Patience

The arithmetic of rain

How many blocks to expect, why they clump, how slowly luck averages out, and what a pay-per-share pool really sells.

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