P2share: how to turn any network (or testnet!) into a bitcoin miner

[VzxPLnHqr]

@cmp_ancp

If we don’t burn, the old miners would have a gigantic amount of shares, at a point that new miners couldn’t even compete.

This is not correct, at least not in a linear “will work-for-shares” issuance model. It it only correct if you assume that shares are issued in a some other manner which gives early sharechain miners an “advantage” with regard to required work (expected # hashes) per share they receive. That is what Bitcoin itself did, and that is fine for Bitcoin (without it, we could never even contemplate the p2share model!). However, part of the confusion is that the original post did present such an issuance model where shares were issued non-linearly in the shrinking-pie Bitcoin-like way.

However, the more refined linear model I proposed, coupled with a suitable difficulty adjustment algorithm, explicitly fixes that objection.

@cmp_ancp

he’s getting paid by its work, but if he doesn’t lose shares, the amount of work spent one time would be valued multiple times.

The “paid multiple times for the same work” concern doesn’t apply in the linear issuance model.

Every new unit of work adds new shares and proportionally dilutes all existing shares. Because selection is random over all shares, every share, regardless of when it was created, has the same expected value. There is no persistent extra advantage from “early” work; it’s continuously diluted by later work.

To describe behavior cleanly, fold difficulty into expected value per hash:

• Let EV_sc be the expected sats per unit hash on the sharechain (this already accounts for sharechain difficulty and share price).
• Let EV_mc be the expected sats per unit hash on mainchain.
• Let P* be the share price at which EV_sc = EV_mc.

Then miners simply arbitrage:

1. Mining decision (where to point hash):

Condition	Mining action
EV_sc > EV_mc	Mine on sharechain
EV_sc < EV_mc	Mine on mainchain
EV_sc ≈ EV_mc	Indifferent

2. Trading decision (what to do with shares):

Market share price	Trading action
Price > P* (“too high”)	Sell shares (including newly mined)
Price < P* (“too low”)	Buy shares (if you want more exposure)
Price ≈ P* (“just right”)	Indifferent; no strong trade implied

So all shares have the same expected value, and the “right” behavior is just: point hash where EV per hash is higher, and trade shares when their market price deviates from the fair P*.