If a Bitcoin miner participates in PoX, then it can guarantee that it will win sortition 100% of the time simply by omitting every other competing block-commit transaction. While a Bitcoin miner would participate in PoX insofar as they would send BTC to the addresses in the PoX reward set, the miner could safely make these BTC values as small as possible – e.g. as low as the dust limit, or 5500 satoshis – because it is the only competitor. They would also charge themselves zero transaction fees.
To the Bitcoin miner that does this, a Bitcoin block is now effectively worth the Bitcoin block reward, plus the Stacks block reward, minus the minimal PoX commit value. If someone creates a block-commit transaction and sends it to the mempool, and attaches a Bitcoin transaction fee that is worth at least the expected Stacks block reward plus the minimal PoX commit value, then the Bitcoin miner would include this competing block-commit and set its PoX commit value to the minimal value. This is because win or lose, the Bitcoin miner earns a block reward equal to what they would have won had they been the sole sortition participant.
I’m not sure yet how this plays out if there are N competing block-commits. It could be that rational miners will accept block-commits with BTC transactions fees that are as low as the block-commit’s expected value (i.e. Stacks block reward, multiplied by the probability of winning). Would need to think more about this game.
Bitcoin miners pay less than non-Bitcoin miners insofar as Bitcoin miners don’t pay transaction fees, but historically, we’d used the phrase “discount mining” to refer to Stacks miners who Stack their STX and pay themselves the block-commit BTC (i.e. they can send lots and lots and lots of BTC in the block-commit because they know they’ll get it back, and in doing so, vastly increase their likelihood of winning sortition). There’s a mitigation for this particular form of discount mining described here: https://github.com/blockstack/stacks-blockchain/issues/1315.
What should we call this pathological mining behavior when it’s Bitcoin miners participating in PoX? “Bitcoin miner discount mining” sounds too long