bips/bip-hashrate-escrows/appendix-1.txt

==== Two Withdrawals at Once ====

Currently, the documentation and code describe a situation where only one withdrawal can proceed at a time.

In other words, as WT^s are proposed, only one can make progress toward the finish line. As a result, a given side-to-main transfer will always take between 3 and 6 months.

However, it might be best to use a maximum of two transfers at once.

If there were more simulataneous withdrawals, the worst-case transfer duration would improve.

See image: bip-hashrate-escrows/two-groups.png?raw=true

The worst-case withdrawal time obeys f(n)=3+(3/n) months, where n is the number of simultaneous withdrawals.

N=2 is the most desirable choice for several reasons. First, it delievers the greatest marginal benefit (of 1.5 months). Later choices only deliver 0.5 and 0.25 marginal months.

Second, n=2 can be implemented in a clever way: by allowing a withdrawal to freely advance, if and only if has an ACK-score of 6575 or greater, and if it also has the largest ACK score. In other words, the withdrawal that is furthest along can advance (or retreat) for free, if it has already made it at least halfway to the finish line. With this change, our new M4, is either an "abstain" for the sidechain (in which case nothing happens to any ACK scores), or else it will be in one of two cases: old_M4 + "the largest advances", or new_M4 + "the largest retreats". As a result the number of M4 possibilities (of which the next section is concerned) only increases by a factor of two (instead of exponentially).

It is possible to troll this rule, by getting two (or even three) withdrawals to have 6575+ ACK scores, and then getting them to *tie* for first place. So, if there are any ties, the ability to "bonus move" would be disabled until all ties are broken.