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BTW, if you are going to add and subtract mistakes, be sure to use miai counting. Things do not add up with deiri counting
I lack both the knowledge and the intuition to comment on this, but, even on the basis that a little knowledge is a dangerous thing, I'll venture to query it and be the Aunt Sally for the forum.
Miai and deiri refer to Japanese accounting systems. In go, boundary-play miai has nothing to do with alternative points, but reflects the accounting idea of just 'look and compare' and is essentially a form of single-entry bookkeeping. It counts the profit and loss in a transaction. Like all single-entry systems, if applied to a whole business or a tax-year, or the current count of a whole game, it is prone to errors that are not caught (because entered only once) and it gives management, or you the player, poor information with which to see the bigger picture. It is the accounting of the school playground, where kids swap marbles for toffees. It satisfies an immediate desire to assess the value of a transaction (in go terms, it measures the urgency of a situation) but is no way to run a life or a business. If you do run a business in this crude way, say as a self-employed person at home, your end-of-your figures may fortuitously work out correctly, but they may not and you may get an unexpected tax bill.
De (out) and iri (in) refer to double-entry accounting. British and American d-e systems vary a little, I know, and the Japanese system has its own nuances, too, but I believe they are all based on the notion that you enter any transaction into two ledgers (or columns), one for outgoings and one for incomings so that when you total up one ledger the result should tally with the total in the other. The basic idea is that you then have two sets of reconcilable data, so that you have a stronger chance of picking up errors or frauds. Even at this basic level I see haze, but since people go on long courses to learn d-e bookkeeping, I suppose I should expect that.
But d-e accounting apparently also has another important function. It provides a vast array of useful information for management. The basis of this idea, as I understand it, is that single-entry (miai) measures Gain = Profit - Loss (what's in front of your nose) whereas double-entry (deiri) measures Equity = Assets - Liabilities (big picture). The essential difference between the two is that miai implies paying in cash immediately for everything to get an immediate (and possibly negative) gain, but deiri means you can hold off on actual payment and count the long-term value of an asset without cashing it at once. You can also play off one asset/liability against another.
Still, assuming I'm somewhere near the truth with that, in theory, if no counting mistakes are actually made and even if one person is driving through a fog and the other through the sunshine, the two systems should at the end of the year/game, come to the same destination/result. In other words they should both "add up". Enlightenement, please!
On a separate tack, talk of miai amd deiri in go always ends up bogged down about which system is meant. Whilst this in part is because of uncertainty over what each system means, I think the ambiguity of certain terms like 'point' doesn't help. Is there not scope to define new units? E.g. deiri points are dits and miai points are mits?