Go endgame values with area counting: part 2, sente

Sente

In part 1 of this series we evaluated gote endgame moves using area counting instead of territory counting. Now it’s time to look at sente moves. It’s basically the same thing, but our local tally difference is now $1$ instead of $2$, so that’s what we subtract.

$2$ intersections are at stake, so this is $2\cdot 2 - 1 = 3$ points in sente. If you remember the derivation from last time, the switch from $2$ to $1$ makes sense, as the local tally was explicitly part of that formula. We subtracted out the local tally in our derivation so that the players don’t get credit just for playing stones.

Territory counting, by area?

But wait a second, I thought we were dong area counting! Shouldn’t players get credit just for playing stones? Well, actually, we’ve been computing territory-counting endgame values using an area-counting method, so we have to subtract the tally to get the numbers to agree.

It would be totally legit to count endgame values by area, although I’ve never heard of anyone doing it. In that case we’d give extra credit for White’s additional stone in Diag. 1c and call this a $4$-point move. In fact the miai value (we’ll get to that) for every move would just be one greater than before. That’s because every move in area counting is worth $1$ point right off the bat just for existing on the board. We’re used to just treating that $1$ as a baseline so we only give credit for the value that exceeds it, in which case we end up with territory-based values.

Miai values

I grew up with what is known as deiri counting, where you look at the difference in points between Black going first and White going first (the “swing value”), and then qualify it with gote or sente. Then to compare these numbers to decide where to play you have to use rules like “sente is worth double”.

Miai counting (aka “absolute counting”) instead tries to find the actual value of a move so that they can all be compared on a single scale. The reasoning behind the method is beyond the scope of these posts (see the references section in the next one), but the math is simple: you just divide the swing by the local tally difference.

Now the previous section should make a little more sense. For both gote and sente moves, we’ve been computing the swing value by taking the swing in area (which is twice the number of intersections at stake) and subtracting the tally. Now to get a miai value we’re dividing by the tally difference. That means that the miai value is (area-swing - tally) / tally, which we could also write as area-swing / tally - $1$. There, just like we said, all moves are more valuable by $1$ in area counting.

$$V_T = S_T / \Delta T = S_A / \Delta T - 1$$

So you don’t have to bother with subtracting the tally difference if you use miai values and don’t care that your numbers will be different by 1 from everyone else’s.

Next: ko.