Bass's Over-Simplified Endgame
"Bass's Over-Simplified Endgame" or "BOSE" is a theoretical construct for making it easier to discuss and evaluate endgame positions where the whole board position is not known. As such, it has some utility when one wants to make general comments on endgame without actually reading out every possible variation. It is the brainchild of a Finnish 3 dan called Tuomo Salo.
BOSE uses the following simplification rules:
- Every move has a value. Values are always integers, and are equal to the point swing caused by the move.
- You do not know in advance how many moves of which values will be available later.
- Every move is gote. All remaining sente plays are ignored; the player who could play them in sente will always get to play them.
- Ko and ko threats are not considered. A proper evaluation of the value of a ko would require a correct analysis of the entire board, which would defeat the purpose of the exercise.
These simplifications remove most of the ifs and buts from a typical endgame analysis, and naturally also cause inaccuracies that make BOSE an unusable substitute for proper endgame analysis.
However, for the purpose of creating rules of thumb and making general guesses about the endgame, the system is quite adequate. The main benefit gained with these assumptions is that it becomes possible to estimate the value of the remaining endgame while knowing only the value of the biggest remaining gote play.
Here is how one could use BOSE to make an informed guess about the best move even when the whole board position is not known.
Black b causes a 4 point swing compared to white getting to play the hane on this side. However, playing here is gote for white too, so b is called a 4 point gote play.
Which black move is better, a or b?
The correct answer according to proper endgame analysis is "it depends".
Since the problem speaks nothing about any other moves, we may assume that these two moves are the biggest ones available. Therefore, if black takes one, white takes the other. So we have two possible outcomes:
If black chooses a, black has the sente to play elsewhere. However he lost one point compared to the diagram below.
Here black has gained one point compared to the previous diagram, but white has sente.
A proper endgame analysis would say something along the lines of "if playing elsewhere first is worth at least one point, then black can safely choose a. If playing elsewhere is worth nothing, then black should choose b".
Now, in a real game it can be a real pain to figure out the exact value of playing elsewhere. You'd need to read out every variation up to and including the final kos, which can be a formidable task to perform without a single mistake, especially if you have less than 30 seconds on the clock. This is where BOSE can become useful.
Using BOSE one can make an estimate of the value of the remaining endgame elsewhere on the board only by finding the biggest available move, which is something that has to be done anyway. According to the estimate, on average the endgame is worth half of the biggest available gote.
So instead of reading out all the variations, black can just look for the biggest move, and if he should find a 3 point move anywhere on the board, he can immediately choose a with confidence; it is very unlikely that he made the wrong choice.
If, instead, black could find only one point gote moves, then b would be a very good call, as the average endgame will only gain 0.5 points for white. (Obviously it is difficult to lose more than 1 point when the biggest move is that size).
And finally, if the biggest available move is two points, then all bets are off; a and b should then be considered equal, but only on average.
If we really know nothing about the rest of the board, then we can use simplification 2 to determine that it is very likely that the next biggest move is 4 points, the same size as the biggest move shown in the diagram.
Using the same estimation tool as before, we can estimate that the value of tenuki is somewhere on the order of two points, so as a general rule a is the better move.
Kudos for most of the simplification ideas go to the authors of "When To Play A Reverse Sente".