HolIgor / Attempts on sente turned gote

I want to continue here the discussion started at my log page.

The problem is treating the sente move as gote. When this is possible and what could be the gain.

Let us suppose that we have the usual endgame situation with the normally balanced gote part.

I would call the normally balanced gote part of the yose the situation in which the starting side wins half of the largest move.

I would call the subnormally balanced gote part of the yose the situation in which the starting side wins less than the half of the largest move. The limit of the subnarmally balanced yose part in the total miai situation in which the starting side wins nothing.

I would call the gote part of the yose supernormal if the starting side wins more than a half of the largest move. The limit of this is the situation when only one move is left and the winner takes it all.

Ok, let us imagine a row of stacks with the values from 10 to 1. It is ideal normally balanced game with the win of 5 for the strting side.

Let us imagine that there is also a sente move. This move by itself gives the starting side (let's call that side black) 1 point. If ignored than black can take another 11 points from white with the next move.

The problem: a) when black should play that sente; b) when white shold play the reverse sente taking that one point?

If black plays 1 point move immediately then white should not reply but take the 10 point move. If now black takes 11 points and white 9 points, the balance would be 1+4 = 5 againts 10+9-11 = 8. Black lost.

If white replies immediately then she preserved 11 points but black won by 6.

There is something wrong in these considerations. One has to apply proper notations.

Bill: I think I understand you now, but please verify. The stacks we may represent like this: {10 | -10}, {9 | -9}, ... , {1 | -1}. The sente is not so clear. Is it like this: {12 | 1 || -1}.

It is plainly wrong for Black to play the sente now. It cannot be played with sente until the stack on the table is worth 5, i. e., {5 | -5}.

HolIgor: Yes, that's what I wanted to say. There is a time to play sente and there should be a procedure to check whether one should tenuki.

Bill: Well, let's look at a smaller problem with that sente, but the stacks range from {6 | -6} down to {1 | -1}. Black has the move.

Should Black play his sente, even though White will not respond? If so, the result will be

 -6 + 12 - 5 + 4 - 3 + 2 - 1 = +3

The danger of not playing the sente is that White will get to play the reverse sente. If so, the result will be

 +6 - 1 + 5 - 4 + 3 - 2 + 1 = +8

That's no problem, so Black should take the 6 point stack.

The next question is whether White should take the reverse sente, since it is her last chance to do so. If so, the result will be +8. If not, it will be

 +6 - 5 + 1 + 4 - 3 + 2 - 1 = +4

(The + 1 after the - 5 represents Black's playing the sente at that point.)

So White should not take the reverse sente.

Note that we get the normal result. The usual assumption that the sente are played with sente will hold in this case.