Gérard TAILLE wrote:
Bill Spight wrote:
Gérard TAILLE wrote:
OK Bill, now take the complete game (see the game I proposed but here with a simplier upper side)
{21 ||| 18 | 4 || 0 | -14} + {20|0} + {0|-6} + {4|0}
What is the best sequence for this game if it is white to play?
Let's call the games, G, H, M, and N. I'll us a minus sign to indicate a White moves, a plus sign to indicate a Black move. We start with a mean territorial value of 11½ + 10 - 3 + 2 = 20½.
First, let White play the ever popular hotstrat strategy, taking the average gains in order.
1) - G + H - G + G - M + N = 20½ - 11½ + 10 - 9 + 7 - 3 + 2 = 16
After Black replies in H, the rest is provable correct. Can White do better? Let's see.
2) - H + G - M + N = 20½ - 10 + 11½ - 3 + 2 = 21
That's worse.
Can Black do better than 1)?
3 - H + G - H + G - M + N = 20½ - 11½ + 9 - 10 + 7 - 3 + 2 = 14
That's 2 points worse than 1). Hotstrat wins.
Yes Bill here is my point. In this example you have to begin by this 9½ gote instead of the simple 10 gote.
This is very strange. Isn't it?
Well, first, I goofed and used 11½ (the mean value) instead of 9½ (the gain) in my calculations.
I realized that when I looked over my note and went back and corrected it.
But for a play with a slightly smaller gain than another play to be preferred to that play is not strange. It is not usual, but it is not too uncommon.
Quote:
It seems to me it is due to the potential double sente hidden in the game G.
Edit:
The double sente aspect has nothing to do with it. For instance, let's replace {18|4||0|-14} with {18|4||-7}. That makes G = {21|||18|4||-7}. Remember, H = {20|0}, M = {0|-6}, and N = {4|0}.
First White plays the hotstrat strategy of playing the largest play (on average) first.
1) - H + G - M + N = 20½ - 10 + 9½ - 3 + 2 = 19
Can White do better? Let's see.
2) - G + H - G + M - N = 20½ - 9½ + 10 - 9 + 3 - 2 = 13
That's 6 points better, not just 1 point better.
Edit2: Hmmm. Can Black do better than 2)?
3) - G + G - H + G - M + N = 20½ - 9½ + 9 - 10 + 7 - 3 + 2 = 16
Yes, indeed. That's only 3 points worse.
Interestingly, best play at temperature 0 involves playing the next to largest play twice, once by White and once by Black.
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