{{+22|-6},-3|-7} tax = 0Bill Spight wrote: I expect that this is obvious, but what are the minimax results when Black plays first and when White plays first?
Oh, double sente move is easy. I have already defined that.Gérard TAILLE wrote:The definition should be as near as possible as the common understanding of go players (which is not really defined in real life is it?).Bill Spight wrote:How about this?Gérard TAILLE wrote:My feeling : a "double sente" exists as soon as you accept to define it!
A double sente is a combinatorial game such that both sides of its thermograph are vertical.
We can also take this other suggestion: Other possible definition : by definition we have a double sente area if x,y >= n
Surely, with your fine knowledge of the problem, you will find more easily than me, what definition will fit the unclear but common understanding of double sente move in real life of go players.
No harm done? What do you think of the two double sente examples from Kano, 9 dan's, Yose Dictionary? Do you think they are good examples upon which to understand double sente?I am quite convinced that, by just adding such defintion, a lot of new players will adhere to the theory, especially if you find some interesting behaviour of such double sente move. Because adding such pure defintion cannot harm why not trying our best?
Bueno.Gérard TAILLE wrote:{{+22|-6},-3|-7} tax = 0Bill Spight wrote: I expect that this is obvious, but what are the minimax results when Black plays first and when White plays first?
black plays first => minimax = -3
white plays first => minimax = -7
{{+20|-6},-4|-6} tax = 1
black plays first => minimax = -4
white plays first => minimax = -6
{{+18|-6},-5|-5} tax = 2
black plays first => minimax = -5
white plays first => minimax = -5
well I would say:Bill Spight wrote:Bueno.Gérard TAILLE wrote:{{+22|-6},-3|-7} tax = 0Bill Spight wrote: I expect that this is obvious, but what are the minimax results when Black plays first and when White plays first?
black plays first => minimax = -3
white plays first => minimax = -7
{{+20|-6},-4|-6} tax = 1
black plays first => minimax = -4
white plays first => minimax = -6
{{+18|-6},-5|-5} tax = 2
black plays first => minimax = -5
white plays first => minimax = -5
What about this combination?
{+22|-6},-3|-7} + {10|0}
Bill Spight wrote:Bueno.
What about this combination?
{+22|-6},-3|-7} + {10|0}
Black can do better at temperature 0.Gérard TAILLE wrote:well I would say:
black plays first => minimax = +3 = 10 + (-7)
white plays first => minimax = -3 = 0 + (-3)
Oops yes Bill, I am a stupid boy!Bill Spight wrote:Bill Spight wrote:Bueno.
What about this combination?
{+22|-6},-3|-7} + {10|0}Black can do better at temperature 0.Gérard TAILLE wrote:well I would say:
black plays first => minimax = +3 = 10 + (-7)
white plays first => minimax = -3 = 0 + (-3)
Now how about integer temperatures up to 5?Gérard TAILLE wrote:Oops yes Bill, I am a stupid boy!Bill Spight wrote:Bill Spight wrote:Bueno.
What about this combination?
{+22|-6},-3|-7} + {10|0}Black can do better at temperature 0.Gérard TAILLE wrote:well I would say:
black plays first => minimax = +3 = 10 + (-7)
white plays first => minimax = -3 = 0 + (-3)
(-6)in sente and then (+10) => +4
I can see that the game {+22|-6},-3|-7} becomes {+20|-6},-5|-5} at temperature 2 and the minimax -5 cannot change above that temperature.Bill Spight wrote:
What about this combination?
{+22|-6},-3|-7} + {10|0}
Now how about integer temperatures up to 5?
Since not all players use values but players with a weak understanding of endgame only use an informal understanding, the common go players' understanding of double sente would be informal. However, some players have not reflected yet that local versus global considerations of double sente differ. Therefore, the common go players' understanding of double sente does not exist. Concerning global considerations, some players are aware that one should not always play a double sente immediately because it might be relatively small while other players (with a weak understanding of endgame) are not aware of that and instead believe overly simplistic traditional advice to play in double sente as early as possible. Only for local considerations, we can identify some common go players' understanding of double sente: that either player's local play is sente meaning an immediate reply by the opponent. In only informal terms, we cannot better characterise why an immediate local reply should be necessary.Gérard TAILLE wrote:The definition [of a double sente] should be as near as possible as the common understanding of go players
Sorry Robert to be here a player with a weak understanding of endgame but let me try to treat myself.RobertJasiek wrote:Since not all players use values but players with a weak understanding of endgame only use an informal understanding, the common go players' understanding of double sente would be informal. However, some players have not reflected yet that local versus global considerations of double sente differ. Therefore, the common go players' understanding of double sente does not exist. Concerning global considerations, some players are aware that one should not always play a double sente immediately because it might be relatively small while other players (with a weak understanding of endgame) are not aware of that and instead believe overly simplistic traditional advice to play in double sente as early as possible. Only for local considerations, we can identify some common go players' understanding of double sente: that either player's local play is sente meaning an immediate reply by the opponent. In only informal terms, we cannot better characterise why an immediate local reply should be necessary.Gérard TAILLE wrote:The definition [of a double sente] should be as near as possible as the common understanding of go players
In terms of values, we can characterise why an immediate local reply should be necessary: after either player's local play, the reply is more valuable. That is, the move value in the initial local endgame position is smaller than both replies' follow-up move values. Let us use these variables:
M := the move value in the initial local endgame position.
Fb := the move value in the follow-up position created after Black's start.
Fw := the move value in the follow-up position created after White's start.
Now, we can characterise a local double sente endgame be these value conditions:
M < Fb, Fw.
(This annotation abbreviates "M < Fb and M < Fw".)
However, simply speaking, the mathematically proven theorem says:
A local double sente endgame with M < Fb, Fw does not exist.
The common go players' understanding did not know this yet:)
move is a quite big gote move and an answer by a black hane may be not big enough if it exists some other big gote moves on the board. creates a double sente area (OC in the sense of the definition you proposed above).The game above looks like G1 = {{+22|-6},-3|-7}Bill Spight wrote:OK. Thermographs do two things. The thermograph of a game finds the mean value of the game, and it finds the result of minimax play in the game, starting with each player, at each temperature.
What else does your skeptic desire?
A double sente by definition is a finite combinatorial game whose thermograph has a left wall, L = u, and a Right wall, R = v, such that u > v.Gérard TAILLE wrote:As soon as you decide to define what is a double sente it exists doesn'it?
To do so, you subtract G2 from G1. I. e., you consider the sum,Gérard TAILLE wrote:The game above looks like G1 = {{+22|-6},-3|-7}Bill Spight wrote:OK. Thermographs do two things. The thermograph of a game finds the mean value of the game, and it finds the result of minimax play in the game, starting with each player, at each temperature.
What else does your skeptic desire?
And my goal is to compare this game G1 with the game G2 = {-3|-7}
As my shop teacher used to tell us, use the right tool for the job.I do not feel it is skepticism Bill. Maybe it is only that I expected more from the theory ?