# Difference Game/ Discussion

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Sub-page of DifferenceGame

### Voodoo?

Froese: Is it just me? Sounds like some kind of voodoo practice...

• Why also mirror the "negative position"? Confuse the reader? :-)

Bill: We are just mirroring the original position to make an even starting position before making the plays to compare.

• In "Example 1 Game (i)": Isn't it White's turn? Why is Black playing first?
Bill: In the comparison of positions we let each player play first. To compare different plays for one player we compare positions resulting from the different plays. We want to know which position is better, if any, and that does not depend upon whose move it is.
• In "Example 1 Game (ii)": Why does White win? White has 17 points on the left side and Black 18 points on the right. B+1.
Bill: I have redone the diagrams to make that clearer. The stones framing the position are alive.

Froese: Ah, thanks. I think I got it.

Tom: Playing the difference game is not as much a voodoo practise as it might at first appear. Borrowing from the example above, but swapping the colours on the right.

Modified version of Example 1

Suppose we wish to test whether the left hand position is (under all ko free circumstances) at least as good for black as the right hand position. There are two possible ways in which one could try to argue that this was not the case.

Firstly one could say 'But white has a superb move on the left hand side'. Possible ways to refute this argument are to say 'white has just as good a move at a on the right hand side' (true) or to say 'black can refute with ' (false).

Modified version of Example 1

The second way to argue that the left hand position is not as good for black is to say 'Black has a superb move on the right hand side' Possible ways to refute this might be to argue that white has a good counter to (false, black's right hand position is better), or that black has an even better position after black a on the left hand side than after on the right (also false).

Modified version of Example 1

In this example, we see that it is false that blacks position in on the left hand side is as good as that on the right hand side.

The clever thing about the difference game is that each step of this argument corresponds to a move in the difference game! Although, once explained, the difference game is not voodoo, I do think that it is a very clever idea.

### van Zeijst article

ilanpi: The current article in the Daily Yomiuri by Rob van Zeijst is essentially about the limitations of this model. See http://www.yomiuri.co.jp/igo_e/280.htm (link is broken)

Bill: Well, he shows a position that is worth *, not 0. <shrug>

But he also shows an endgame problem with at least one mistake in the "solution." ;-)

ilanpi: OK, thanks. The limitation I was talking about is to put the G and -G on the same board. You must be careful!

Bill: Yes, you must be careful.

### Heretical question

Example 2, Difference Game Setup

Which player, if either, stands better?

Example 2, Difference Game (i)

### Example of wrong notation in difference diagrams

Everything wrong can have a use, at least as example:
tderz: I might not have properly understood the concept of how to use difference games, but Black is dead on the right, even if exchanging first black a, Wb, .
I saw now convention[1].

• On the other hand, simple common sense tells (suggests) me that in the left diagram is better in normal game positions (if L&D not at play).

Why? Because affects also the liberties of the .

• On the other hand, it also affects black liberties (negatively).

These lawyer type "it depends on ..." make clear that there is lot to consider, even in seemingly easy positions.

Bill: See It depends

Heretic Question: is this only difference game concept only useful for easy endgame? (hence , not applicable for best play on the full board?)

Bill: See Whole board difference game. And it frequently applies to best play on the full board, anyway. That is often the motivation for setting up a difference game, to see if one play dominates another, regardless of the rest of the board. See It depends.

Example 2, Difference Game (i)

tderz: This is wrong difference game notation. Convention [1] applies.

Example 2, Difference Game (i)

Black has gote on the left, White sente on the right,
seems better than (as indicated already in [2]).

### It Depends

Bill: That is not as lawyerly a caveat as it may first appear. There are actually two caveats.

Ko caveat: The results of difference games may not hold when kos are involved. That is so if the candidate plays involve kos, and also if they involve ko threats.

First play caveat: If the first player, regardless of color, wins the difference game, then which position being compared is better depends upon the rest of the board.

But if you are comparing plays and the difference game says that one play is better, your only worry in a real game is the ko caveat. And if the difference game itself does not involve kos, and the indicated play is no worse in regard to ko threats, then it dominates the other play, regardless of the rest of the board.

### Whole board difference game

It is possible, but normally impractical, to apply difference games to the whole board. Here is a practical (because small) example on the 3x3 board.

Suppose that we want to compare two possible first plays on the 3x3 board.

Which is better?

Which is better, a or b? (OC, we know that both are bad. ;-) )

Let's set up the difference game.

Corner vs. Side

Black first

Let Black play first. This is a tie, which is good for the second player (White), so let's try the other way.

Black first (2)

After , Black must make another play on the other board to prevent seki. Black loses.

White first

White to play wins, killing Black on the first board and making seki on the second.

So White wins the difference game, and the play on the side is better than the play in the corner.

### Diagrams

rubilia: To avoid confusion about move orders, I have changed the diagrams a little. I think the very first difference game someone gets to see should be as clear as possible. If you can't agree to the change, just restore them. However, even first time readers who aren't used to scientific texts can get an idea of what is G - G, and subsequently, G' - G'' or G - H, if the diagrams illustrate each single step in the easiest way.

Bill: Rubilia, the new diagrams confused the issue. Play should start from the difference game, as constructed. However, I did revise the first diagram, hopefully to make it clearer.

rubilia: I see your point, and I agree that it's clearer now than it was before. Sorry about confusing you. :P

AFAICS, to more than a few players CGT is completely "Voodoo", and that might be a result of, among others, too less illustration. I am quite sure it could help not to drive math beginners off if there was shown a diagram concurrent to every step, like:

Example 1, G

Example 1, - G

Example 1, G - G

Example 1, Ga - Gb

etc.

Of course, not every go player wants to go straight ahead into the deeper parts of CGT. But why to make the entrance less inviting than feasible?

Another question is, if move number markers like and in Example 2, Difference Game aren't more distracting than useful.

Bill: You make some good points. :-) I have added a setup diagram for Example 1. What do you think?

rubilia: Wow, that's great. It's all fine now. :-) (I'd like to keep the above diagrams here as backup to forestall the least questions.)

Bill: Fine. Thanks for your help. :-)

(Yet another didactical improvement (a smaller one, though) would be to promote understanding of terms like "G - G" by associating them to the corresponding diagram, together with the explaining words which are already there.)

[1] Convention for diagrams: Stones next to empty spaces are alive.

[2]

Example 2, Difference Game (i)

If White plays first she wins by 1 point.

John Pinkerton: Does it matter in example 2 that if White plays first, she ends in gote, while if Black plays first he ends in sente?

I think I can understand example 1 based on the conventional notion that Black 1 in the first diagram (main page) is not sente while White 1 in the second diagram is sente. White 1 in the second diagram has a bigger follow up, to destroy 2 points, while Black 1's follow up only destroys 1 point.

Bill: Getting the last move is often the key to winning a difference game (because you are normally comparing positions that are very close in value, and the extra play counts). So, yes, the fact that White ends in gote if she plays first, while Black plays with sente when he plays first is important, because it means that White gets the last play, regardless of who plays first.

John Pinkerton: Thanks, now I see that in this example even if White tenukis and doesn't play White 3 immediately, the potential for White to gain a point there later in the game would make the end position better for White. Black's initial (not numbered) play left this potential and hence was wrong.

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Difference Game/ Discussion last edited by blubb on November 1, 2006 - 17:01