A long time ago I saw a friend playing KGS and always wondered why the number of handicap stones moves from 0 to 2 on the server?

For example:
5k vs. 5k = Even
5k vs. 4k = 0.5-komi, 0-handicap stone
5k vs. 3k = 0.5-komi, 2-handicap stone

Notice the handicap stone skips from 0 to 2 (instead of 0 to 1) when moving up only one rank.

Maybe this applies to other go servers too, I am not sure so I posted this in "Go Rules" sub-forum.

Thank-you.

1 handicap stone is the same as just going first. For a 3 stone handicap, black places 3 stones, then it's white's turn. For a two stone handicap, black places 2 stones, then it's white's turn. For a 1 stone handicap, black places 1 stone, then it's white's turn...

The real oddity in handicap games is the komi. If we accept that 6.5 komi is fair compensation for playing second in an even game, then between players with one rank difference, either of the following would be fair:

B plays two stones, W plays next, W receives 6.5 komi;
B plays one stone, W plays next, B receives 6.5 komi.

Since the weaker player does not actually receive this komi in a handicap game, small handicap games are relatively difficult.

This is good to know. So KGS gives free placement for first handicap stone, and fixed placement for all others.

Hehe, yes it's confusing. Also standard handicap placement is corners first, which are worth about 14-points. But when people often think of playing with extra points instead of stones I often hear "1-handicap stone = 10-points."

But it's just for fun and learning, so I don't usually worry

Based on the assumptions that 6.5 is fair compensation then the first situation you state is the same as B no komi (.5 to avoid tie) but moving first but the second situation is giving B two handicap stones with W having no komi.

The way I view handicap to make it easier to understand is to have each level of strength worth 6.5 pts so that komi if played without handicap stones would be

H Blk Wht
0 0.0 6.5
1 0.0 0.5
2 6.5 0.0
3 13 0.0

etc.

That is too little compensation, by roughly a factor of two. Suppose two players sit down to play an even game with a komi of 6.5 points. They decide colors randomly, but then the player who drew W says "I would rather play B; I will give you X points if you pass as your first move". What value of X would be fair? Answer: 13 points. This would make the situation the same as if the initial color choice was reversed.

After rereading what you wrote about in the second scenario with the thought of 13pt/stone I realize I was misunderstanding what you were saying. I agree that the handi-komi interaction is weird. With a figure of 13pts for each handicap then black should be receiving a reverse komi in one stone handicap games. The method I outlined above is just the way my brain makes sense of how the handicap stones are done especially since there is no direct linear relationship when you use the 13pt figure.

Though I do believe that the handicap assumes that the weaker player will make mistakes that the stronger player can take advantage of more easily, but even then the jump from one handicap stone game to two handicap stones is technically a 1.5 stone increase instead of the 1 stone increase you would expect.

I guess that there is a practical assumption that a 2 stone difference is not twice as wide as a 1 stone difference.

mitsun, I'm not disagreeing with you. I'm just trying to clarify some parts I found confusing:
Let Tom be the player who drew W, and the other player John.

Tom drew W. Tom says "I would rather play B" (same Question 1: what does this have to do with anything?),
Question 2: Is Tom keeping W or is Tom switching to B ?

Case 1. If Tom switches to B, and they play even, then Tom should give John the 6.5 komi.
Case 1(a). If Tom switches to B, AND Tom wants John (who is now W) to pass, then it becomes a regular 2-stone game (W gets 0.5 komi).
Case 1(b). If Tom switches to B, AND Tom wants John to pass John's first move, AND Tom still asks John what is X? -- Is this your real question, mitsun?
If this is indeed your real question, you're asking Question 3: "What's the correct komi for W against a 2-stone handicap?"
I believe if you ask a pro this question, you may get the answer: let's play 500-1000 games this way, and find out.

Case 2. If Tom stays as W, AND he wants John (who remains B) to pass,
then the question is, are they still playing even or not?
Case 2(a). If they're still playing even, then John should give Tom 6.5 komi,
so it's just as if W were to go first, instead of the normal B.
Case 2(b). But if Tom stays as W, AND Tom wants John to pass, AND Tom wants to keep the original 6.5 komi, then...?

Question 4. (Maybe this is the same as Question 3) How did you get 13 points?
I know 13 = 6.5 + 6.5. But 6.5 is the current komi for an even game.
So where's the logic or reasoning to add 6.5 to itself? ...Rather, where's the empirical data to support (6.5 + 6.5)?

Thanks.

My experience is that, in turn-based play, additional handicap stones are worth between 6-8 points, in blitz they're worth about 15 points, and in normal games about half way inbetween. (Based primarily on OGS and KGS games)

If black passes as his first move, and receives 13 points compensation for that, then, because white already had 6.5 points, the game is now: white starts, black gets 6.5 komi (net komi, we subtract white's 6.5 from black's 13 here)

Since this exactly mirrors the usual situation (B starts, W gets 6.5), then if the usual situation is fair, then so is this one.

You can also define proper komi by imagining two players sit down and bid for the right to play first, offering each other points. Well informed players (you can bump this up to players who know perfect play for go) will probably be quite willing to offer 6 points but not 7--hence the value of komi as 6.5.*

Mitsun's example is more or less this idea applied to handicap stones.

* That's based on experience.

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Interesting observations about the inconsistencies with handicap stones.

Indeed, personally, I win much more than 50% of my games against people 1 stone weaker (even though I am just over the 2k mark), and lose much more than 50% of my games against people 1 stone stronger, with the current system of having the komi for white at 0.5 in 1-stone handicap games. It always puzzled me until now.. I guess the handicap system really isn't perfect. (Indeed maybe if white had a -3.5 to -6.5 komi in 1-stone handicap games, it might even the scales).

Personally I think it seems to balance out more at 2-stones handicap for some reason.

By this I mean that if you are in the middle of a rank, you seem to win more or less 50% of the time in two stone-handicap games with stronger or weaker players. Of course I am just expressing my opinion, I have no stats whatsoever. (of course some of this also depends on your ability at handling handicap games, which in my opinion requires a someone distinct strategy)

Do you think someone could make the case that it would be a good idea to change the system? Has the handicap system always been this way?

The good thing is that since the stronger player has an extra slight advantage in close matchups, it's extra motivation to improve!!

I see HH already answered this. Does that explanation make sense? I think this argument is a pretty good proof that the value of an extra move at the start of the game is two times komi.

mitsun, sorry, it's still unclear. Maybe I misunderstood something:
(1) Normal, even game. W to play . W already got komi = 6.5 pts:

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(2) As I understood HH, this is identical to (1), except for the colors. B to play . Net result: B already got komi = 6.5 pts:

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So (1) and (2) are identical, just switch the colors.

But (3) is this: W to play -- What is the fair komi for W?

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(3) is entirely different from (1)/(2), no?
In other words, (2) just reduces to (1). (1) = (2). They don't tell us anything about what happens in (3).

OK, 13 is a reasonable GUESS for komi for W, but we still need pro data to support this, yes?

Another way to look at it: it took pros many years of experiments and data to get to komi = 6.5
(historically, something like from 3.5 to 4.5 to 5.5 to 6.5 and now in China, even 7.5).

They established komi = 6.5 (or 7.5) for the initial condition of an empty board.

So, if we want to know the fair komi for a 2-stone game, we must go through the same process:
many thousands of real pro games.

Because now the initial condition has changed from an empty board to a 1-stone board.

We cannot simply take the result (komi = 6.5 or 7.5) from one set of experiments (initial condition = empty board)
and use logic to derive (2*komi) and apply it to a different initial condition (1-stone board).
Yes, we can guess (2*komi), but to test our theory, we must do actual experiments: real pro games.

Similarly, for a 3-stone or higher handicap games, we're changing the initial condition each time.
We cannot just say the komi for a H3 game is (3*6.5), or (4*6.5) for a H4 game, etc.
We must look at real pro data to fine-tune the fair komi.

Did I misunderstand the question all together?

I think this has been more or less answered by others in this thread, but basically it's like this:

Even + komi = No handicap
Even + no komi = 1/2 stone handicap
Even + reverse komi = 2 Stones + komi = 1 stone handicap (Note this equivalence is the same as saying 1 move = 13 points)
2 stones + no komi = 1.5 stone handicap
2 Stone + reverse komi = 2 stone handicap.
etc

I don't remember the exact links off hand, but I believe there's a pretty good discussion of this on either sensei's or in the old RGG archives. As far as I can remember, on KGS (since that was the original question) the idea was that reverse komi is confusing at first for some (who let's be honest, the majority of which won't be terribly concerned about the mathematical precision related to handicap stones). Instead of trying to deal with constantly explaining a mathematical nitpicking used for handicap accuracy, it was easier to implement a simple system and have the rating system take into into account the fact that 2H games were really 1.5 in software. For those handicapping purists who wish to use the reverse komi, it's simple enough to set, and it will still be properly calculated.

First, the handicap does not skip from 0 to 2. Taking Black without komi is considered equivalent to having 1 handicap stone.

Second, there is a problem, which I think that the KGS rating system takes into account.

Historically, there was a time when the strength difference between pro ranks was greater than today. Here was the handicap schedule:



Modern amateur rank differences are equivalent to twice these rank differences. Thus, this would be a reasonable handicap scheme:



Or



Plainly, the traditional amateur handicaps favor White. The problem starts with 5 kyu vs. 4 kyu.

How much should komi be? That is an empirical question. Proper komi for pro even games is still an open question. But it seems that a komi around 7 is reasonable. Komi should decrease as the players get weaker, because they are less able to utilize the handicap stones. My guess is that DDK komi should be around 3 or 4.

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