Comments/Ratings for a Single Item

Due to advances in opening book theory and the introduction of chess
supercomputers in recent times, I regard the most recent estimates of the
first-move-of-the-game advantage (by white) in Chess as the most reliable
and accurate available.  These fall generally in the 54%-56% range as wins
for white.  Specifically, I find the "chessgames.com" results of 55.06%
and CEGT results of 55.40% wins for white the most compelling.  Also, it is
noteworthy that the CEGT results (involving computer AI players
exclusively) eliminated what a few fuzzy thinkers once considered a
legitimate possibility that "psychological factors" were solely,
artificially responsible for white's first move advantage.

I was intrigued by Joe Joyce's assessment that white's first move
advantage, as established statistically, is higher than one would
intuitively expect.  So, I devised a method to define and quantify it
mathematically based upon what is dictated by the white-black turn order
itself to discover what is actually predicted.  The amount of the 
all-but-proven first move advantage by white now seems quite appropriate to
me.

Note:  The following table can be adapted to any chess variant with a
white-black turn order.  Its use is not restricted only to Chess.

first move advantage (white)

white-black turn order

http://www.symmetryperfect.com/shots/wb/wb.pdf

2 pages

I've read that the average game of Chess runs appr. 40 moves.  So, I
completed series calculations for 40 moves.  However, anyone is free to
extend the series calculations as far as desired using a straightforward
formula.

Of course, white's first move advantage is greatest at the start of the
game, gradually reduces and is least at the end of the game.

The "specific move ratios" simply compare how many moves each player has
taken up to every increment in the game.  [The ratio is optionally
presented at par 10,000 for white.]

The "average move ratios" average all of the specific move ratios that
have occurred up to every increment in the game.  [The ratio is always
presented at par 10,000 for white.]  

In the example provided, a simple (unweighted) average is used whereby no 
attempt is made to unequally weight the value of the first move of the 
average-length game (white's move #1) compared to the value of the last
move of the average-length game (black's move #40) in accordance with
their relative importance.

At par, the "chessgames.com" results can optionally be expressed as
10000:08162.  

At par, the CEGT results can optionally be expressed as 10000:08051.

The table results are 10000:09465 (at black's move #40).

This accounts for only 27.45%-29.59% of the observed statistical advantage

(for white) which brings us to the crossroads:

Those who support the theory that the last move of the game (the checkmate
move) is the most important and valuable should employ a steep weighted
average defining this linear function.  Unfortunately, doing so will cause
the table results which are already too low for Chess to become
significantly lower, rendering the irrefutably-existant first move
advantage utterly inexplicable.

Those who support the theory that the very first move of the game is the
most important and valuable should employ a steep weighted average defining
this linear function.  Fortunately, doing so by the appropriate amount will
cause the table results which are too low for Chess to become significantly
higher, roughly in agreement with the observed statistical advantage (for
white).

Okay, HG, it seems to me you are essentially saying that any game with
promotion would have pretty much the same white first move advantage, if I
understand you correctly. At least, it appears to me that it follows from
everything you've said. 

The "linearity" that bothers me - it's because it is set up after the
game is over - there is a calculated win. This comes about because one side
is advanced a rank. I ask how this happens. If white just starts out on
ranks 2 and 3, then the advantage for white is literally a shorter distance
to promote, and the game is unfair at that point. If the players fought it
out until that point was reached, well, 3/8ths of games are draws, which
means 5/8ths are won or lost. I don't have a problem with saying that
white outplayed black enough to gain the step and thus the game. 

If the position at our starting to contemplate the situation is such that
white wins, then either the situation was set up unfairly to begin with, or
white outplayed black enough to create the situation. Am I missing
something? [I could be - my sinuses been messin' with me lately, and that
will turn me brain-dead.] Why doesn't black have equal chances to promote?

> it seems to me you are essentially saying that any game with promotion
would have pretty much the same white first move advantage, if I understand
you correctly. At least, it appears to me that it follows from everything
you've said.

Well, nearly so. There could be additional advantages on top of being
closer to promotion that can be achieved an just a few moves, and they
would add to the first-move advantage. Like 'developing' pieces, e.g. by
increasing their general mobility, or specifically directing them against a
weak spot in the opponent's setup.

Another caveat is that the promoting pieces should be short-range. In a
game where only Rooks promote (to Dragons, say, like in Shogi), advancing a
bit would not be helpful. They could promote in a single move wherever they are; this only depends on whether the file is open, not on their location in the file.

In Chief there is no promotion, so advance is not likely to be worth much,
as the initial position is already quite open. (I could imagine that even in
Shatranj, with hardly significant promotion, advancing all pawns of one
side by one rank would still be helpful to that side, because he can use
the open rank to laterally move his pieces, especially Rooks.) But IMO
there still should be an advantage to having the move, as moves can be used
to set up an attack formation. In particular by concentrating your pieces
for attacking on a single point along the lines of the opponent formation,
which is laterally spread over the entire board.

Spreading is bad strategy if there is nothing worth defending. Against a
concentrated opponent, part of your army will be outgunned, and there is no
compensation where your army outguns the opponent, because there is no
opponent to kill there. (And taking the undefended area does not provide
any gain, as empty area isn't worth anything in absence of promotion.) So
part of your power is wasted. This is why I think of the Chief array as
'undeveloped', so that sitting idle is a bad idea, and will quickly lead
to a lost position if you do it too long. (And the opponent uses the
opportunity to contract his forces in the central 6 files of the board
laterally, say).

Derek, that's an interesting little bit of figuring. And your win %ages
throw a stronger light on the problem. With a 55% - 45% white ad, white
wins an excess of 22%. Figure ~ 38% draws - Derek, are there more stats
available from those datasets? - and knock 19% off each number, to get an
estimate of the pure won-loss stats, and you get 36 - 26, or about a 38%
excess of white wins over black wins, a + 1/3rd to + 2/5ths range for 1st
move ad. 

Here's a question: what are the average lengths of white victories vs
black victories [vs draws]? Does white win faster than black? Or to put it
the other way, does black need extra moves to win to make up for white's
advantage? [And how do draws compare? Does that tell us anything?]

As for the most important moves in a game, hasn't it been your experience
that in decently-played games, there are usually a few turning points? I
wouldn't think the first or the last move would be *the* most important. I
would expect maybe half-a-dozen moves or more to be of roughly equal
importance, anyway.

All of the stats I referenced came from the Wikipedia article.
I cannot say whether or not other important stats,
discoverable somewhere on the internet, were not noticed by 
the editors there.

I strongly opinionate your theory must be correct that, 
due to the first move advantage (by white), victories for 
white require fewer moves (on average) than for black.

No matter how important a given number move is, I 
notwithstanding always ascribe the move preceding it to be 
slightly more important because it was critical to making the 
given number move which followed it possible and so forth.  
Moreover, both players normally have many choices.  
Ultimately, the move that precedes all others and cannot 
itself be preceded is the very first move of the game 
(by white).

Very very interesting topic. I try to put some input:

1. About a minimal modification of FIDE chess for lowering the 1st-move ad.
If promotion is so much important factor in causing the 1st-move ad, we can
just weaken the promotion, i.e. promoting the pawn to a ferz.

2. What do you think about the 1st-move ad of Balanced Marseillais chess?

3. I think it is quite safe to say that, in general, with the increasing
complexity (size of the game tree) of a chess variant we have a decreasing
the 1st-move ad, due to the “noise” factor. In that respect I expect
the 1st-move ad is much low in Chief than in FIDE chess.

4. I read in Arimaa the 1st-move ad is considered null (even if it is a
race game). What do you think about that? Maybe not null but very very
small… The reason maybe is because the very high complexity of the game.
(Or maybe it relevant the shortrange nature of the pieces too.)

5. About detecting the strength of the 1st-move ad in Chief. You can play Chief with the first player passing the first 5 (or more) turns.

The first move advantage (for white) is negligibly small in Marseillais
Chess (balanced).  Since this is aside from the topic at hand ... If you
are interested in the numerical breakdown for the white-black-black-white
turn order, send me a private message (E-mail) and I'll gladly send you my
3-page file (*.pdf).

Arimaa has a special set-up step at the start of the game where white
(gold) arranges all his pieces on the board, and then black (silver) gets
to arrange his own pieces after seeing white's arrangement, and then white
gets the first move.  Seeing your opponent's piece arrangement before
arranging your own pieces can only be an advantage, so in this case each
side receives an asymmetrical advantage in the opening, and it's not
obvious how to compare them.  It may be less a case of the first-move
advantage being small, and more a case of these two advantages canceling
out.

Or not; I'm just speculating wildly.

Thanks Derek for the pdf.

Jeremy you are totally right. I don't know why I forgot the arranging
phase in Arimaa. Of course this is a relevant factor, even if we don't
know how strong this factor is compared with the other 2 I have told (high
complexity of the game and shortrange pieces).

Maybe I should talk about Shogi instead. (By the way, a new discussions has
been open about the first move advantage in Shogi.) Shogi is very close to
Chess but it seems much more balanced. Why?