Comments/Ratings for a Single Item

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.

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).

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.

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).

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.

> 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).

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?

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).

> so however many turns it takes to promote that first pawn, that's as
fast as the game can possibly go, so I do see it as fast.

Well, so apparently in any game with promotions the promotions will
eventually become 'fast', no matter how deep the board, or how slow the
Pawns. So it doesn't really put a restriction on anything, when you said
before that 'promotions can only affect a game when they are fast'.

> And by "linear", I mean in that situation, there is nothing else you
can do. It has gone from game to puzzle once there is a guaranteed win that
a human expert can conceivably see.

But this is how all Chess-like games end: either in a mate-in-N checkmating
problem, or in an elementary end-game like KQK or KPK.

The point of my example is to show that even a small advance in games with
promotion becomes totally decisive, no matter how deep the board. A large
fraction of the games will reach a position which is drawn, but would be
won if one of the sides had just advanced one rank. So you cannot afford to
wait for the opponent to come towards you even if he is still very far
away, as you could in 16x120 Chief. Just letting him step one rank forward
(even if only his Pawns do it, or some of his Pawns) turns so many of the
possible endings of the game from draws to losses that it gives you a
significant disadvantage.

If you are in a position with a Pawn structure that would make a lost Pawn
ending, even if you have still pieces it gives you a significant
disadvantage, because you can no longer afford to trade the pieces. Many
winning strategies of the opponent could be based on this (putting you in a
position where you can only prevent the loss of more Pawns by trading), and
you cannot match them with the reverse threat.

In your last example, HG, promotion is the only thing that can happen to
change the current game state to one in which a win can occur. And the
pawns are essentially isolated, so however many turns it takes to promote
that first pawn, that's as fast as the game can possibly go, so I do see
it as fast. And by "linear", I mean in that situation, there is nothing
else you can do. It has gone from game to puzzle once there is a guaranteed
win that a human expert can conceivably see. Or, maybe better [and maybe
not], once the situation has clarified enough that it is calculable through
to mate. 

I think I want to go back to what 53% - 47% actually means, and how I see
white's FIDE 1st turn ad as very significant. That 6% difference is ~1/8th
of the 47% black points or nearly 13% right there. But ~3/8th of the games
are draws, and to see a pure win-loss percentage, I discard these, and see
about a 34% - 28% win-lose there, translates to a roughly 23% advantage for
white. That is the number I am trying to reduce toward zero with the Chief
series.

HG, your comment shows up okay in this thread. Sorry I don't have the
technical skills to correct the main comments page. And as far as losing
lengthy posts, you have my complete commiseration and understanding. A
software update and auto-reboot killed the lengthy comment I was about to
post.

Jeremy, I cannot answer your question exactly about first move advantage.
Ben has the right of it from a FIDE perspective. The "noise" I talk
about
is essentially the jockeying for position players do during a game. And I
do see the noise of the games as they change away from something with a
1st
move ad to something without, or essentially without, as drowning out the
ever-diminishing 1st move ad at some point. If the 1st move ad is 0.1%,
but
the statistics are only accurate to +/- 0.05%, then the 1st move ad could
be just the extreme end of normal fluctuations. It's statistically very
unlikely, but possible. I think it is legitimate to say there is no 1st
move ad in that case. Now, if the 1st move ad is reduced by 95% - 99+%, I
concede you are right literally, but I would consider it both a moral
victory and "close enough for government work". 

But I would need a statistical "proof" there was a first move advantage
of any size in Chieftain Chess, because I really have trouble visualizing,
given the specific rules and setup of this game without promotion, how
there can be a 1st move ad for white if black can skip the 1st turn
without
detriment. I see no need for all chess games to follow only the behaviors
exhibited in FIDE, and no others. Please note this does not mean there is
no advantage in continuing to move without an opponent response, nor does
this mean that once the armies close, either side can afford the luxury of
skipping a move without the very high likelyhood of losing pieces. It is
just that this cannot happen in Chief in the beginning because the pieces
are not close enough together.

HG, you said it well when you said the setup in Chief leaves the pieces in
lousy positions. From a chess perspective. I see it from a wargame
perspective, and see 2 idealized armies, each with 4 equal divisions,
arriving in remarkably good order at the edges of a battlefield. That good
order is very flexible, allowing a fairly rapid deployment of forces and
pretty easy shifting around, in the immediate area. Only 4 of 32
pieces/side are even out of immediate command control in the setup, and
not
only are they all supported by units in control, but those 4 units can be
brought within control range on the first move, and 2 of them moved.
Players start with very tight control of their armies. The problem to be
solved in the game is that the force is spread evenly across the board,
and
with all short range pieces slowed a little by leader requirements, it not
only takes a few turns to concentrate your strength, it takes a few turns
to come to grips with your opponent, more or less telegraphing your
offensive strikes. [A good reason for 4 or even more moves/turn/player.]
You must get your whole army in close and tight before you can do any real
damage. The tactics and strategy of the game are different from FIDE,
which
I see as more of a "sniper" type game, where long range pieces shoot
across the board for an attack. It's the difference between a boxer and a
puncher, maybe. But this is why I say there is no first turn advantage in
the original Chief, and I would want to see the numbers for an ad in Chief
with promotions before I would grant it. I won't deny I see the strong
possibility of a 1st turn ad **EDIT: in Chief with promotions,** but don't
have any reason to believe, given 
the above, that it is anywhere as close to significant as it is in FIDE.
Promotion should reduce the number of draws in Chief, however. And I
already have a "chief" icon without the gray shading, to distinguish
between "royal and non-royal" chiefs. And there is the further option of
allowing promoted pieces to "self-activate", which would not count
against any individual leader's activation point for the turn, but which
would count against the total activations allowed/turn, something
successfully playtested in larger Warlord variants.

Uh?

What I posted yesterday in response to Joe now shows up as a post of
George???

I think it only makes sense to talk about an advantage in the context of
fallible play. It is a well-kow problem that 'perfect play' from a drawn
position based oly on game-theoretical value of the positions is very poor
play, often not able to secure a win even against the most stupid fallible
opponent. E.g. take a position from the KBPPKB ending, which is drawn
because of unlike Bishops. Perfect play by the strong side will then
usually sacrifice its Bishop and two Pawns after some moves, being very
happy that KKB is still a theoretical draw. Good play distinguishes itslf
from perfect play in that you try to induce your opponent to make errors
(which is no longer possible in KKB, but quite easy in KBPPKB). This,
however, requires opponent modelling: you have to know which errors are
plausible. Otherwise you get silly play, where the stronger side tries to
trade all material as quickly as possible in a drawn situation (hastening
the draw), because he sees that after any trade the opponent has only one
move that doesn't lose, namely the recapture of the traded piece. This
would work quite well against a random mover, but most opponents are
stronger than that.

Well, as long as white sometimes wins and black sometimes wins, the
"noise" is large enough to overcome all other factors SOME of the time. 
But if you collect a giant database of master-level games and find that
white is winning 53%, then I think it still makes sense to say that white
had an advantage, regardless of the theoretical perfect-game result. 
SOMETHING has to be responsible for the fact that white wins more often
than black.

So if white wins only 1% more than black, or only 0.1% more, or only 0.01%
more, at what point do you declare that the noise has "overwhelmed" the
signal and that there is now "no" advantage?  I don't see any
non-arbitrary way to draw a line anywhere other than zero exactly (i.e. the
point where the advantage passes from white to black).

So I'm assuming that the "advantage" is the hypothetical difference in
win rate between white and black that we would converge upon if we sampled
an ever-larger number of games played by "skilled" players.  The
definition of "skilled" is a bit hand-wavey and probably depends on
context, but I think the rest of that is rigorous.

It seems that most of you already know this, but maybe it's still helpful
to note that there is a definite answer for who wins chess given perfect
play on both sides (white, black, or neither [draw]).  This is true of any
chess variant that involves a fixed turn structure, perfect information
(& no randomization), and finite length (here's where we need something
like the 50 turn rule).

So, in the mathematical sense, any such chess variant either has a perfect
1st turn, perfect 2nd turn, or absolutely no advantage.

Joe keeps referring to "noise", which is how we can manage to talk about
a 1st turn advantage without the mathematics making it boring.  So far no
one has actually defined the framework of the question, but it seems
generally to be accepted as referring to people's current thoughts on
optimum strategies, and how those interact.  I suppose to make this
rigorous we would want to define the fuzzy value of positions (it's
unclear how to do this, though current chess programs are probably a good
starting idea), then allow for some randomness in the players' moves that
biases toward high value positions.  Then I think we should say there's
"no" advantage if the probability distribution of wins-draws-losses given
this framework has no advantage with statistical significance.  So we say
there's no advantage if the noise drowns out whatever perfect mathematical
advantage actually exists.  (I think this is essentially what Joe has been
saying?)

> Ah, HG, to me the setup you describe is maybe too linear to adequately
represent the situation.

No idea what you mean by 'too linear'. But note that this could be the
initial position of a very siple Chess variant, and has only short-range
pieces.

> I agree things like this can happen in a game, somewhere, somewhen, but
only after a considerable amount of precursor action.

The point is that in games between strong, approximately equal players most
games eventually get to the stage of a Pawn ending, or where you can
threaten to convert to a Pawn ending. If all such Pawn endings are always
won for one side (because he advanced one rank more than the opponent), it
has a huge impact on the win percentage.

> Further, I see the 75 moves as minimal, because that is the least amount
of time it takes for anything significant to happen in the game as it is
set up. Nobody can win or even really threaten another piece seriously in
less than 75 turns, so I do see that as a minimum number of turns to
promotion.

Again not sure what you want to say with this. You mean that irrespective
of the depth of the board, promotions are always 'fast'? But then this
doesn't seem to mean anything.

> Throw in a knight or two, and you change the equation. But then neither
of us can say for sure what would happen then [although probably not much,
once you consider what a couple pawns and a knight could do against a
couple pawns and a knight, when all pawns are passed but 75 moves from
promotion...]

Well, with more pieces without mating potential you obviously have to add
more Pawns as well, or it will be a trivial draw (because you can easily
devote a minor to blocking a Pawn, or even sac it). But I don't think it
changes much. There will be many positions where you win when you move them
up just a single rank, which are draw whan you don't.

The only way to know the impact for sure is to play a couple of thousand
games, where you advance one of the sides comapred to the other (i.e. FIDE
on 8x10).

I feel I need to ask again whether you are arguing about the SIZE of the
first-turn advantage, or the EXISTENCE of the first-turn advantage? 
Because you said earlier you were arguing over its existence, but all of
your arguments seem to be about its size.

You could be a thousand moves away from mounting a credible attack, but
that doesn't mean the value of a move is zero.  After you move, you will
only be 999 moves away from a credible attack, which surely must be at
least a tiny bit better than 1000?

Your typical player probably won't notice that advantage.  But then, a lot
of players probably don't notice the first-turn advantage in FIDE, either.
 Small is not the same as zero, and what counts as "small" depends on how
good you are and how many times you're playing.

And zero first-turn advantage isn't even necessarily desirable.  Suppose
we have a game where players are allowed to pass on their turn, the initial
array is symmetrical, and the players know that there is no first-turn
advantage.  Since there is no first-turn advantage, passing is (by
definition) at least as good as anything else you can do on your first
turn, so you might as well pass.  Then the second player is in exactly the
same position as the first player on his first turn, so he might as well
pass.  So not only is the perfect strategy obvious, it's also incredibly
boring.

But even if passing isn't allowed, the first player either has a move that
is EXACTLY AS GOOD as passing--which I'm not sure is possible, and I
don't think it changes the outcome compared to allowing passing--or else
the best possible move is WORSE than no move at all, which means we've
simply traded a first-turn advantage for a SECOND-turn advantage.

All else being equal, I think we want the first-turn advantage to be
"small".  We might even want people to be uncertain whether the advantage
lies with the first player or the second player, perhaps by using an
asymmetric starting array or placing special restrictions on the first move
(such as moving half as many pieces as normal).  But if you could somehow
prove that the first-turn advantage was exactly zero, I think that would
probably end up being bad (not so much because the advantage was zero, but
because you were able to prove it).

Ah, HG, to me the setup you describe is maybe too linear to adequately
represent the situation. I agree things like this can happen in a game,
somewhere, somewhen, but only after a considerable amount of precursor
action. Further, I see the 75 moves as minimal, because that is the least
amount of time it takes for anything significant to happen in the game as
it is set up. Nobody can win or even really threaten another piece
seriously in less than 75 turns, so I do see that as a minimum number of
turns to promotion. Throw in a knight or two, and you change the equation.
But then neither of us can say for sure what would happen then [although
probably not much, once you consider what a couple pawns and a knight could
do against a couple pawns and a knight, when all pawns are passed but 75
moves from promotion...]

As for the extra commoner, It can be a guaranteed win. What is necessary is
to form a wall across the board with all your pieces, including your 4
chiefs and 1 extra commoner, then slowly move it forward until you can pin
the opponent against a side and force an exchange of pieces and finally,
chief for commoner. This requires you hang onto all 4 chiefs. With them and
1 commoner, you can wall off the board, then start your advance. It will
take much maneuvering, as you must always block the opponent from either
breaking out or exchanging one or more leaders.

Too bad my long answer I posted to this is now gone.

Anyway, the most important point was that I didn't agree: On the 8x80
board take a symetric position with a King, a and f Pawn for white on the
4th rank, and a King, c and h Pawn for black on the 77th rank (counting
1-80).

You would only have to move that entire position up 1 rank, and it becomes
an easy win for white. Despite the fact that promotion is at least 75 moves
away.

Nuts, I'm still not clear enough. HG, thank you for being willing to
consider that Chief has no first move advantage. To clarify my position,
it's very clear that black has to start responding within a few turns of
white starting to move, or black will be crushed. And a move advantage will
show up after a few turns. On the 16x120, or the 8x80, black *has* to come
up to meet white, or clearly black cedes an advantage to white. 

To clarify what I mean by "fast" promotion, I mean promotion can occur in
a minimum of turns, that it's only 2 or 3 steps [moves remaining] to
promote. This can occur any time during the game, and may occur 78 squares
down the chessboard in turn 497. "Fast" is meant only for the immediate
situation, not how long it takes to get there. And that is why you are
clearly right that there is an advantage to pushing down a very long board,
if you can push far enough. On the 8x80, if I met you at row 30 instead of
row 40, there still wouldn't be any significant value to promotion.
However, if I met you at row 8 or 10, then clearly there is a value to
promotions down the road, because we know promotions happen on 8x8 and
10x10 boards, and you would have the advantage. Somewhere between row 40
and row 8, pawn advancement goes from only a tactical value to a strategic
one, in the sense that each square advanced becomes more meaningful for
promotion, and is not just meaningful for local position. 

My 30% figure is the edge white has in wins when draws are discarded. It
was based on a white-black points win total of 54-46. If we accept the
lower figure of 53-47, then white has won 6% more, for a ratio of 6 divided
by 1/2 of 53 + 47 = 6/50 = 12% edge to white. If you recalculate and
discard 3/8th of the games as draws, a ratio I also gave earlier, then the
pure white wins to black wins ratio is on the order of 30%. With the
53%-47%, the white wins to black wins without draws works out to [about] 34
wins to blacks 28 per 100 games, or 6 divided by 31, about a 24% win
advantage for white. I find this number very significant, and a very strong
signal of white's 1st move ad. And that's where I get the higher numbers
from.

> We may be coming to agreement on one aspect of the first question,
> that its small board size affects FIDE's 1st move ad.
> The 16x120 and 8x80 boards have pretty much settled that, no?
> Any objections?

Well, I am not sure how you consider it 'settled'. In 16x120 Cheiftain I
am prepared to believe there is no firs-move advantage. For 8x80 FIDE I
think the advantage persists, because letting he opponent advance would
give him he advantage of being closer to promotion, even when he is still
completely out of range for hostilities.

> Promotions need to occur reasonably fast to be of value.

No, why? In FIDE promotions can (and usually do) decide games in the
end-game. Like in KPKP or KBPPKNPP. Who wins in a Pawn ending is usually
decided by who's pawns are most advanced (promotion races). He who Queens
first simply uses his Queen to block, and hen gobble up the opponent Pawn.
Just being there one move earlier is completely decisive.

> On the second question, is it possible that black's skipping
> one turn in Chief does not seriously - that is, do something
> like give white a 30% win advantage in games that are not drawn - 
> affect black's winning chances? Is it possible that with a one or
> even two move advantage, white only wins 20% more, or even 10?

Yes, of course that is possible, or even expected. In FIDE the first-move
advantage is only 3% excess score, so one tempo (the difference between
being white or black) is only 6%. So numbers like 10%, 20% or 30% are
really unheard of. They are in the range of having a one or two-pawn
advantage, so that a single move is not even worth that much in the
presence of hanging pawns.

Of course I don't know what the advantage in Chieftain Chess is for having
an extra commoner. (And I would be surprised if you did...)

Mats, I freely admit I prefer games with absolutely equal chances, but they
aren't the only kind I try to design. To me, perfect balance is an ideal
which cannot always be achieved. But to deliberately design a game where
the chances for white are set as high as +30% is not something I would set
out to do. 

Like Jeremy, I would ask you if chess variants must have a 1st turn ad, or
for you specifically, Mats, is a 1st turn ad a necessity for a good chess
variant?

Okay, we actually have 2 questions going here simultaneously, and they are
the initial one - why first move ad in FIDE, and secondly, does Chief have
a 1st move ad? 

We may be coming to agreement on one aspect of the first question, that its
small board size affects FIDE's 1st move ad. The 16x120 and 8x80 boards
have pretty much settled that, no? Any objections? If not, then the
potential for promotions is a source of White's first move advantage, how
important yet to be determined. 

Do you think it fair to say that promotion potential is at least somewhat
based, then, on mobility? Promotions need to occur reasonably fast to be of
value.

On the second question, is it possible that black's skipping one turn in Chief does not seriously - that is, do something like give white a 30% win advantage in games that are not drawn - affect black's winning chances? Is it possible that with a one or even two move advantage, white only wins 20%
more, or even 10?

OK, I buy your 16x120 example. It works by virtue of the fact that advance
isn't worth anything. With an extremely deep board, and short-range
pieces, most of the moves needed to build an attack formation are needed to
cover the distance, and the opponent can grant these to you if he is
prepared to fight 'with his back against the wall', and only start to
react when you get in range.

But this argument would already fail when there are promotions. In FIDE on
an 8x80 board letting the opponent sneak up to you basically means that he
has promotion in range, while your pawns effectively become non-promoting.

And I don't think this is very relevant for square or 'landscape'
boards, where approach can be a free side effect of lateral movement of
your pieces, so that the opponent would have to start reacting immediately
on your lateral displacements.

Okay, Jeremy, yes, I do see the general properties of a game as including
the general size, shape, density, "hotness" if I can use that word [and I
don't really know what it means exactly], rules set and piece make-up. I
see FIDE as a very small, overpowered game that is built to be a shoot-out.
And rather often in shoot-outs, [s]he who shoots first wins. I would expect
very small, overpowered, very dense and regular in shape chess games to
likely have a first turn ad. The exact amount of the 1st turn ad is
dependent on the specifics of each game. For example, I would have to argue
Modern Shatranj must have a lesser 1st turn ad for white, because most of
the pieces are short range. Just the change to the double-step pawn move
makes a difference in the stats, I would have to believe. 

However, I don't see that a 1st turn ad *has* to exist in a chess variant.
Heh, obviously, but I mean that it is not something I see as an inherent
part of chess. Let me try an extreme example. Let's stretch the Chief
board from 12x16 to 120x16. Now, instead of pieces being ~5 squares apart,
they're 115. No piece moves more than 3 squares, and no piece may move
unless it is within 3 squares of a leader, all of which move 2
squares/turn. In the first 50 - 100 turns, as the pieces are moving up to
initial contact, surely the black pieces could see what the white pieces
were doing, and adjust "on the crawl" rather than on the fly. [For that
matter, you can set up a number of different board configurations in
"3-Board Chess", which set white and black up on the back ends of 2
different boards, and the 3rd board is placed between the first 2. You get
a rectangular 8x24, with the pawns 20 squares apart. You get an "L", with
the pieces and pawns having to go around a corner. You can also stagger the
boards, with a pair or each pair being offset 1-4 squares... What does that
do to first turn ad?] 

And here's where the importance of reversibility comes in. If you get a
few pieces too far forward, so you can see they will be overwhelmed by the
opponent, you can retreat them faster than your opponent can re-form an
attack. With such short range pieces, retreating 1 square is often enough
to totally disrupt an attack. And this is a legit tactic/strategy.
Sometimes you can bait your opponent into overextending, and gain a piece
or two. In Chief, careful play after that gives you the game. 

Now, the difference between 3 and 5 squares is greatly different than the
difference between 59 and 61 squares. Is it worth it to spend 50 - 60 turns
to promote? What happens to the rest of your pieces if your opponent has
all that time to attack freely? Clearly, promotion is only of benefit in
games where the promotion line is close. The reason promotion works as it
does in FIDE is that the pawns can be/are threatening promotion after
they've moved twice. The double step and a single step puts a pawn 3
squares from promotion. That's mobility for a pawn. A third step, and
they're worth a piece. And in Chief, it would take 50% longer, because
you'd have to move the Chief up with the commoner piece [50 commoner moves
and 25 chieftain moves, say.] And then you've still got to get it back to
the action. 

The need for a leader to move any piece also slows down the game a bit. It
is more than compensated for by 4 moves/player-turn, but that is why a
rapid advance doesn't work - you are just advancing with a part of your
forces into range of your opponent's army. Once you've made contact, all
the moves get much hotter, but effective actions require several turns to
set up. If you can't make a realistic threat in the first handful of
turns, assuming your opponent moves after you've moved twice to start,
then what happens to 1st turn ad? The reason I ask you to push pieces for a
few turns is to demonstrate that there is no adequate attack than can be
made in less than at least 4-5 turns, and maybe more. 

Historically, an attacker has needed 2-1 odds overall to "guarantee"
success against a defending force. [And 3-1 at the point of contact to win
that battle.] You have to do some serious maneuvering and a good bit of
trading to make any headway against any reasonably competent opponent. And
it is possible to do so in the original game, but I see high level
Chieftain Chess as [almost] always a draw. Oddly [to most] the game is too
small to provide enough possibilities to good players, like a very small Go
board. [Small Go's are solved, aren't they? 7x7, 9x9] Warlord: Border
War, which uses stripped-down short range chess pieces, leaders with
different command abilities, and terrain, is a proof-of-concept game. 

Games on the Battle of Gettysburg [US Civil War] have always been a
favorite of mine, as have games on the Battle of the Bulge [WWII, Ardennes]
which are both meeting engagements. It has occurred to me I could do a
decent Battle of Gettysburg, if not adequately enough with the Warlord
rules, then with expanded rules which incorporate additional capture modes
from Ultima/Baroque. Infantry would get custodial capture as well as the
standard replacement capture, essentially surrounding, cutting off, and
starving out an enemy. Artillery could gain a limited form of rifle
capture, which would likely depend on facing. [Or even a version of the
"coordinator" capture, by shooting a piece that is within range of the
cannon and another piece.] Other pieces could gain an overrun capability,
or capture by jumping. All these in addition to standard capture by
replacement. 

Any of these games would be, move by move, a chess variant. But if first
player has an advantage, why could I not slightly expand the size of the
board, and start all the pieces a little farther back, and let black go
first? Would this give black the advantage, or, in this very large
[~100x100] game, would the exact balance between distance moved and the
extra, earlier first turn for black just cancel out, leaving white with the
"real" first move advantage?