Comments/Ratings for a Single Item

Okay, maybe I can combine Jeremy's and HG's questions in a discussion of
the "center". Certainly, control of the center is very important in these
sorts of games, or in most actual battles, for that matter. But "the
center" is a somewhat nebulous concept when expanded from FIDE to
Chieftain and Warlord. On a 12x16 board, the "center" is a 4x8 strip
containing 32 squares. Much easier for both sides to get into in force, and
far harder to control. On the Border war scale of 16x24, the "center is
going to be around 6x12, 72 positions to control. And the "edges" are 6
squares deep. 

At the larger sizes, control of the center often means the opponent's army
is broken. But there is no first move advantage to controlling the center,
because the board is so large, maneuvering around in it a square or two
closer to one side or the other - consider the logistics of invading the
opponent's home territory, where the army and command structure are
initially established. It takes time to gather the troops and press
forward. 

However, no static defense has seemed to work. It's always been the case
that if a player cedes the initiative, the other player can pick a spot to
attack where the attacker can guarantee overwhelming force. It is annoying
that so many of the games on Courier are gone or inaccessible, but please
look at the 2 games of Warlord being played now to get a little idea of the
flexibility of the games, and why I say the first turn advantage has to be
washed completely away at some point.

The Border War playtest I ran Thursday night allowed promotion, but neither
player bothered. Even with 12 moves/turn [48 piece armies at start,] it
wasn't worth it to send some units off to try to fight their way through
the opponent to promote. Although there were 4 geographic targets - towns -
in the center of the board, so that made it less worthwhile to bother with
promotion, because victory was to the player who could occupy 3 of those 4
towns at the beginning of that player's turn. 

I think that the center of the board geographical objectives would have to
give the same effect as promotion, and they aren't all the way across the
board. And I still don't see the need to say there is a first turn
advantage. It's possible there is one, but I have to say I see it as lost
in the noise. 

Just so you know, Jeremy, this series of games is also meant to show that
there can be humanly playable super-large games, boards on the order of
100x100 squares. These games are scalable. Border War at 16x24 is 4% of a
100x100 board. How many steps do you want?

Something else I didn't think of, but which could play into this, is piece
density. In FIDE, it's 50% to start. In Chief, it's 33%. In Border War,
it's 25%. FIDE is deliberately cramped, with the pawns placed as they are
to blockade the player's own pieces. And the cramping is maintained by the
pawn's peculiar basic move and capture rules. That feeds into the first
turn advantage, which you can see as a sort of head start on freeing
yourself from the bondage of the pawns. Very often a mate is achieved with
the passive help of the victim's own pieces, which block possible escapes.

Yes, the FIDE starting position is particularly bad, so it is very possible
that having the move there gives you more advantage than having the move in
an average quiet middle-game position would give you. But this was not the
point under discussion. And the same holds for Great Shatranj, and even
shorter-range variants. The initial position of Chieftain Chess also
doesn't look so hot to me. It doesn't have the pieces at all in the
formation I would like to have them in before engaging the opponent in
tactics.

Jeremy, HG, you ask for evidence that there is no first turn advantage and
all I can offer is empirical evidence and logic. I will cheerfully examine
the first few moves of Chief with either or both of you, and we can all
work on showing a first 2 turns advantage in Chief. I am pretty much
arguing that you cannot even demonstrate a credible 2-move advantage for
white in the original Chieftain. 

I suspect you don't fully appreciate the effects of irreversibility on
pawns, nor the greater room for pieces in Chief. As evidence, HG, you said
this:
"[T]ypically any constellation of opponent pieces can be cracked if you
are given the time to organize your pieces in a constellation needed to
crack it. So a game of chess is a constant race between concentrating your
attack force, and the opponent strengthening the spot against which you
direct that attack. Being allowed to do two quiet moves in a row (which is
what happens when the opponent loses 1 tempo) makes it more likely you will
win that race."

Reversibility and more room means the position you are attacking can be
ceded without any loss of pieces at all. A position doesn't crack as much
as it shatters. And all I can offer for all these claims is empirical
evidence. I invite either or both of you or anyone else interested to push
pieces for a while to actually see why I say what I do. Chief is a very
varied chess variant; it does not at all act like FIDE because it is
structured differently. I see that difference in structure eliminating
first-turn advantage, with the empirical evidence that you cannot show any
effective initial attack, even with a 2-move advantage for white, because
black has too many counters, and gives up only a little territory.

HG, again: "Only in positions where nothing can be achieved no matter what
(i.e. a static defense exists that has no weak spots weak enough to succumb
to even total concentrated attack of all enemy material), a tempo loses its
value. Such fortresses are quite rare."

I submit they are impossible in Chief, unless the player making the
fortress has already "won" the game by accumulating enough extra material
to construct such a fortress. A static fortress can be breached by an
active attack. Chief is designed to be a game of attrition, but is very
unforgiving. If you can get a piece or two up on your opponent, you can
probably force a win. Forting up doesn't work, empirically, in any of the
games. People who tried it lost. The key to Chief is always maintaining the
exchanges so you do not go down in total pieces on the board. An active
attacker can, with maneuver, hit 1 spot with an overwhelming attack which
will leave the attacker a piece or two up, in my experience. Two of the
four non-leader pieces can create forward forks which can/will stymie a
static defense.

The Warlord games are more forgiving. You can get a couple pieces down, and
still win a reasonable amount of the time. At least, now, in their infancy,
you can. But the Warlord games are less susceptible to computer play than
Chief is, I believe. Certainly at the larger sizes, the games are much more
complex in a chess sense than any typical chess variant, even rather large,
complicated ones. They can be complex even in a wargame sense.

What you claim all proves my point. If there is no viable static fortress,
it means that if one side is just sitting and waiting, starting form an
equal (say symmetric) position, doing no moves at all, he will soon find
himself in a lost position. So apparently the moves the opponent did were
worth something. Which means having the move is an advantage, and passing
your turn weakens your position.

The reversibility of the moves doesn't mean anything. Withdrawing pieces
takes moves. You cannot do that when you pass your turn.

I don't think deriving a few lines of opening theory can tell you
anything. How would you 'prove' that FIDE has a white advantage?
Encyclopedias have been filled with variations, and even the best lines for
white do ot result in a forced gain of material, not even a Pawn. So where
is the advantage?

Joe, notice that all the theories you have advanced to explain the lack of
a first-turn advantage are general properties of the game, NOT unique to
the opening array.  The reversible pieces don't suddenly become
irreversible in the late game; the short-range pieces don't turn into
long-range ones; etc.  If those properties were sufficient to prevent a
move from having value, they would prevent ANY move from having value, not
just the first or second one.

But as Muller points out, it seems pretty obvious that you will quickly
lose if you pass ALL of your moves, which means moves must have some value
at some point.  IF there truly is no first-turn advantage whatsoever, the
reason needs to be something special about the opening array, NOT the
general properties of the game.  The things you cited MIGHT make each move
less valuable, but they cannot possibly reduce the value all the way to
zero.

And while it is conceivable that there is something special about the
opening array that puts the first player in a position of zugzwang, it is
intrinsically unlikely.  Most possible positions in most Chess-like games
are NOT instances of zugzwang.  And the facts that the opening array
appears to be a "calm" position, and that the pieces are reversible, both
make it substantially LESS likely to be a position of zugzwang--after all,
if my second move can be to reverse my first, and my opponent cannot do
anything to hurt me in the meantime, it is difficult to see how the first
move could have harmed me.

Asking us to verify the non-existence of a first-move advantage by pushing
a few pieces around is silly.  Based on this conversation so far, the
first-move advantage in FIDE is barely large enough to be noticed by
masters (it's estimated at approximately one "quantum of advantage"). 
Perhaps you understand Chieftain Chess as well as a master understands
FIDE, but the rest of us certainly do not.  Hypothetically, Chieftain could
have a first-turn advantage that is substantially larger than FIDE and it
would still be all but impossible for us to demonstrate it to you.

We "proved" the existence of a first-turn advantage in FIDE only by
recourse to a statistically-significant sample of high-level games.  Unless
you have a similar statistical collection for Chieftain, then none of us
have any real evidence one way or the other, so we are reduced to arguing
generalities--and IN GENERAL it is safe to assume that a randomly-selected
Chess variant has a first-turn advantage.

HG, Jeremy, am I wrong in thinking you are both arguing from a similar
point of view? Believe me, I am sorry I cannot come up with statistics to
demonstrate my points. But are statistics the only thing you will accept as
evidence? Grin, if so, we will probably have a bit of a wait before
"proof" comes in. [If anyone would like to "help" me run one of HG's
programs (aka: basically do it for me - I am no longer any good at that
sort of thing and never programmed) please contact me. ;-) No, I'm not
expecting to hear from anyone!] 

I will say that 10 meters is far less important at the beginning of the 10k
race than it is at the end. One of the features of Chief is that it is
deliberately made to slow down the initial combat by a turn or three. In
that sense, white is "merely catching up to black in the race" - that is,
coming close enough to black to press a decent attack. It does take a few
turns to put together a decent attack. And that's why I say there is no
first turn advantage, because you cannot press home any attack quickly. You
literally have to marshall your forces first. Is there a first move
advantage in wargames? As chess pushes toward wargames, I think you'd have
to expect changes in behavior.

Jeremy, we need to define terms so I'm not talking past you. I see the
set-up as a general condition of the game, in the sense that all the setups
in the Chief series [but not necessarily the Warlord series, because some
of those setups are very close together - A Clash of Arms and Civil War,
for example, might very well show a first-turn advantage] are made to
prevent rapid and effective initial attacks. FIDE thrives on rapid and
effective early attacks until you get to the high levels. And then it
thrives even more on early and rapid threats. The design of Chief includes
an organization/rally phase in the very beginning, where you order and
advance your army to contact. 

Here, HG is where I see the effect of promotion. In running through game
situations in my head, it is clear that promotion would change Chief, and
my claim of no first move advantage is very suspect. Because obviously, the
2 turn move advantage I give white does cause black to give up a little
territory, and if promotion occurs, white clearly has a small advantage,
because they go 5 squares to promote, and black goes 7. In Chief, that 2
square difference means not only do commoners have farther to go, the
Chiefs must also advance one extra time to allow movement, to match the
free move white got. [However, grin, I would like to see some statistical
proof that a 2 move advantage actually exists for white in Chief. Just
because I can see it and agree with you doesn't mean it exists, right? ;)
]

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?

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, 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?

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?

> 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...)

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.

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.

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.

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.

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).

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?)

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.

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.

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.

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.