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Joe, just to be clear:  are you saying you believe that white has NO
first-turn advantage in Chieftain Chess, or are you saying that you believe
white has a first-turn advantage, but that it is SMALLER than the
first-turn advantage in FIDE Chess?

I think it is entirely plausible that weaker pieces will lead to a smaller
first-turn advantage, since the weaker your pieces, the less you can
accomplish each turn, and therefore the smaller the value of a turn.

But saying that there is NO first-turn advantage is equivalent to saying
that the null move, if it were allowed, would be the best possible opening
move.  Do you recommend moving as few pieces as possible in the early part
of a Chieftain Chess game?  Do you think that the best possible second move
is to reverse the move(s) made during your first turn?  If not, it seems
unlikely that the null move is really optimal.  Zugzwang certainly exists
in Chess, but it's pretty rare.



Also, your proposed "Moving 1 Square Chess" rules for knights appear to
boil down to "knights move as wazirs". You mandate changing parity every
move, but a wazir move changes color, so it will always change parity,
while a ferz move preserves color, so it will never change parity.

Hi, Jeremy. Yes, I am saying that I believe Chief has NO first turn
advantage. In discussions on BGG, I've gotten the idea that the math would
thus indicate the best move would be to pass on first turn. [This is the
first time I've seen a useful way to look at that idea - your question set
off the chain of thoughts in my head - thanks!] In a strictly mathematical
sense, that may well be true. Just for starters, advancing most of the
pieces on turn 1 would put them out of command control, thus weakening the
army, and so being contra-indicated. Further, moving pieces toward the
enemy makes them more vulnerable and easier to get to and kill, so moving
toward the enemy would seem to be contraindicated. Interesting and
thought-provoking

So apparently that alone might show there is no first turn advantage. If
all the values for aggressive moves on turn 1 lower your total army score,
then there is no first turn advantage.

I'd like to keep going here, but I gotta run. You are right about the
knight being only a wazir - then need to play off king or king and queen
squares to get some color-changing. However, in end of game, wazir N might
be okay, as it does tour the board. It does become as strong as rook, but
then it can't jump any more so it could use a little consolation... :)

So, is your personal standard strategy in a game of Chieftain Chess to
maintain a holding pattern and let the enemy come to you?  If both players
do that, it seems like the game would be awfully boring.

Grin, Jeremy, I have never lost any version of Chief online, and very few
have managed a draw against me. I did make a stupid blunder in an early
face-to-face playtest game, and resigned rather than continue the game.
That's my only loss. I have very high hopes for my newest Warlord
opponent. He has picked the game up very fast and very well. And so far he
enjoys the scenarios. While he lost our one completed game at the end, he
won more than one of the battles within that game. Yes, I am looking for
someone who can beat me, [and then beat me again.]

I will be happy to demonstrate my preferred style to you. It is not
passive. I see it as Cautious - Opportunistic. I suspect others could see
it as Aggressive - Reactive. I see the game as similar to a boxing match.
Both fighters can stay in their corners throughout the bout, and neither
gets hurt. I would find that boring. If someone stays in their corner, so
to speak, I go in and get them. If they come out, I go out to meet them,
bobbing and weaving and jabbing and feinting as best I can. 

The series of games is meant to eventually simulate a wargame. Chief showed
me the way. The Warlord scenarios are a nice step toward realizing that
design goal. Chief is the first stop on [one of] the right road[s] to that
goal. It's a good game in its own right, but it's a signpost to where I
want to go. Warlord begins to show the potential of this approach. It's a
better game than Chief, more refined, less obviously chesslike, with rough
edges smoothed down and a more wargamish feel. You can lose not only an
exchange, but a piece or two, and not be in more than serious trouble,
rather than at death's door. Of course, you better be able to compensate
for a good thumping, but the point is you can, often enough. If you are
good enough against that particular opponent at that time.

Okay, let me venture into the math underpinnings on this. If you can
mathematically demonstrate there *must* be a first turn advantage for
white, no matter how small, then I will predict in the 1-square game, the
"noise" will wash out the signal effectively totally. And the signal will
emerge from the noise very slowly, as the ranges of the pieces increase
toward the modern. That is apparently what I predicted anyway, since both
our explanations can fit the prediction above.

In Chief/Warlord, if there must be a first-turn advantage, then it *must*
be miniscule, because it doesn't become obvious if white gets 2 first
turns in a row [black passes turn 1.] The major part of the game is
[nearly]mathematically chaotic, as far as I can tell. If there were an ad,
which I doubt seriously, then I think it would be effectively washed away
by the many turns of deterministic but effectively/essentially/[actually?]
chaotic behavior. I don't see how a signal gets through that. Step through
my first Chieftain game with Carlos Cetina, and my last Warlord: a Clash of
Arms game with elkitch, for a look at the range of behaviors the series can
display. 

*To fix the knight move in 1-square, base the parity on the other knight
and the king, then the queen and the king, and finally on the moving knight
and king, with the color of the king's square being the determinant color.
The last condition will freeze the N as a wazir for the rest of the game,
but that's the default state I want. Does that sound better? 
Rule: If other piece and king are on opposite colors, move to king's
color. If they are on same color, move to opposite of king's color.

This would simulate the normal move of the Moo, the strongest stepping Knight, spread over two moves. Even so, I suspect that a 2-step Chess - Rook as Wazbaba, Bishop as Fearful, Wueen as Pasha, rest as their FIDE selves - would be far closer to FIDE Chess as Wazirs and Ferzes are switching pieces. In fact I would even venture that 1-step to 2-step would be a bigger step back to FIDE Chess than 2-step to 3-step - Rook as Guardian, Bishop as Wrestler, Queen as Liondog.

> Is there anyone who would seriously argue that white
> retains any first move advantage? If so, how? Enjoy!

I see no reason why white would not have any serious first-move advantage
here. The game will be horribly drawish, of course, so any advantage is
likely to be small. In Shatranj the draw rate is about 70%, and has even
more pieces weakened, so you really need a lead of 3 or 4 pieces before it
becomes a winning advantage. Although the change w.r.t. FIDE that causes
most of the drawishness is probably that Pawns promote to a worthless
piece, and this is not made worse here.

But the basic mechanism remains valid. The initial position is not an
impenetrable fortress, nor can such a fortress be reached before the enemy
can engage you. If you just sit and wait, allowing the opponent to set up
his plan, he will be able to achieve a decisive break trough. That the
pieces move slowly hinders defense just as much as attack. If anything, it
makes the advantage of a tempo larger. If the opponent spreads out his
pieces, while you pile up your material just in front of his King, he will
be too late to involve the pieces on the wings in his defense, and will get
checkmated. If he contracts all his pieces around his King, you will direct
your attack to one of the wings, to create a breakthrough there and promote
a few Pawns. Pieces are still sufficiently stronger than Pawns that you
cannot afford to ignore promotion. So with nearly full material on the
board there is no static fortress that is impervious to attack.

Charles, you're right, the stepwise moo is a better representation of the
N move for 1-square. The difficulty with using it in a board game is that
the move of the piece is dependent not on the current state of the board,
but on the previous state of the piece. If someone were to implement a
massive computer analysis of the game to see if mobility is the key or any
factor in first-turn ad, that rules set or something very like it should be
used, to simulate FIDE as closely as possible. 

The parity check, while violating the letter of the law for N moves, tries
to keep the spirit of the law, admittedly somewhat poorly as it mandates
whether or not the knight switches, does have the advantage that it is only
dependent on the current state of the board. Computer implementation of the
"moo rule" would be all but necessary if players wanted to use it instead
of a parity check. Changing icons for the knight would be more than just
useful. Heh, if this turkey ever gets written up, you got the first
optional rule.

HG, I don't see why/how a first-move advantage would stay strong as piece
ranges decreases. From the BGG discussion, I get there are "hot" and
"cold" positions, and the hot ones are where whomever has the move has a
significant advantage, In FIDE chess that is very well-played, every move
is hot. The same does not pertain in Chief. Or at least I believe it has
been demonstrated that any possible first-turn advantage is so minimal that
black can pass on turn 1 without detriment. So at a minimum, first move
advantage is effectively gone. Therefor, the changes from FIDE to Chief
have eliminated the first move advantage. 

There are 5 changes, 2 of which I believe are irrelevant. Those 2 are: 1 -
chief is multimove, and 2 - chief has some additional movement
rules/restrictions, the leader rules. The 3 changes I see as at least
potentially relevant are: 1 - the greatly limited movement; 2 - expanded
board, extending the time it takes, even if only by a turn or two, to first
meaningful contact; 3 - all pieces can move both forward and back [and both
left and right.] And all 3 of these items come down to mobility in one form
or another. So am I wrong about why there is no sensible first turn ad in
Chief? Or doesn't what happens in Chief apply to FIDE? What am I missing?
Because if it's mobility in Chief, then a loss of advantage should occur
in 1-square, even if not to the same extent, no?

What do you mean by "demonstrated"?  You have some proof of the absence
of first-turn advantage in Chieftain Chess?  Could you perhaps share this
proof?

I am so far unconvinced.  You tell me that you pretty much always win your
Chieftain games, which suggests you have not played against any opponents
that seriously tax you, which in turn suggests that you have no sample
games with high-level play on both sides to use for reference.  But you
also say that you win with an aggressive strategy, which suggests that you
think you can get some advantage by doing something rather than idly
maintaining your position, which suggests that tempos have value (at least,
you are playing as if they do).

Unless you have solved the game or you have a large, high-quality
statistical sample showing that black wins at least as often as white, I'm
not sure how you could demonstrate the absence of a first-turn advantage,
nor does such an absence seem inherently likely to me based either on your
testimony or from reading the rules.

Keep in mind that the first-move advantage in FIDE Chess is thought (at least by Betza) to be approximately the minimum advantage that MASTER level players will notice in practice; I would hazard that no one currently alive is as good at Chieftain Chess as a master-level player is at FIDE, and so it seems plausible to me that you might not easily notice the first-move advantage even if it were LARGER than the one in FIDE.

Grin, we can have a theoretical argument or we can play one of the
variants. Or one can use Game Courier to look at a game that shows a little
of the behavior these games can display:
h t t p : / /
play.chessvariants.org/pbm/play.php?game=Chieftain+Chess&log=sissa-joejoyce-2008-346-851

I would be happy to play a public game against anyone who wishes, to
illustrate what I mean. I am in a bit of a quandry; if someone says "I
don't believe in X", but won't look at where I claim X occurs, how am I
to demonstrate X? 

Grin, I could try to argue from authority and say: "How likely is it that
I, an editor at CV.org, would make such a bold statement without very good
reason to believe I'm right?" but I have no authority and no more
knowledge about the theory of games than I have authority. :) I'm a
tinkerer with a bump of curiosity and a little persistence. And sometimes I
can see the obvious when it's right in front of me.

I did not design Chief with anything like first turn advantage in mind. [In
fact, a good case can be made that Chief designed itself one midday.] But
as I played the game, I saw that any reasonably competent player could take
black and pass the first turn without detriment - *any* reasonably
competent player. To me, that screams any first turn advantage is
effectively gone, dropped below "noise level". What other possible
explanations can there be? My question about this is if Chief results can
actually be used for looking at FIDE. Are the multi-move and leader
features of the game enough to preclude us from using Chief to illuminate
anything about standard western chess?

> HG, I don't see why/how a first-move advantage would stay
> strong as piece ranges decreases.

Well, let me put it this way then: Suppose I am going to do a race between
two grasshoppers (the animal, not the chess piece), and I give one of the
two a lead of 100 hops. Which one will stand the better chance to win?

Now suppose I do the same thing with two ants, giving one a lead of 100
paces. Who has the better chances now?

If Chieftain Chess has no first-move advantage (something I consider by no
means proven, and in fact unlikely), IMO it can only be because it does not
have promotion. But I would only accept Chieftain Chess has no first-move
advantage if it was demonstrated in computer self play.

I have not analysed Chieftain Chess, therefore I cannot contribute to that
discussion.

ut here is another factlet showing the superficially very similar games can
have very different first move advantages: Sam Trenholme analysed some
Carrera Variants with different first line setups with respect to first
move advantage in this posting:

http://www.chessvariants.org/index/displaycomment.php?commentid=23842

The numbers range from

White           win     loss    draw    games

ranbqkbnmr	46%	43%	12%	1010 

to

rmnbakbnqr	53%	37%	10%	1011 

which is remarkable. (I won't take the numbers too seriously, because the
draw rate is suspiciously low. I expect human master play to have more
draws.)

The low draw rates could be due to the very fast time control (10
moves/sec), which might lead to bungling drawn pawn endings because an
unstoppable promotion is beyond the horizon. For 10x8 Chess the normal draw
rate is 16%, though, so the numbers are not that far off.

However, the statistical significance is weak. They were all measured from
about 1000 games, which would have a standard deviation of ~1.6%-points in
the average result. But since many different positions were measured, it is
extremely likely some of them would be off by more than one standard
deviation, in either direction. So in an experiment like this (doing a
dozen series of 1000 coin flips with a perfectly fair coin), the difference
between the highest and the lowest percentage of heads between the series
will almost always be 6%.

And of course it cannot be excluded that one of the setups is not
tactically quiet (e.g. because of unprotected Pawns in the array). In a
tactical situation the advantage of having the move can of course be
enormous. (E.g. 2 Queens, when unprotected Queens are attacking each other,
and 4 Queens when in addition each side has a passer that can only be
stopped by the opponent's Queen.)

But in principle this is the correct way to measure the first-move
advantage. If it is in doubt whether variants with only short-range pieces
have a first-move advantage, just let a computer play a few thousand games,
and count the number of black and white wins. (E.g. using Fairy-Max and
letting it play Great Shatranj, which is a supported variant with onlty
short-range pieces.)

To continue with the race metaphor, I see the race as a 1 step advantage,
but in FIDE, it's a giant step, and in Chief, or 1-Square, it's 1 foot
stepped forward [or 4, in the case of Chief] on that multi-legged insect,
and the race is 1000 body lengths. It's lost in the noise of all those
feet going all that distance. Maybe in 1-Square, it's 1 body length, but
no more. Again, a very weak signal. I'd love to test it. If I can find
someone who can help me set it up and run games, I'll do so. Can FairyMax
be modified to play Chief? 

HG, you are quite right that I did not mention promotion or the lack
thereof, as a difference between FIDE and Chief, and I should, but I would
put it in the category of "no effect", working on the naive belief that
the "pawns" are already promoted to commoners, which have an interdiction
capacity. Not believing you would say something like that without good
reason, I thought about it for a while. I believe that you are likely right
in saying pawn promotion is one of the mechanisms for white's ad. It is
testable. Are there statistics on ... okay, found this: h t t p : / /
chess.stackexchange.com/questions/420/pawn-to-queen-probabilities-chart

"I have some partial statistics for the question, from the Million Base
1.74 database, a collection of 1742057 games. 77218 of these games (4.4%)
feature at least one promotion.

I counted 49970 promotions for white (54% of all promotions) and 42519 for
black (46%). Here are the destination square statistics ..."

However, we are told here: h t t p : / /
en.wikipedia.org/wiki/Promotion_%28chess%29

"The percentage of games involving promotions can be misleading because
often a player resigns when he sees that he cannot stop his opponent from
promoting a pawn. In the 2006 ChessBase database of 3,200,000 games (many
grandmaster- and master-level), about 1.5 percent of the games contain a
promotion..."

And there I got stuck. I didn't find any stats on reasons why games were
resigned. The most interesting number I saw was the white-black promo ratio
of 54-46, the numbers I've been using for total points scores. But this is
already long and I've got a few things to do. I'll argue the points
later, and thanks for the new perspective.

If the race metaphor is accurate, I would expect the head-start to be
compared not to the length of the runner's stride, but to the length of
the entire race.  I would guess that a 10m head-start would be much more
likely to be decisive in a 100m sprint than in a marathon.

Perhaps we should not be looking at the mobility of individual pieces, but
the length of the overall game?  Piece mobility would likely be a factor in
game length, but board size, number of pieces, and several other factors
could also be highly significant.

Hey, HG, thought I'd said that if I get a little help from a family member
or two, I'd try to run FairyMax for a while to generate some numbers, but
I didn't notice it when I scanned the thread. So I'll try to get some
numbers run. I agree Great Shatranj is a reasonable test case [thought I'd
said that, too :) ] and should show some effects - even if the leaping
ability counteracts the shorter range a bit. GtS often features re-grouping
turns, a few turns spent shuffling pieces around to get some attacking
weight together. Shouldn't that feature tend to blur out first turn ad?

Jeremy, 10 meters is a lot in the 100, but not so much in the 1000, and
little enough in the 10,000 that it's almost a fair start. As for turn
lengths, GtS goes around 50 moves, iirc, but that's very rough. Chieftain
runs around 35; 40 to the bitter end. The latest versions, the Warlord
games, seem run shorter, ~25ish turns for Clash of Arms. But at 4
pieces/turn, each player is making 100 - 150 moves [at least] in a game to
get a decision. As for number of pieces, all the Chief variants discussed
here have 32 +/-2 pieces, on boards that range from 10x12 through Chief's
12x16 to 12x20 for the free, hidden set-up Warlord: A Test of Wills. No
Chief variant discussed here has pieces that move more than 3 squares; none
of the variants has any piece moving more than 4. The average move in all
variants is under 2 squares.

Now, as to promotion vs mobility. Promotion occurs rarely, in roughly 3% of
games [average of 4.4% and 1.5%] but influences a lot more. As a reasonable
initial estimate, we could say 30% of games end because one player
demonstrates pawn promotion. And the only statistic we have shows promo
numbers mirror won-lost-drew point totals, so pawn promotion can account
for maybe 1/3 of the advantage, tops. What is the other 2/3? And why does
white promote more often than black, anyhow? I would think the underlying
reason is the enormous mobility of the pieces. And this should show up as
an evening out of the pawn promo ratio in GtS. If enough games could ever
be run. And now it's past my bedtime. I'm enjoying this conversation
entirely too much - thanks. ;-) To be continued...

If white gets to take an entire turn before black starts, then I think
it's appropriate to measure game length in turns, not in moves (if
different).

Though I've seen several double-move Chess variants that restrict white to
a single move on the first turn in an attempt to counteract the first-turn
advantage; have you considered a Chieftain variant that only allows white
to make half the usual number of allowed moves on the first turn?

Looking at millionbase stats seems a bad idea. Have you for instance looked
at which fraction of the games ended in an actual checkmate? If they are GM
games, it will be close to 0%. Yet I think we would agree that checkmate is
pretty important for deciding games, and that dropping the checkmate rule
would reduce the number of won games to an exact zero.

Resigning in the face of a promotion is only one effect that distorts the
stats: something doesn't actually have to happen to hugely affect the
game. The gain due to promotion in FIDE is decisively large, so players
will prevent it at all cost. Even if it means sacrificing a Rook, or
similarly decisive material, for the passer. The threat of promotion is
enough to decide the game, and many games are decided that way. Compare
this to the number of games that is lost by one of the players insisting on
playing an illegal move. I'm willing to bet you that is close to 0% as
well. Can we conclude from this that it is pointless to require players to
play legal moves, and that allowing them, say, to move Bishops from one
color to the other would have no effect on the game?

Promotion is part of the main dynamics that decides Chess games, by
amplifying small advantages: you use tactical superiority to grab a Pawn,
use the Pawn majority to create a passer. Which he then can only stop from
promoting with a piece, tying up one of his minors. Which gives you more
tactical superiority elsewhere on the board, so you can gobble up more
Pawns there, etc. The fact that a passer binds one of the opponent's pieces
can already be a decisive advantage, without him actually having to
sacrifice that piece for the Pawn. He will always prefer losing another
Pawn elsewhere, or having to sac an exchange or minor to prevent mate, over
allowing the promotion. But he would of course not have done that if Pawns
did not promote to something of significance.

It is well known that in the absence of Pawns you need a much bigger
material advantage to win: the draw margin is somewhere between 1 and 2
Pawns, while without Pawns an advantage of a minor is not enough. (Only
exception is KBBKN, but you could claim the B-pair bonus to be responsible for that.) This is entirely due to the Pawn ability to promote; take that away, and even adding one or two Pawns for only the leading side would hardly have any effect on the outcome.


As to the 'insect metaphor':

Yes, it is correct that the lead has to be
considered in relation to the length of the race. But I think also in this
respect the metaphor is good. Because if there was no variation in the
length of the strides any lead, no matter how small, would always be
decisive. What makes the race interesting is that step size varies, which
is the main source of Joe's 'noise'. So a somewhat more detailed
analysis would take into account the variability of the ant steps and
grasshopper hops. Suppose both the hops and steps have a standard deviation
of their length that is 10% of their average length, and that all steps are
independent. Then the STD in N steps grows as sqrt(N). If the ant needs 10
times as many steps as the grasshopper needs hops, it means the uncertainty
in the ants their positions when they reach the finish line is about
sqrt(10) = 3 times larger (in step STDs) and equally smaller (in absolute
distance) than that of the grasshoppers. While their difference of the
start was 10 times smaller. So it seems the ants have better chances to
overcome the initial headstart, suggesting that the advantage would indeed
tend to zero with the step size. (But note it does not tend to zero
proportional to the step size, but proportional only to its square root!)

This analysis, however, hinges on the assumption that the STD of individual
steps and hops was equal as a percentage of their size. That need not be
true, and one can argue that for Chess pieces it is very wrong. Because
sliders have a large variation in the distance they can cover in a single
turn (on a board with obstacles), while for SR leapers this is pretty much
fixed. Kings and Pawns need a much better predictable number of moves to
get to the other side of the board than sliders have. A King will never be
able to catch up with a passer, no matter how large the board is. (Hence
the 'rule of squares'.) With fixed-length steps the trailing ant is
doomed, while with highly variable hops (because of wind gusts) the
trailing grasshopper stands a chance, even though he has only fewer hops to
close the gap.

So it is not obvious to me that having short-range pieces only would lower
the first-move advantage, rather than exacerbate it. In Pawn endings, a
tempo is often all decisive (e.g. 'outpost passers' are usually a winning
advantage, because the opponent needs an extra move to gobble them up),
rather than just a 1/3 Pawn advantage...

Jeremy, I've considered letting only 2 white pieces move on turn 1. I
just
don't see that it makes any difference at all. However, I am perfectly
willing to offer alternate rules packages, and I will add that as an
optional rule for those who wish.

HG, in thinking about your arguments, I've decided we can add promotion
to
the chief series quite easily, although I am not entirely sure of its
effect on games until I push pieces a bit. For Chief, I would promote the
commoner piece only to a non-royal chieftain, using the other chief icon
without the grey band for the promoted pieces. In the Warlord series,
especially the larger games, I am inclined to promote skirmishers also. 

*********

What effect does this have on the promotion argument? Please understand I
am not trying to be sarcastic here. The promotion aspect totally
blindsided
me, and I am still trying to grasp its implications. I cannot tell in
Chief
what it will do, but I haven't tried to analyze that yet. It depends on 2
things: 1] whether white can grab a slightly larger share of the board;
and
2] whether that extra few squares actually translates into an increased
chance for promotion. 

It seems the extra squares grabbed, if any, should lead to a slight
advantage for white, in having less distance to go for promotion. But the
values of the pieces are not that disparate to begin with. And the
infantry
is the best piece to have a bunch of in the endgame, generally, because it
has the property of interdiction - leaders cannot just move directly past
infantry, stopping in an adjacent square, as they can for all other
non-leader pieces. It's a common tactic to trade long range pieces for
infantry at various points in the game. And the board is 12 squares deep,
so that means white has to get through an active defense that can afford
to
trade non-promotable pieces for those that do promote, for 5 squares
instead of 6. 

The noise level in Chief is high, and it only gets higher in Warlord. If I
understand correctly, it is argued that there should/must be a first turn
advantage, even in the very large scenario I playtested last night. Once
again, I have to leave the computer, so I'll post this and continue
later.
In the meantime, you might look at this page in the CVwiki, and note the
current, no-longer-experimental scenario, Border War.
http://chessvariants.wikidot.com/warlord-2
At what point does a game become so complex and so different from the play
of FIDE that in spite of every move in the game being a simple chess move,
there is no first move advantage?

I wouldn't expect that the addition of noise would EVER completely
eliminate the first-turn advantage, just make it less significant.

Assuming that players strictly alternate full turns, and that nothing other
than the positions of pieces affects the game (e.g. there's no time
limit), and general chesslike properties such as perfect information, the
only way I can see to have NO first-turn advantage is if the first player
has literally nothing useful to do with his turn.  No possible piece
development, no moving forward to claim extra territory, no starting to
launch an attack or race for a promotion, NOTHING.  And I question whether
that would even be desirable.

Wouldn't the argument that white's advantage is due to pawn promotion
actually just boil down to my argument one step removed? Why does white
promote that much more often that black? Because white moves first...?
Still no mechanism. My argument is that the mechanism is the "infinite"
ranges on a very small board with irreversibility built into the move
structure accounts for the white win percentage, even if white's wins are
70% determined by the effects of pawn promotion. Why wouldn't/doesn't
black get exactly the same benefits from promotion as white, and thereby
block white from getting an advantage? Mobility. That's what makes the
average step so big that black cannot even out the race over the short
course. 

The arguments presented to me seem to amount to saying that the average
step is large, and tends to put most of its length into moving white toward
the goal of winning, at a 4:3 ratio when draws are dropped. The ratio could
be 5:4, but isn't likely to be as high as 3:2. I see the individual steps
more as a kind of semi-random walk in Warlord, where one or even several,
do not necessarily advance the player toward the goal in any meaningful
way. But the steps are never large with respect to board size, where in
FIDE, the available steps become larger on average over the course of the
game. Certainly, it is the case that in most FIDE games there comes a time
when the scope of the pieces is not limited to 3 or less squares in any
direction, thanks to piece densities. That nver occurs in the much larger
Warlord games.

Well if White could do nothing useful with their first move, the advantage would pass toi Black rather than be eliminated altogether. Such a rule cannot be applied to the FIDE array anyway, as there are no sideways moves until some pieces have moved anyway. You could insist that White move a Knight on the first move and the corresponding Rook on the second, but that would really give Black the advantage.

I'm not sure what effect a rule that White had to start with a one-step Pawn move would have. In the long term it would hand Black the tempo advantage, but it would still give White the chance to open up their diagonals earlier than not having the first move would - and give White some advantage of initiative.