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?