Single Comment

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...