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Comments by Derek Nalls

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Symmetrical Chess CollectionA game information page
. Collection of several large symmetric chess variants with only line pieces.[All Comments] [Add Comment or Rating]
💡📝Derek Nalls wrote on Wed, Oct 19, 2016 01:07 PM UTC:

Spherical Chess 400 description

The section entitled "game-ending conditions", pages 35-40, addresses this matter that you mistakenly presumed that I neglected.  Apparently, you are stuck in conceiving of endgames in terms of standard Chess with a crippled king.

Home page of The Chess Variant Pages. Homepage of The Chess Variant Pages.[All Comments] [Add Comment or Rating]
Derek Nalls wrote on Thu, Sep 15, 2016 09:51 PM UTC:

HGM:  I had the same thing happen to me once years ago.  I have never trusted the comment system since, apparently with good cause.  I have always copied, pasted & given a file name to any message I intended to submit.  Except for an untimely power blackout, taking a little extra time to do this will save you misery in the future.  I'm sorry this happened.

Computer resistant chess variants[Subject Thread] [Add Response]
Derek Nalls wrote on Wed, May 18, 2016 12:29 AM UTC:
Intelligent Adversary Searches

Sac Chess. Game with 60 pieces. (10x10, Cells: 100) [All Comments] [Add Comment or Rating]
Derek Nalls wrote on Wed, Dec 16, 2015 10:59 PM UTC:
Editors: We need the ability to delete one of our own comments for whatever appropriate reason.

Derek Nalls wrote on Wed, Dec 16, 2015 10:33 PM UTC:
You requested a third party opinion. I have playtested Muller's relative piece values in CRC and found them to be extremely reliable. In fact, I was so intrigued by my verification of his correct (yet surprisingly high) value for the archbishop that I revised and expanded my own work to drive deeper into the underlying geometric & arithmetic foundations in a somewhat successful attempt to gain a theoretical understanding as to why.

Computer resistant chess variants[Subject Thread] [Add Response]
Derek Nalls wrote on Tue, Dec 15, 2015 04:43 PM UTC:
"Humans typically suffer more than computers from large branching

Although the quoted remark is not generally untrue, I find generalizations

about the playing strength of humans at any particular game of little,
practical use because it varies radically between individuals.

A game with a high branching factor will (almost) certainly throw a dense,
cognitive fog around the tactical & strategic play of a novice, human
player [in the majority] yet an experienced, incisive human player [in the
minority] can usually see through this dense, cognitive fog to
consistently, correctly identify the most important offensive and/or
defensive move on the board and execute it.  Humans are better than
computers at quick-and-accurate pattern recognition which is conducive to
being able to play many chess variants well.  Computers use different,
non-geometric techniques to evaluate potential moves, anyway.

By contrast, I do not take exception to generalizations about the playing 
strength of computers at any particular game because they are predictably,
reliably useful.  The best available hardware running the best known 
programming, customized to play a given game as well as possible, is the 
given assumption.

A game with a high branching factor will certainly trap a computer player
within a search ply where it becomes intractible (i.e., unable to complete
it in less than a tremendous amount of time).  All except the most trivial

chess variants with the lowest branching factors become intractible at some
point.  Critically, it is a matter of how many plies can be completed
before this occurs (if very long time controls are allowed) and whether or
not this average number of completed plies represents a formidable AI
opponent to an intelligent, competent human player.  If not, there is a
serious problem which can only be overcome by heavy pruning within an
evaluation function.

Light to moderate pruning will not address the problem to a non-trivial 
extent.  Heavy pruning is risky.  Any errors in the evaluation function are
potentially catastrophic and there are many places for such game-specific
errors to exist unknown.  If an evaluation function occasionally throws
away from consideration a move(s) that needs to be made, then the human
player will likely soon discover tactics to routinely, successfully beat
his/her computer opponent every time.

Derek Nalls wrote on Tue, Dec 15, 2015 04:13 AM UTC:
Inventing chess variants strictly to be "computer resistant" is not a
worthy goal.  It is intentionally disruptive.  However, inventing chess
variants to be theoretically deep (i.e., possess a high branching factor)
is a worthy goal (amongst several other, desirable game characteristics). 
Of course, it is probable to also be "computer resistant" incidentally.

Derek Nalls wrote on Thu, Dec 10, 2015 03:19 PM UTC:
Spherical Chess 400

There is really only one game left on my Symmetrical Chess website anymore.
 Greg Schmidt (the Axiom programmer) and I have tried in a few ways and
failed to make it computer AI playable at a minimal, decent level.  I think
we now share the opinion that such a goal is not achievable with
state-of-the-art computer hardware technology and programming.  From what
you express, I think this game may interest you more than Go, Arimaa or
Gess.  Feel free to write me for details.

Chess with Different Armies. Betza's classic variant where white and black play with different sets of pieces. (Recognized!)[All Comments] [Add Comment or Rating]
Derek Nalls wrote on Sun, Apr 5, 2015 10:35 PM UTC:
I didn't say or infer anything about making stalemate a loss.  That would be unfair to one player and you didn't specify which player- white or black, the attacking player or the defending player.  Yes, the stalemate rules in FIDE Chess also annoy me because it is possible to design chess variants that are absolutely drawless without decreasing fairness.

Derek Nalls wrote on Sun, Apr 5, 2015 03:08 PM UTC:
Making it possible for the king to be captured as a game-winning condition is significantly simpler than numerous check & checkmate rules.  In effect, it ends the game once move sooner.  Also, making the royal piece incapable of movement would render a game similar to Chess much less drawish.

Derek Nalls wrote on Sun, Apr 5, 2015 12:39 PM UTC:
I have no idea why any competent game designer would choose to imitate the maze of overcomplicated rules associated with checkmate from FIDE Chess that unnecessarily create a wide "draw gulf" but unfortunately, there are many thousands of such unimaginative, similar chess variants available.  Sorry, I have a tendency to conceive of chess variants potentially as the infinite variety of unique, non-trivial differences from one another that they are in theory.  In practice, they fall short.

Derek Nalls wrote on Sun, Apr 5, 2015 12:25 AM UTC:BelowAverage ★★
Despite their intractability (in most cases), it is true (as an existential theorem) for all turn-based, two-player chess variants that, with perfect play, a decisive, game-winning advantage exists for either white or black.  Furthermore, this advantage will be amplified where the armies are unequal and/or asymmetrical.  The fact that the problem fails to "bite us" because the quality of play needed to reveal it is out of reach for both human or state-of-the-art AI players does not render it insignificant.  It just has little practical effect.

Chess sets I wouldn't buy[Subject Thread] [Add Response]
Derek Nalls wrote on Sat, Mar 22, 2014 01:06 AM UTC:
... but it is only $249 US.

Zillions-of-Games: Review. Review of Windows program for playing user-programmed Chess variants and other strategy board games.[All Comments] [Add Comment or Rating]
Derek Nalls wrote on Mon, Aug 12, 2013 05:50 PM UTC:
ST:  Although I haven't studied it, you can probably salvage Schoolbook Chess by changing its turn order to white-black-black-white.  This will reduce white's advantage to a tolerable level.

First move advantage in Western Chess - why does it exist?[Subject Thread] [Add Response]
Derek Nalls wrote on Tue, Sep 25, 2012 02:46 AM UTC:
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).

Alibaba. Jumps two orthogonally or diagonally.[All Comments] [Add Comment or Rating]
Derek Nalls wrote on Thu, Sep 20, 2012 12:43 AM UTC:
In some of HG Muller's earliest comments under different topics, he did his best to explain in detail why the bishop-knight compound (or archbishop) has a significantly higher piece value than the naive sum of its parts in Capablanca chess variants.

Computer with multi-move cv[Subject Thread] [Add Response]
Derek Nalls wrote on Wed, Sep 19, 2012 02:07 AM UTC:
The average game of Chess with a white-black turn order runs 40 turns
(moves) per player.  So, the average game of Marseillais Chess with a
white-black-black-white turn order should run 20 turns per player.

Derek Nalls wrote on Wed, Sep 19, 2012 02:03 AM UTC:
From Wikipedia-

It's hard even to estimate the game-tree complexity, but for some games a
reasonable lower bound can be given by raising the game's average
branching factor to the power of the number of plies in an average game,
GTC ≥ b^d

Derek Nalls wrote on Wed, Sep 19, 2012 01:39 AM UTC:
The branching factor of Marseillais Chess would be 35, the same as for

First move advantage in Western Chess - why does it exist?[Subject Thread] [Add Response]
Derek Nalls wrote on Wed, Sep 5, 2012 05:51 PM UTC:
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 Nalls wrote on Wed, Sep 5, 2012 12:04 AM UTC:
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 "" 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

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

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

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 "" results can optionally be expressed as

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

Derek Nalls wrote on Thu, Aug 9, 2012 11:17 PM UTC:
Via causality, the small advantage white holds at the beginning of the game
(in Chess), given appr. equal quality play for white & black, gets
amplified into a large advantage by the end of the game roughly consistent
with known win-loss stats for white & black.

[Bravo to Occam's Razor.]

Derek Nalls wrote on Thu, Aug 9, 2012 10:46 PM UTC:
Drake Eq Calculator

Just an aside.

Derek Nalls wrote on Thu, Aug 9, 2012 03:18 PM UTC:
I think there is a likely chain of events in Chess whereby ...

Having the very first move in the game along with control of a white-black
turn order tempo gives white a head start toward development.  This, in
turn, gives white an irrefutible advantage in mobility throughout the
opening game and results in a small positional advantage.  A small
positional advantage should be built into a large positional advantage.  A
large positional advantage should be built into a small material advantage.
 A small material advantage should be built into a large material
advantage.  A large material advantage will probably, eventually enable
white to checkmate its opponent (black).

If all of the links in this chain of events (plus any I have overlooked)
are solid, they may account for the observed win-loss discrepancy between
white & black without resorting to any mysterious theories.

Derek Nalls wrote on Wed, Aug 8, 2012 11:21 PM UTC:
"The first event in a causal chain can be important. I completely fail to
follow the "always" part. Perhaps you can find a hurricane that wouldn't
have formed if a particular butterfly hadn't flapped its wings, but not
every flap of a butterfly's wing causes a hurricane."

Please don't take my mention of the butterfly effect literally?
I am not seriously asserting that it (and anything similar) explains the
first-move-of-the-game advantage for white.  However, I am asserting that
the advantage for white in having the very first move in Chess carries all
the way thru the midgame and endgame to the last move of the game and is,
in fact, greater than virtually all Chess players have the complex
foresight to appreciate.  After all, Chess is a deterministic game of
perfect information.

You seem to want to argue with established facts and plausible attempts by
others to explain them.  Naysayers typically offer no or few ideas.

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