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then you prosume wrong, he he, it is a leaper +
i made the comment 2 down, forgot to enter name, i was just saying that i
thought the mammoth has to be stronger than the rook, it is alfil +
dabbaba + wazir + fers, that is a heavy piece, i know just the alfil +
king moves is a strong piece, the mammoth is a killer at short range, all
over the pieces like oprah on pork chop nite :))

Mats, of course a jumping Mammoth is stronger. My 10x8 scheme gives a
value of 6.7778 to it then, which is nearly identical to an Archbishop's
value of 6.8580. Regards, Reinhard.

Are you sure that you got this right? The Mammoth (Mastodon) *jumps*
 one or two steps diagonally or orthogonally. It cannot be as valuable
 as 6.8. Those evaluation systems don't work because they don't take into 
account how pieces *relate* to each other. Nor does the simple counting of 
squares work, i.e., its factual power, because it doesn't take into account 
that the Mammoth has to flee to every threat and cannot strike back. For 
instance, if a rook is threatened by a queen it can strike back on the 
orthogonals. The Archbishop can strike back against a threatening bishop, 
queen, or knight, but a Mammoth must generally back off before any threat. 
I argue that the Archbishop must be clearly more valuable than the 
Mammoth.

The Mammoth seems ideal for testing the reliability of evaluation systems.

Hi Mats, yes, I handled the Mammoth as a fully jumping piece. Your
arguments whether the piece is not save towards distant threats is a
TACTICAL argument, which has nothing to do in average piece value
considerations. Be aware, that a Mammoth also has the chance to escape
such threats by his numerous move possibilities. And - as already earlier
stated - real exchanges would have to consider the actual positional
implications of all pieces within the actual board situation.

P.S.: I should mention again, that my scheme is calculating AVERAGE piece
values, which have to be completed by positional detail evaluations when
evaluating real board positions.

P.P.S.: See also at http://www.chessbox.de/Compu/schachveri1_e.html

I have investigated the theoretical endgame properties of the Mammoth and
it proved to be significantly stronger than the Rook in this area.

(1) M + K  vs. Q + K  = draw
(2) M + K  vs. R + K  = draw
(3) M + K  vs. B + K  = win
(4) M + K  vs. N + K  = win

Comparatively, a Rook + King cannot win against neither Bishop nor Knight,
in the general case. This implies that the Mammoth is stronger in
theoretical endgames. Moreover, Rook + King generally loses against 
Queen + King, but the Mammoth draws against Queen.

Also, in a theoretical endgame, a Mammoth is well suited for escorting a
passed pawn to the promotion square. Bishop, Knight, or Rook, cannot
achieve this.

So it is stronger than a Rook. I contend that it compares to Rook + Pawn,
i.e. 6. But I refuse to believe that it's as strong as an Archbishop (6.8).

For an index to Ralph Betza's work, see About the Values of Chess Pieces -- Contents. His early attempts at STANDARD values (including Ferz, Alfil, and King/Commoner) can be found here.

Hi Mats, your arguments remind me at those of Ed Trice. This is also true
for basing piece values on 'save' king threats. But I have to insist,
that tactical considerations have nothing to contribute to average piece
value calculations. There are of course board situations, where a Pawn
could capture a Queen, but that is completely irrelevant for those
figures. In a similar understanding end-game considerations are highly
influenced from tactics, thus conclusions basing on table bases are merely
of partial value for fixing average piece values as needed during the whole
game before. 

P.S.: using SMIRF's 10x8 values a Mammoth or an Archbishop both are about
equal to a Rook's value + one Pawn unit or equal to two Bishops.

I made a test where I put an Archbishop + King versus Mammoth + King on 
an otherwise empty board in Zillions. On an 8x8 board Zillions evaluates
Archbishop and Mammoth as equal. But on an 8x10 board Zillions evaluates
the Archbishop as significantly stronger than the Mammoth (so that the
smiley looks unhappy when making the Mammoth move). On a 10x10 board 
the difference increases yet more in the Archbishop's favour, but not that
much. So Zillions thinks that the Mammoth has about the value of an
Archbishop on an *empty* 8x8 board, but this evaluation changes when the
board is bigger. This corroborates what has been said recently, although
I'm unable to interpret Zillions' numbers.

As an aside, another of Greenwood's variant with this piece is Tamer Spiel (a 2002 variant) where it is called the 'Lion'.

- Sam

Sam, for this game I investigated many initial positions, even non-mirrored.
This was the only one I found that was good, I think. Why I didn't choose
the 'natural' positions of bishops and knights had to do with the fact
(if I recollect correctly) that the enemy mastodon would lose its natural
development square on b3, b6, i3, i6. Also, the flank pawn would also be
initially threathened by the bishop, which would be a hindrance to
castling. It's possible that my 10x10 version of MastodonChess is better, at 
least more strategical. Thank you for the information on TamerSpiel. 

--Mats

I think the solution to the castling problem is to use the castling rules that grotesque chess has.

- Sam