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No warrentee is provided on the following idle speculation. Any damages
resulting from incorrect application of others work is not the problem
of the author.
<p>
Since I wrote this, Ralph has revised his estimate of the value of the
Crooked Bishop back down to about a Rook (see:
<a href='../piececlopedia.dir/crooked-bishop-revisited.html'>The Crooked
Bishop Revisted</a>). (Peter Hatch's revision, if I understand it
correctly, if correct, would only
make 0.04 of a Rook's difference, or about 1/5 a Pawn.) That means my
estimated value for the
Eaglescout is off. Using Ralph's colorbound correction number of 1.15,
the value of the Eaglescout can be calculated as:
<blockquote>
<pre>1.15 * 4.5 + 1.5 = 6.67 Pawns</pre>
or
<pre>1.15 * 5.0 + 1.5 = 7.25 Pawns</pre>
</blockquote>
depending on what value you use for a Rook. This is roughly equivalent to
the value of a Cardinal:
<blockquote>
<pre>1.15 * 3 + 3 = 6.45 Pawns</pre>
</blockquote>
(There appears to be missing 2nd correct factor for the Knight's
contribution, since the Knight is no longer color switching -- surely that
ought to be worth something?). Anyway, that makes the Eaglescout worth a
bit more than a Cardinal, but not that much, but still noticable weaker
than a Queen. However, given the Army seems strong enough or too strong,
there's nothing wrong with that.
<p>
This downgrading of the value of the Eaglescout makes me wonder again:
is the strength of the army due to the combination of the pieces, or is
perhaps the value of the Left- and Right-Rhinos and maybe Crabinals higher
than estimated?
The Knight's contribution? I looked at the page and the Eaglescout is W plus zFF, no Knight there. You describe the army as seeming equal at the start, but picking up steam. This is logical because every single piece has at least one part of its move that increases in strength as the board empties out; the knight-move part of the Rhino, the lame 0,3 of the Gnohmon, the halfling B of the Crabinal, and the zFF of the Eaglescout. Given that you also have two kinds of pieces with some jumping ability (helps you get developed in the early game), it wouldn't seem so surprising if the total army is stronger than the sum of its individual piece values. That's my guess, anyway. No warranty expressed or implied, do not remove this tag.
The comment about the Knight's contribution was regarding the Cardinal (not Crabinal) whose value I was comparing the Eaglescout against. It seemed to me that a color-switching piece paired with a non-colorswitching piece might also have some sort of correction factor, smaller than the 1.15 for colorbound pieces, but greater than 1.0.
It's an interesting point that I hadn't noticed before, but indeed all of your classic armies for CWDA have at least some pieces that suffer somewhat in the endgame. I can see now where an army without any pieces with endgame weakness would be unbalanced. So much to take into account!
How are the left and right single-step rhinos worth about a rook when they're effectively lame 2 atom-pieces, while rooks are worth 3 atoms?
Tim, The Rhino can move one step in any direction and stop on that square (same as a non-royal king) as well as turning 45 degrees in the appropriate direction and moving a second square. The non-royal King move alone is worth 2 atoms. If the second move comonent if it were a leap would also be 2 atoms. To allow for lameness, mutiply by .7, so add 1.4 atoms for this component for a total of 3.4 atoms. The piece is substantially stronger than a Rook. You may be confused by some incarnations of the Rhino requiring the first step to be orthogonal -- such a piece is indeed worth only 1.7 atoms, less than a Knight.
A curious thought hit me -- the Fighting Fizzies pieces all gain strength in the endgame and are easy to develop and seem to work together well. I wonder what a CWDA army would look lke designed on opposite priciples? Massive raw power, but hard to develop, awkward to work together, and lose value (or at least don't gain value) in the endgame.
The value for lameness that Ralph was using at the time this was written was 0.5, which would make the these versions of Rhinos three atoms. And while indeed they are perhaps a bit strong, I don't think they are really 3.4 atoms worth.
The correct value depends on what magic number (square emptiness probability) is chosen. I go with Ralph's uppen end estimate of .7 With his lower end estimate of 2/3 then the value of the SS Rhino would be 2 + 2 *(2/3) = 3 1/3 The Gnomon is a different matter: its lame H move must be multiplied by .49 or .44 as there are two interventing squres.
Ah, my bad. Saw Rhino, got superglued into my brain that it moved orthagonally first always. Should be a Left/Right Single Step Double Rhino... Well, actually, it shouldn't since it's long, unweildy and sounds like it's contradicting itself.
you're bishop is too strong! how about having either a two square bishop plus crab or four square bishop plus lame barc or crab barc would probably be better being weaker than a crab after all the meticulous masher's bishop was a four square bishop plus lame dabbaba so this should be mid strength but then again if you had the four square bishop plus lame crab the army would be devoid of leapers
Aronson to be next prolificist to study in couple of follow-ups, please re-familiarize, even if not having time to play each CV, all of these. Amphora, Anti-King, Chaturanga-4-84, Cyclical Armies, White Elephant, Transactional, Train Wreck, Toto40, Toe-to-Toe, Star Pool, Snark Hunt, Ruddigore, Rolling Kings, Rococo, Royal Amazon, Prisoner's Escape. That's about half for now. Here separating into Right Rhino and Left Rhino also eliminates their multi-path character. The piece named after Betza, the Gnohmon, in this Army for Chess Different Armies is fbNfbWnH. f means forward, b back, and 'H' come from Betza's article ''Ideal & Practical Values V'' for (0,3) mover non-leaping. Gilman does not actually re-name the latter component with (0,3) Tripper, because that one fully leaps the fixed length.
Here is Aronson's different armies and Betza's study, http://www.chessvariants.org/index/displaycomment.php?commentid=622, back at comment only number 622. They all should be 39 points, as Lawson claims for Pizza Kings after his calibration. http://www.chessvariants.org/d.betza/chessvar/cda/meticulous.html represents Meticulous Mashers by Betza. There are over ten more Chess Different Armies, some only in comments, and let's put them up occasionally as I know where they all are and in that they are each nominated as per below. To evaluate at NextChess they will all be thrown together. So Muller's nomination(#30) now becomes instead re-interpreted as for all Chess Different Armies on 64, since he dabbles in Betza too with approval. That is the way Schoolbook(#10) represents all the dozens of Carrera-Capablancas as well. Therefore, Lawson's Pizza Kings and Streetman's Spartan, Aronson's F.F. as well as all the Betzas in the genre will mutually reinforce as the one category inclusive. Then the determination will be how the lot on regular slight 64 stands up to Hatch's Fantasy Grand(#17) on big 100 squares. The intention has been to exclude Betza beyond Black Ghost(#18), but the joint production will solve the CDA problem arising in Betza's already stating it is presumptive #1 of year 2100.
> So Muller's nomination(#30) now becomes instead re-interpreted as for > all Chess Different Armies on 64, since he dabbles in Betza too > with approval. Most certainly not! My nominaton is specifically for Spartan Chess, i.e the Spartan army vs. FIDE. Most armies proposed for CDA are awful and offending my taste. Apart from FIDE the Clobberers are really the only army that has pieces of high-enough regularity to not qualify as 'ugly'. But it falls short a long way by the imaginative design of the Spartan army, with its dual Kings, the completely novel duple-check rule, and the alternative Hoplite Pawn. So the fact that 'I dabble in Betza' can NOT be taken as evidence that a nomination of Spartan Chess can be taken as nomination of CDA in general, anymore as the fact that I dabble in Shogi means that Spartan Chess meand Shogi, or the fact that I have dabbed in Falcon Chess means that Spartan Chess means Falcon Chess...
World Rhino Day is September 22!!!!!!!!!!!!!!!!!!!!!
Replacing the Crabinals with Barcinals is desirable.
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