Comments/Ratings for a Single Item

So far I cannot see a compelling reason to reject the idea of a Frog Chess variant (as I gave in my last post). It seems like there might be sufficient variety in terms of possible playable opening variations. One thing that is a concern is that the frog piece type (i.e. ferz-threeleaper compound) may be somewhat weak in an endgame, considering that I hoped the frog would be more or less at par in value (and usefulness) with a N or B. Like a ferz, the frog sometimes can restrain two passed pawns on its own, but I cannot yet imagine a position where it can cope with three passed pawns, unless it captures one of them immediately. This seems to be a disconcerting minus when comparing it to a bishop or knight's capabilities in endgames, as these pieces at least at times can cope with three passed pawns.

[edit: I've just imagined one case where a frog apparently can cope with 3 passers: Assuming both side's Kings are tied up elsewhere, the basic situation is: White: Frog c4; Black: Pawns: c5, d6 and f5, Black to move. Play goes 1...Pf5-f4 (or 1...Pd6-d5 2.Fc4xPd5 Pf5-f4 3.Fd5-e4 Pc5-c4 4.Fe4-f3) 2.Fc4xPf4 Pd6-d5 3.Ff4-e3 Pd5-d4 4.Fe3-f4 Pd4-d3 5.Ff4-e3 Pc5-c4 6.Fe3-d2 and Black's passed pawns have been restrained for good. However, note it was essential for Black to move first in this case. Below is a diagram of a drawn example of this case (Ks added).]

[edit: Returning to the question of Diagram Designer's nomiclature for a moment, one figurine series I saw while using the Alfairie: Many Piece Set was the series of GreatWarMachine figurines. I had guessed that this does not refer to threeleapers, since the machine figurines still had only two wheels, like in the case of plain WarMachine figurines. I'm curious if anyone knows what a GreatWarMachine is, especially if there's a better known name for the piece type.]

There is a difference between restraining three Pawns statically, and being able to restrain three Pawns under zugzwang. I don't think the Knight can do the latter either.

BTW, Frogs have mating potential in pairs (maximally 30 moves), and together with Bishop (37 moves) or Knight (39 moves). Bishop + Knight also takes 39 moves, worst case.

[Edit] Interesting. I fed your position to Fairy-Max (which indeed thinks it is draw), and then I tried some other Pawn constellations. But instead of trying to prevent their promotion, it plays Fc4-f4-i4-h5-i6-i3, to deliver a perpetual check between i3 and j4! :-)

Thank you for the great info, H.G.!

There is one somewhat disconcerting possibility available to White right at move one due to the setup of my Frog Chess variant idea, though Black may have a number of ways to adequately cope with it (in a way the effect of a frog on move one reminds me of a camel's annoyance value in many variants that may not be of the best quality).

After 1.Fh1-h4 (1.Fc1-c4 by comparison may be relatively harmess, if only since 1...Pc7-c6 doesn't look very inconvenient for Black, and if 2.Fh1-h4 then 2...Pf7-f6 is possible) White's frog is kind of threatening to go to either g5 (obtaining the arguably slightly more valuable B and threatening to deprive the Black K of all castling rights) or to i5 (forcing a trade of the N on i8, which may or may not be a slightly more valuable piece, and causing some slight disruption whether or not Black develops the N, albeit at the cost of some time, which may compensate Black). Black can prevent both 'threats' by playing 1...Ph7-h6, but this seems ugly and might favour White to some extent after 2.Pf2-f4, though this is not entirely clear after 2...Pf7-f5. Note that if instead 2.Fh4-e4 then 2...Pe7-e6 may be needed, but it's fine.

Alternatively, Black can 'counterattack' with 1...Fh8-h5, which might even lead to a massive liquidation after 2.Fh4-g5 (2.Fh4-i5 Fh5-i4?? [2...Ni8-h6 seems okay, but if 2...Fh5-g4 3.Pf2-f3] 3.Fi5-f5# is the Frog Chess version of Fool's or Scholar's mate) 2...Fh5-g4 3.Fg5xBg8 Fg4xBg1 4.Fg8xPf7 (or first 4.Fg8xRj8, and 4.Fg8xPh7 might also be tried) etc., which somehow seems a silly possibility to exist from the setup (though White did 'ask for it'...). Also, Black can move his e-pawn at move one, when White can play 2.Fh4-i5 as planned, incidently threatening the disruptive 3.Fi5-f5+ if Black had chosen to move his e-pawn two squares forward. Yet another possibility is for Black to move his f-pawn at move one.

Actually I have noticed the "camel annoyance" you mention (it also applies to zebras), during my design of apothecary chess 1 & apothecary chess 2, on an even a deeper board. That is the reason why I have introduced the bruhaha squares. I think to some degree this annoyance (caused by the long jump relative to the distance of opposing armies, and the rather low value of such pieces) is present on the H move of the frog (even more so because the board is 8 deep).

Personally I always though Grand Chess, and by extension Capablanca chess family games, lacks minor pieces. Maybe it could be interesting to keep the NR&NB from capablanca and place the frogs on back bruhaha squares somewhere. I don't see how that would meet your design goals :)!

I'd like to ask the community. Are there any other such examples of "camel annoyance". What other ways are to combat it?

I am currently running a test with Fairy-Max where I started the Frogs on d1 and g1. (Because I adapted the game definition for Falcon Chess by changing the move of the Falcon, and the Falcons happened to start there.) This does not seem to pose any problems. The d- or g-Pawn you have to push to hold off the Frog are useful moves. They don't wreck your King-side castle, and liberate your Bishop (now on c8 and h8). Also, you can fianchetto the Bishops in the normal way. I don't think it would be very good to develop the Frogs that way; it helps black more than white. At least, Fairy-Max did not do it very often, and mostly preferred to develop the Frogs to 2nd rank.

My test consists of playing 200 games, from positions where I replaced one Frog of one side by a third Knight, and a one Knight of the other side by a third Frog, so that an imbalance of 2N vs 2F ensues. This can be done in 4 ways. I play 25 games from each of those 4 positions (and then again 25 with the reversed-color positions. The tentative results suggest that the Frog at least is not weaker than the Knight.

Thanks H.G.

I had rejected switching the bishops and frogs in my setup, based on my thoughts about other experiments, because e.g. I thought it might somehow limit the opening variation possibilities more. For example, if White elects to open the long diagonal for his queenside bishop, say on move one, Black would seem to want to only ever develop his kingside knight on the third rank, towards the centre, if he wished to fianchetto (or develop the other way) his bishop of the same colour as White's. Still, this alternative setup may be the lesser evil, if there is one. However I'm not sure my original setup is clearly worse due to the h-file frog leap. It's possible causing kingside disruption in the case of capturing Black's i-file knight doesn't really benefit White, e.g. if Black can arrange to castle queenside in time. However it's not appealing to a beginner to be forced to think at move one as Black, however great the actual hassle may be. It may be the case that both setups are viable, like in the case of 10x8 Capablanca Chess' original and final setup versions.

It would be interesting to weigh/see how close in value a frog is to a bishop on a 10x8 board. A frog has longer reach than a knight, so in a way it is not surprising it competes well vs. that piece.

The final result of the test is this:

19% of the games ended in a draw. (This is low; for orthodox Chess it is about 32%.)

With white, the Frogs scored 59.5% (advantages of 0, +14, +5 and 0 on the individual positions).

With black, the Frogs scored 51.5% (-3, 0, +4, +2)

Color-averaged this is 55.5%, (standard deviation 3.16%). This excess score is approximately 1/3 of the advantage of a Pawn. As this is for an imbalance 2 pieces, it follows that the Frog is about 15 cP more valuable than a Knight. The white advantage in the test was 4%, which is a normal value for Fairy-Max.

The established values for N and B on a 10x8 board are:

• Knight = 300
• first Bishop = 350
• second Bishop = 400 (when on other square shade)
• So it follows Frog = 315

Nice work, H.G.

If my original setup hasn't been tested, I'm thinking of going with your setup as the main one if I eventually do a preset for Frog Chess (possibly offering my original setup as an optional choice for those who wish to try it; if that one does get tried, I wouldn't be completely surprised if the h-file frog leap for White at move one is considered best by far, and even favours White rather too much, perhaps unless Black replies with a similar frog leap):

[edit: One thing I forgot about regarding the placement of the bishops in such a setup is that the analogue to the Advance Variation of the French Defence in chess seems to favour White here, e.g. he can hope for a much easier pawn breakthough on the kingside. Sometimes you cannot have everything you might wish for. This observation might also be true for the original setup of Frog Chess, however.]

Regarding HGMuller's data - very interesting!

The conclusion that on a 10x8 board a bishop is worth 400 (two on the board on opposite colors). If one is captured the lone bishop is still worth 350.

On a 10x8 board I previously learned a guard (non-royal king) is equal to a bishop (using Fairy-max simulations). This means that a guard is indeed significantly more valuable than a knight.

This exactly matches the tests I had done previously, except I never found actual values for the knight and bishop. I only learned that a guard is worth more than a knight and exactly the same as a bishop (using one value for a bishop which is applied throughout a game whether there is one or two).

Nice work.:)

@ V.R. & H.G.:

A small point of disagreement. Though I admit a lot of my piece valuations are arbitrary I personally would never set a bishop=4 full pawns, even if the B happened to be part of the bishop pair, no matter what the board size is. That's since I feel a bishop ought to be able to, in many cases, stop the number of pawns its worth (value rounded down to the nearest pawn when fractional), and as a rule a B cannot cope with 4 pawns (e.g. for chess see Fine's Basic Chess Endings), no matter the board size (granted there are a number of unlikely pawn structures of 4 pawns that can be stopped). However, I know I'm being arbitrary here, as in chess a rook can seldom deal with 5 passed pawns, and it's worth at least 5 pawns by many people's valuations. Thus, a value of up to 3.99 I would find more agreeable for a B.

An endgame question is, can K+2Bs as a rule hope to stop K+7or8 pawns? I think K+1B might stop 4 of the pawns, while the remaining B would have to try to deal with the remaining pawns, but such endgame could be complicated since for one thing the other side's K could try to support different pawn(s) at various junctures. However, I feel that as a rule 8 pawns would be too many to cope with. For what it's worth, Fine's book notes that 2 B's normally win vs. just 4 pawns.

These piece value rules usually fail in very extrame cases. When we say a Queen is worth 9 Pawns, we don't actually mean that a game where one side has a Queen, and the other 9 Pawns, is a close call. We mean that a Queen is better than two pieces worth 5 and 3, and that it is worse than two pieces worth 5. A Pawn is a very ill defined concept, as there are many kinds of Pawns, differing wildly in value depending on their location on the board, and with respect to each other. We all know that a single favorably placed 7th-rank Pawn can already draw a Queen. OTOH, 10 2nd-rank Pawns are massacred by a Queen, in absence of other material. So the odds for non-Pawn material versus large numbers of Pawns are totally dependent on the constellation of Pawns. A Bishop can in fact stop 5 connected passers, if they have all moved up to the diagonal controlled by the Bishop, even under zugzwang. OTOH, sometimes it cannot even stop two isolated passers.

The values should only be used to calculate how many Pawns offer approximate compensation for an imbalance in stronger pieces, if not more than two Pawns are needed. The rule N=3, R=5 follows from that you want the rule to work for imbalances such as NPP vs R and NN vs RP. For R vs 5P the rule is pretty meaningless, as it depends way too much on what kinds of Pawns you exactly have. If NPP-R and NN-RP are both perfectly balanced, it follows that N=3P and R=5P, value-wise. You should not trust it for predicting how valuable large swarms of Pawns are. Piece values just don't work for large swarms. Three Queens also are crushed by 7 Knights (on 8x8), contrary to what any reasonable value ratio Q:N would predict.

Kevin, I don't you understood what HG was saying. First, he was talking about a 10x8 board, and second, he meant that the first bishop was worth 350 cP, and the second was worth 400 cP, for a total of 750 cP, which would actually mean 375 cP each. (cP means centipawns).

I should have noted that another extreme case, perhaps, that I had in mind is, if 2 Ns are set =3x2=6, and 2Bs = 4x2=8, then it would be the case that 2N+2P vs. 2B would be numerically equivalent. However, I myself have used value systems in variants where 2Ns+P would be equal (or approx =) to 2Bs, and I found I was a bit uncomfortable with even that conclusion. [edit: I did happen to get what H.G. was saying about the board size, at least, Nicolino, though I guess I missed his point about the difference in the 2nd bishop's value, though it's still not clear to me.].

I've edited my last post, for those who missed it.

You are lucky. It threw away my (long) post.

So let me just say Nicolino is right: a pair of Bishops is 750cP, and beats a pair of Knights + one Pawn by 8-9%, (all other pieces present). About half of what you get from the advantage of a Pawn. Deleting B+P for one, and R for the other, gives a perfectly balanced game, just as deleting N+P for one and one B (i.e. the second) from the other.

If I'm permitted to drop into this discussion my take with the concept of valuing pieces in terms of pawns is like the economical concept of valuing  products in terms of coin. This means that the concept of a pawn is an abstract concept of measure unit (if 1 coin is not very comfortable just think about 1 meter). So the sentence "A knight worths 3 pawns" does not actually mean that one may always exchange a knight for 3 pawns, although in most cases on average that is the case. It actually means that it worths 3 somethings (like coins or meters), where one pawn (unit of measure) indeed on average worth one pawn (the chess piece). I think a more basic way to state what HG is saying is that especially in the case of the pawn: a pawn rarely worth a pawn (if you get my joke :)!). I many times think that this measurement scale is not linear like in the 7n vs 3q example, it could be even multidimensional in some weird games where 2 types of pieces are extremely sociable towards each other (I can give no hypothetic example now so if one could help here) .

That is indeed a good way of expressing it. An actual Pawn could be worth anything between 0.5 (isolated edge Pawn or doubled Pawn) and 2.5 (7th-rank protected passer) Pawn units. Note that most strong Chess engines, (which put enormous effort into optimizing their piece values) typically use 80cP as the Pawn base value (and 325, 325, 500, 950-1000 for N, B, R, Q), and then award separate bonuses for passers, depending on their advance (and whether they are protected), and penalties for being isolated, doubled or backward. So I guess 100cP corresponds approximately to an isolated, not-too-advanced passer. Protected passers are better, far advanced passers are better.

Note that a Rook is not able to stop two connected 6th-rank passers. OTOH, on a 10x8 board it has no trouble at all anihilating 5 isolated 2nd-rank passers.

Regarding my Frog Chess variant idea, with the latest setup (H.G.'s), I had a thought on how to salvage the French Defence analogue, at least in the case of the Advance variation analogue. After 1.Pf2-f4 Pf7-f6 2.Pe2-e4 Pe7-e5 3.Pf4-f5, Black can try 3...Fg8-f7, 'threatening' the disruptive check on f4, defending the pawn on i7 one more time, and introducing the idea of moving the other frog to g8 to reinforce the squares g5 & h7 once again, besides the frog (ferz-threeleaper compound) just moved (plus move a step closer to permitting queenside castling if desired, though this may be hard due to a White N maybe going to d5). White can play his d-pawn up a square, but it seems it won't be simple to soon force an advantageous pawn breakthrough on g5, or draw significant concession(s) from Black to stop it - Black might advance his own pawn to g5 if need be. I'm beginning to like H.G.'s setup more, but I'm still not sure if my original one is worse. In the case of that one, I'm thinking that in the case of a French Advance analogue, perhaps 3...Pg7-g5 might be the only move that is at all palatable for Black. Otherwise, the possibility of Qe1-i5[+] at times seems disconcerting, for example.

H.G's setup:

My original setup:

Frog

I've edited my previous post, especially to add 2 more diagrams.

A question: has anyone come up with a value in pawns for a ferz-alfil compound piece type (modern elephant) on a 10x8 board? I'm thinking of still using an experimental variant idea or two with such pieces, and I'm wondering how close in value other people think the modern elephant piece type comes to a knight on such a board. The values I have cooked up for the minor pieces involved put this piece type about 3/4 of a pawn less than a knight, which just might be rather off.

Diagram for Hannibal Chess variant idea (I might switch the various bishops and elephants around for a second, optional, setup, too) - for what it's worth I think Black might cope with the French Advance analogue here too, if only by the hybrid Dutch-like 3..Ph7-h5 move, also true in the optional setup (clearly I like the French Defence, in chess)[edit: this fails, it seems, due to 4.Ni1-h3, and if 4...j7-j6 5.Nh3-j4, but in the case of the optional setup, 3...Pg7-g5 just might be playable]:

[edit: If the name of this variant idea is a problem I can change it, though I saw a similar precedent in 'Cleopatra Chess' in the CVP alphabetical index.}

[edit: below is optional setep:]

[edit: Modern Elephant:]

On 8x8 a pair of oppositely shaded Modern Elephants is worth about as much, or perhaps marginally less than a pair of Knights. But no doubt some sort of pair bonus will be involved, making a lone Modern Elephant somewhat less than a Knight. (Wild guess: N=325, first Elephant = 305, second Elephant 335.) I don't think the relative value of N vs FA will be affected much in going from 8x8 to 10x8. (The Bishop will profit a lot from this, though, mainly because it happens much more often that its forward slides hit the enemy lines, rather than the board edge.)

Note that in Spartan Chess there appears a Lieutenat piece, which is a Modern Elephant that can also make a color-changing non-capture sideway step (FAsW). On 8x8 this is slightly stronger than a lone Bishop or Knight.

If the diagonal jump doesn't cause a problem for developing the piece, the Phoenix (WA) seems a more interesting piece than the Modern Elephant.

HG,

Isn't the Spartan chess captain in Betza notation FAmsW?

HG,

Isn't the Spartan chess captain in Betza notation FAmsW?