Comments/Ratings for a Single Item

The Cannon can double-pin pieces, and when it gets on the back rank, it can sometimes threaten multiple compound pieces and trade itself for one of them. However, I had Zillions-of-Games play twelve games. For each amount of thinking time, I had it play two games, one in which White had no Cannons and Red had no Nightriders, and vice versa. Here are the results:

1. For one second, the side with Cannons won both games.
2. For two seconds, White won with Nightriders, and it was a draw when White had Cannons.
3. For three seconds, the side with Nightriders won both games.
4. For five seconds, the side with Nightriders won both games.
5. For ten seconds, it was a draw when White had Cannons, and Red won with Cannons.
6. For fifteen seconds, the side with Nightriders won both games.

Overall, Nightriders won 7 games, Cannons won 3 games, and 2 were draws. This provisionally suggests that Nightriders are more powerful, but it's not conclusive. Since Zillions-of-Games has its own biases that may have influenced the results, games with other engines would help give a more thorough analysis.

I would think that Nightriders are stronger than Cannons, but certainly worth testing. I'll set ChessV up to test this out overnight.

I have started a test with Fairy-Max. It is not exactly Grand Cavalier, because Fairy-Max did have some problems with that, which did not seem worth solving. (Only start positions with a completely filled rank of 'pawns' and all pieces on the back rank can be configured. So I put the Cannons in the corners, and Cavaliers in front of them on 3rd rank. The Cavaliers that the Cannons then attack in the opening position are protected anyway, and such minor details in the opening position should not affect piece values. Worse was, unexpectedly, that since I handle promotion through a table (to allow square-dependent promotion like in Grant Acedrex) Fairy-Max also promotes 'pawns' on their own back rank! Normal Pawns of course can never get there, but I could not afford replacements like Cavaliers that can move backwards. So I replaced those by forward-only Half-Maos.)

Of course the piece values are a bit uncertain at this time, and I used the standard values for 10x8 board for the pieces. Except that I never measured the value of a Half-Mao. But that should be close to that of a FIDE Pawn. (A full Mao is worth half a Knight in a FIDE context, so a half-Mao is probably less than a Pawn, but the fact that it can promote gives it again something extra.)

For one player I replaced a Cannon by a Nightrider in the nominal start position, and for the other I did the opposit. So the imbalance is two Nightriders vs two Cannons, where each player still has one Nightrider and one Cannon in addition to that. From these positions I then play a long match, at 40 moves per minute (classical time control).

As the test is running, I can already conclude that the Cannons gete crushed. The player with the 3 Nightriders scores around 80%. I will report the exact results when the test finishes.

I have completed a run of 100 games with different time controls and tiny random adjustments to evaluation parameters. 50 games were played where white has two nightriders and black has two cannons and another 50 the other way around. The side with the nightriders won 61 games, the side with cannons won 9 games, and there were 30 draws.

Granted, ChessV is scoring the pieces with the evaluation parameters I have given it, and that can certainly affect play. I've given the nightrider a value of 500 and the cannon 400/275 (midgame/endgame) because those were my best estimates, but there could be a self-fulfilling prophecy aspect to this. Tonight I can try it again with a higher value for the cannon. I don't think that will change the overall outcome, but it would be interesting to see what effect it has.

You get many draws. I hardly had any.

When white had 3N+C vs black 3C+N (setup below), white won 101 games, black 26, and 1 draw (79.3%).

With reversed colors black won 73 games, black 20, and 3 draws (77.6%)

Total result: Nightriders vs Cannons 176-48 (78.6%). Statistical error 3.3%.

I used C=350, N=460, Q=851, Half-Mao = 74. In my experience there are no self-fulfilling profecies here: if you let the engine believe the wrong piece is the more valuable, the better piece would still win. Because no matter whether their believe is correct or not, one of the players would still avoid they would be traded for each other. So the imbalance stays around a long time, during which you measure how much damage the pieces do to others. (Unless you go to extremes like Pawn > Queen, then it will of course quickly sac its Queen for a Pawn, as Pawns are way to weak, abundant and exposed to avoid such a trade.)

In fact the performance of the piece that the engine thinks is most valuable would suffer from this, ('leveling effect'), whether the believe is correct or not. Because its deployment will get hindered by the need to avoid 1-1 trades, from which the piece that is believed to be worth less does not care about that.

HG, what pice do you call half-mao, because the cavalier is actually a full Mao as it can go back!

Indeed. So I used Half-Cavaliers instead of Cavaliers. These only have the four forward Mao moves. I already explained why. I don't expect that to affect the piece values much. (Except of course that it has a different value itself.)

HG,

I missed the reason for using half maos the first time. I'm sorry!

I ran the test again with the value of the Cannon set to 500/400 (midgame/endgame), Nightrider still set to 500.  This time the Nightriders won 41, the Cannons won 8, and there were 51 draws.  So this increased the cannon's win percentage slightly and the number of draws dramatically but not the overall outcome.  Given this, I think we can safely conclude that the Nightrider is worth than the Cannon, meaning the results of my first test were more accurate.  That test had a 76% win percentage for the Nightrider, which is very close to H.G.'s result of 78.6%.

As an aside, here are the Betza mobility scores of the pieces:
Equus Rex 12.60
Queen 15.91
Marshall (RN) 14.77
Paladin (BN) 12.65
Nightrider 9.87
Rook* 9.01

* The cannon will be somewhat less than this, but I cannot calculate it.  I also cannot calculate the Cavalier presently.

I now put an Interactive Diagram in the Grand Cavalier Chess article.

The piece values guessed by the Diagram were Cavalier = 239, Cannon = 275, Nightrider = 520, Queen = 1080. (This is not exactly reproducible, as the value guessing involves random sampling of positions). If I sneak in a Rook amongst the pieces, it gets a value very close to that of the Nightrider.

This seems to confirm the Xiangqi wisdom that a Cannon is slightly better than a Horse. (The Diagram uses a 25% filled board for determining piece values, and at that stage there would still be plenty of mounts.) And that each of those is only worth about half as much as a Rook.

Trading Cannon for Nightrider would then be equivalent to gaining a Cavalier.

H.G. wrote: "Trading Cannon for Nightrider would then be equivalent to gaining a Cavalier."

This is what Play Tester managed to do against me in our two games of Grand Cavalier Chess thus far, almost at identical turns with White and Black for him, in the opening stages of the games. My belief in the values that H.G. wrote of in the quote above was so strong that I simply resigned both games - perhaps I should have played on in each game, in the slim hope of recovering against a skilled CV opponent.

You get many draws. I hardly had any.

Yes, it seems I have a problem.  I am using time too agressively ... It is not running out of time as such, it is just getting to the point where it is moving instantly with a search depth of 1 because there is no time to do anything more.  And, with a search depth of 1, the sides are stumbling around until a draw is called in positions that should be won.  I am working on updating my time allocation now.

Well, beware that I was not really playing Grand Cavalier, but was using Half-Maos instead of full Maos for the Cavaliers. It is not implausible that this made a lot of difference: no possibility for Cavalier back an forth movement.

Yes, it seems I have a problem.  I am using time too agressively ... It is not running out of time as such, it is just getting to the point where it is moving instantly with a search depth of 1 because there is no time to do anything more.  And, with a search depth of 1, the sides are stumbling around until a draw is called in positions that should be won.  I am working on updating my time allocation now.

I have observed this too, but I did not knew how to reproduce it. My workaround was to give enough time (2mins+7secs for example).