Amazon: 12
Chancellor: 8
Archbishop: 6
Dragon King: 8
Dragon Horse: 6
Centaur: 5
Nightrider: 5
Gold General: 5
Silver General: 4.5
Cannon: 5
Xiangqi Horse: 4.5
Nightrider: 5
Cannon Bishop: 4.5
Mann: 3
Camel: 2.5
Dabbaba: 2.5
Alfil: 2.5
Xiangqi Elephant: 2
Ferz: 3
Wazir: 3
Completely wrong. Chancellor is only 0.5 Pawn weaker than Queen, Archbishop only 0.75 Pawn, so on this scale they would be 8.5 and 8.25. It is more usual to value a Queen as 9.5, though.
Even a pair of Ferzes is about 0.25 Pawn weaker than a Knight. A Wazir is even worse, especially when it starts behind a closed rank of Pawns, hardly worth more than a Pawn. Alfil and Dababba are nearly worthless; less than a FIDE Pawn. (In Shatranj the Alfil is considered to be of PAwn value, but Shartanj Pawns are worth less than FIDE Pawns because of their poor promotion.) The Xiangqi Elephant is even weaker, as it is an Alfil that can be blocked. Two Xiangqi Horses exactly balance one FIDE Knight, and to suggest they are worth 50% more than a Knight is ridiculous, as they are just Knights that can be very easily blocked. It is similarly ridiculous to value Silver and Gold higher than Man, as these are just crippled versions of the latter, lacking 25% or 37.5% of its moves.
A Cannon is worth less than half a Rook, as is well known from Xiangqi. In the opening it could be worth a bit more, because on a crowded board you still have good prospects to trade it for a more valuable piece.
All this measured in tens of thousands of computer games.
Here is a better way to determine whether the Archbishop is worth more than a Chancellor:
https://gothicchess.info/10x8_piece_values.pdf
Completely wrong. Chancellor is only 0.5 Pawn weaker than Queen, Archbishop only 0.75 Pawn, so on this scale they would be 8.5 and 8.25. It is more usual to value a Queen as 9.5, though.
Even a pair of Ferzes is about 0.25 Pawn weaker than a Knight. A Wazir is even worse, especially when it starts behind a closed rank of Pawns, hardly worth more than a Pawn. Alfil and Dababba are nearly worthless; less than a FIDE Pawn. (In Shatranj the Alfil is considered to be of PAwn value, but Shartanj Pawns are worth less than FIDE Pawns because of their poor promotion.) The Xiangqi Elephant is even weaker, as it is an Alfil that can be blocked. Two Xiangqi Horses exactly balance one FIDE Knight, and to suggest they are worth 50% more than a Knight is ridiculous, as they are just Knights that can be very easily blocked. It is similarly ridiculous to value Silver and Gold higher than Man, as these are just crippled versions of the latter, lacking 25% or 37.5% of its moves.
A Cannon is worth less than half a Rook, as is well known from Xiangqi. In the opening it could be worth a bit more, because on a crowded board you still have good prospects to trade it for a more valuable piece.
All this measured in tens of thousands of computer games.
It seems strange to me that two Xiangqi horse would be equal to one knight. I would have thought they'd be worth 70% of a knight or so given the standard assumptions about values with respect board density usually have a magic number close to that. Is their lameness really cutting their value in half?! I always just called them 2 points.
Incidentally, does anyone know the value of a Xiangqi horse as a component rather than as a piece itself? Like is an archbishop several points more valuable than a horsebishop?
I would think if the Xiangqi horse is 2 points, then a horsebishop should be like 7. If the Xiangi horse is 1.5, then the horsebishop might be as low as 5.
The xiangqi horse is just kidding. It's actually 1.5, while my Xiangqi teacher says it's 4.5.
Amazon: 12
add a half or so because it is a lot of power in one piece, and way too many forking directions
but the levelling effect makes sure it isnt insane (in most games)
Chancellor: 8
12 forking directions, and the rook masks the colorswitching of the knight
add a half or so again
Archbishop: 6
ok this is stupid
both pieces mask each other perfectly
and it is a tricky piece
queen level, id say 8.5 or 8.25
Dragon King: 8
oh yes a ferz is worth 3 points
no, adding ferz to any piece is 1.5
so this is 6.5
Dragon Horse: 6
adding wazir to any piece is also 1.5
so 4.5+.5 for loss of colorboundness (and colorswitching) and can mate is 5
Centaur: 5
3+3.25=6.25 i think (non royal king > knight imo)
Nightrider: 5
it is very tricky in the opening and wins straight up against a rook in 6 pawns per side (coz it can win pawns behind closed structures easily)
and tricks
so 6ish
Gold General: 5
oh wow a piece literally worse than a non royal king is better
3.25 - 2 diagonal retreats
well, the strength of nonroyal king comes from endgame
so the retreats... maybe 2.5
Silver General: 4.5
same logic, but the loss of back and side orthogonal moves is even worse everywhere
so 2.25 or maybe just 2
Cannon: 5
this isnt a rook
id say.... if its 3 then trade with knight would be reasonable...
if 2.5 opp will not want, so cannon is kinda useless
around there, but trade it asap
Xiangqi Horse: 4.5
worse than a knight
the lameness means that the piece loses the.. one advantage of a fide knight
1.5 is reasonable
Nightrider: 5
Cannon Bishop: 4.5
same logic as cannon rook so 1.5ish but trade it asap
Mann: 3
id say add .25
Camel: 2.5
a colorbound knight with awkward moves? on 8x8 its 1.5 or worse but with opening trickiness
so depending on what it can win
but objectively 1.5 is correct
Dabbaba: 2.5
1/4 of the board, 4 directions?
1
Alfil: 2.5
same logic so like .75 or even .5
Xiangqi Elephant: 2
oh a worse alfil...
.4 or .3
Ferz: 3
1.5, everyone agrees
Wazir: 3
1, everyone agrees
my opinion
The xiangqi horse is just kidding. It's actually 1.5, while my Xiangqi teacher says it's 4.5.
It’s 4.5 (actually I think it’s 4 personally) while setting the xiangqi pawn as 1 on a 9x10 board. I think the unit is different for those two cases.
The units are surely different, as in Xiangqi the Rook (Chariot) is considered 10. So about double the scale used in evaluating the Chess pieces above. The 4 would then translate to 2.
The values, and explanations for them given by Ilampozhil25 are quite good, and computer matches from start positions with material unbalance indicate very similar values. The opening value of a Xiangqi Horse in a FIDE context is indeed 1.5, on the scale where Rook=5. The blockability ('lameness') of the Horse is a large disadvantage in that case, especially since two moves can be blocked on a single square.
We should keep in mind that this disadvantage is reduced when the board population thins towards the end-game. On a nearly empty board there isn't much difference anymore between what you can do with the XQ Horse and the FIDE Knight, so the end-game values must converge to each other. (Some Xiangqi rules of thumb have the Horse increase from 4 to 6, and the Cannon fall from 6 to 4 in the course of the game.) And the Xiangqi board is already much less populated in the start position than FIDE Chess: there are also 16 pieces, but they are on 90 squares rather than 64. So the Horses experience less obstruction from the start, which might explain their lower opening value in the FIDE context.
Yeah using rooks (chariots) makes the point easier to understand since they are the same.
Centaur is at least 6 + synergy bonus.
A XiangQi or ShoGi pawn is worth half a FIDE pawn or less. A XiangQi Pawn that crossed the river is worth a FIDE pawn. A Wazir is less than 1.5 FIDE pawn, so forward is 0.5, sideways is 0.5, and backward is less than 0.5.
The color lock cuts the piece value, while synergy increase value. The Mann is worth 4 FIDE pawns by synergy. The Ferz is worth more than a Wazir, but less than half a knight so their sum is less than a FIDE Knight, but their sum is a Mann. Yet, a Ferz without color lock is worth 2 FIDE pawns.
Board size also have a large influence on piece value. On a 10x10, the Mann is worth less than a Knight.
The Man is hardly worth more than a Knight on 8x8. What it gains in synergy (because of orthogonally adjacent targets) it loses in speed.
Force checkmate with lone Mann, versus cannot force checkmate with two knights.
True, but mating potential only contributes very little to piece value. Almost always sufficiently many Pawns are left to provide it. There are many more positions where a Man is not able to stop a passer from promoting than where a Knight cannot do that.
What can you say about the energy of a Centaur HGMuller 
Centaur is quite strong. Something like 7.5 or 8, on the scale wher Q=9.5.
A Mann is like 2.6 pawns without the checkmate potential. Yeah, the checkmate potential is a larger weight to the Mann. A Knight is like 2 pawns without checkmate potential. Sums do worth more than their parts.
But I can't understand that knight and man give such a big bonus as they are catogorized as slow ranged pieces. This means that Centaur has an unusually high bonus of two pieces that are relatively slow. 7.5 is closely near Archbishop which is given 7.75 i've seen.
Synergy is strong, and a check with Wazir move of the centaur force the king to go orthogonal away from the centaur. A check with Ferz move of the centaur force the king to go diagonally away. Obviously, if the centaur is not protected, capture it.
A lion is much stronger even as a short range piece. It moves as twice as a king (potentially capturing two pieces) or once as one of dabbaba, alfil, or knight. The second mode of movement is to jump over a wall of allied pieces. When the second king move return to the original square, players bypass this by just removing an adjacent enemy piece without moving the lion. It is listed as an explicit 3 way to move the lion because novice cannot see the two separate king moves.
Best way is to think of a lion as having two king moves, the first may share a square with an allied piece.
But....to win fairy chess variants, all I just need is to know how much each of these fairy pieces cost. So:
Queen = 9
Rook = 5
Bishop/Knight = 3
Pawn = 1
King = oof
So which fairy pieces cost which values?