Comments by nargott
Maybe, it's not an efficient approach, but changing and testing only the one type of pieces doesn't suffer from the openings as all different army. Also, I don't know how much evaluation of pieces affects to engine's decisions. Then it's better to get these values first.
In any case, it's more effective to test it by parts, for the first iteration 100 games per unit.
Hello! Thank you, but it's not hard for me, because there is only 10-15 units, not hundreds, which I usually work with. Hard are only limitations that I set: no any exotic peaces, no any strange extra moves and no any special rules. And now I need to understand, is it a perfect balance now, or not.
The automatic tests are interesting type of balancing tools, and it's a very big privilege to have it for chess, but it is unclear how they can be trusted and what limitations they have. Because the engine have features that may affect to results, or may not, and this is provisional, not real statistics of games played by real people. And for statistics there are very small numbers yet.
At this post I will publicate and update statistics:
Pawn = 63,0% of 1000 games (+/- 2%)
Dragon (RN, Chancellor) + pawn f = Angel (Q), 51,9% of 500 games (+/- 3%)
Phoenix (BN, Archbishop) + pawn f < Angel (Q), 46,0% of 500 games (+/- 3%)
Exchanging the Queens also affects to pawns, so the advantage of Angel may be only 75% of the full, because other 25% difference pawns gains for the better promotion.
2 Wyverns (R>1) + pawn f > 2 Griffins (R), 54,1% of 500 games (+/- 3%)
2 Pegasus (jR3) > 2 Griffins (R), 53,6% of 500 games (+/- 3%)
2 Werewolves (N+) = 2 Knights (N) + pawn f, 52,5% of 500 games (+/- 3%)
2 Unicorns (Nx) > 2 Knights (N) + pawn f, 58% of 500 games (+/- 3%)
2 Hunters (B>1) + 2 pawns f/c = 2 Monks (B), 48,1% of 500 games (+/- 3%)
2 Centaurs (jB2) < 2 Monks (B), 39,9% of 500 games (+/- 3%)
8 Fairies (px) + Phoenix (BN, Archbishop) > 8 Footmen (p) + Angel (Q), 60,2% of 100 games (+/- 3%)
7f Guards (p+) + Dragon (RN, Chancellor) < 8 Footmen (p) + Angel (Q), 42,4% of 500 games (+/- 3%)
Current equalities:
Dragon = Angel - 0.6
Phoenix = Angel - 1.0
Wyvern = Griffin - 0.3
Pegasus = Griffin + 0.2
Werewolf = Knight + 0.6
Unicorn = Knight + 0.8
Hunter = Monk - 1.1
Centaur = Monk - 0.4
Fairy = Footman + 0.2
Guard = Footman + 0.15
I think that auto statistics can't be very exact, because of experience of other strategies shows that a balance depends on player's skills and styles. The balance will be different for grandmasters and novices, for humans and engines, with openings' books and endgames' tables and without it. But it is important to ensure that the basic balance of the matchups is within acceptable limits, 40-60% rather than 70% or higher. And the automatic tests can be useful for adjusting units evaluation as provide an alternative, machine evaluation as one of the approximate marks.
So I will test separate units by 3 iterations: 100, 500 and 2500 games (200, 1000 and 5000 for basic pawn evaluating), that gives an accuracy of 0.25, 0.1 and 0.05 per unit (0.05, 0.02 and 0.01 for pawns). Then I will launch 1000 games for each match-up and 500 for mirrors. Mirrors are important to get statistics about white and black balance. All games will be launched at the minimal time limits, 1 sec per turn, because it provides greater accuracy per spent time.
Overall (by the 1 iteration of test):
Hero = 3.0
Footman = 1.0
Knight = 3.25
Monk = 3.5
Griffin = 5.0
Angel = 9.5
Guard = 1.15
Centaur = 3.1
Werewolf = 3.85
Wyvern = 4.7
Dragon = 8.9
Fairy = 1.2
Hunter = 2.4
Unicorn = 4.05
Pegasus = 5.2
Phoenix = 8.5
1) This is surprising that Centaurs are much stronger than Hunters
2) These values can't be used as average powers because they show only unit's potential from the very beginning of game; the side which have better potential, have better chances commonly
3) The starting power of Queen-type units is really high, much more than 2 Rooks
4) These values (starting powers) don't correlate with average power, neither of orthodox pieces, nor of new peaces with my calculations, that's why better accuracy is not important, and I think I will stop on the 2nd iteration, 500 games per unit.
I have an idea for weakening Orcs, to deprive them of the right to castling, but at first, I need to collect their massive statistics before it and after it to ensure that this measure is really necessary.
I also love your pieces, specially the Werewolf and the Unicorn that are new to me.
Thanks, they are very basic units, because the move of orthodox Knight often explained the same way as moves of Werewolf and Unicorn are. But the Knight is jumping over the first square, while the Unicorn/Werewolf can stay there.
Werewolf/Unicorn were the first invented units but later Pegasus became my favourite unit, because its movement is very easy but its abilities are wonderful and I was very surprised why there are many such units as R2, R3, R4, R5 which are only weaker versions of Rook, but no one is jumping R3, although the Pegasus is the strongest basic orthogonal leaper which is balanced (jumping R4 is imba on 8x8 boards). Pegasus is a real antipode of Rook (Griffin), playing on the same lines but by the opposite way, preferring closed rather than open lines.
The "jumping rook" and "jumping bishop" pieces are known as "ski rook" and "ski bishop" (think of ski jumping!) for a long time, for a reference see, e.g., here: http://www.mayhematics.com/q/mccs.htm
I was very surprised when I didn't find the same pieces in fairy lists, because in my opinion they have very simple, almost basic, mechanics of move, much easier and more obvious than most fairy pieces. Someone had to invent something like them.
Since your Chess Variant is a themed or Humans, Elves and Orcs, some artistic freedom in piece nameing is generally granted, But I think you are going overboard in renaming the Human pieces (the standard Chess pieces) only to create unnecessary confusion.
I like orthodox pieces but don't imagine what the Bishop, Rook and Queen do at the battlefield and why they are battle units? I understand that the orthodox pieces are likely to retain their old names, but still suggest alternative names. On the other hand, orthodox names may be used and reserved as type names, for example Griffin, Pegasus and Wyvern are Rooks.
Also, the name Phoenix is given traditionally to another piece (WA) and should not be reused.
Yes, but I can't imagine any other unit as elvish "champion". Maybe the Dragon, but the Dragon is already used by Orcs. The Pegasus is almost ideal alternative, but it makes the Angel and the Dragon incomparable with them and need to find extra new names (and for the Elvish Rook too).
A Centaur is usually understood as a KN compound piece (also known as knighted King or crowned Knight). The piece you name Centaur is usually known as Ferfil (Fearful being a wordplay on that) or as Modern Elephant.
I'm thinking to rename Centaur to Harpy, but doubt because the Harpy is the 3rd flyer unit (Wyvern, Dragon). The Elephant is bad because it associated with clumsy, but this unit is much more agile. The main problem of "usually known" names is the same as orthodox names - they are not thematic (if we include several pieces to the same army) and often not logic.
There is a huge number of different names of fairy pieces, and it is a problem for any developer. Because if you want to use, for example, the image of the Dragon or the Griffin to thematic army, suddenly you find that these pieces are already exist but they do not at all what you need for the game and for the balance.
The names are controversial, but at least now they are 100% relevant to the theme and how these units work (for all new people who don't know any peaces besides orthodox). I can't find another good names, to achieve two goals at once, that's why I had chose only thematic names. I'm opened to new suggestions for names, but thematic and logic are the most important aspects.
Maybe, I should rename Fairy to Sprite, and Pegasus to Valkyrie. Valkyrie is something that can be Elvish Queen instead of Phoenix, but which name give to Elvish Rooks?
If I'll want to make Elvish Pawns have leaping push like spartan pawns:
h:70 15,E4 17,E4 16,5 15,6 17,6
E4 means this leaping push?
If I'll want to make Orcish Pawns have promotion only to Nightriders (unique unit, which is absent in starting army), then I would put the Nightrider to #7 (or #9 black), moving the Orcish Queen to the end of list, it will work correctly?
I think that promotion to Nightriders is "positive" nerf making Orcish games more interesting than standard promotion (to Dragon usually). And this is better than a ban of castling or a single ban of promoting to Dragon. I like Nightriders but as a rare option, not at starting army (because it is upgraded Knight and have difficult move). It is interesting that although Nightrider is stronger than a Rook/Wyvern, it can't checkmate a bare King (need the second Nightrider). The same story with the other Orcish Knights - Werewolves.
Eagles are bad because there are Griffins (Human Rooks), which are hybridize eagles. Ents are good, but require redefining all the Rooks from flyers to something siege. There is no problems for Orcs because of Cyclops instead of Wyverns. But there is a problem for Human, because the closest analogue is Elephant (instead of Griffin). As an alternative there is a (sieged) Tower, usually associated with the Rook (by image), but I'm not sure that it is a good unit.
In general, there is a very interesting idea to use exactly Tolkien's setting, but I'm afraid that I haven't enough imagination to find matching units for all 3 races.
Current statistics with Fairy-Max:
Human-Orc: 40,1% (human) by 500 games
Orc-Human: 43,6% (human) by 500 games
Human < Orc, 41,85% by 1000 games (+/- 2,5%)
Elf-Orc: 42,3% (elf) by 500 games
Orc-Elf: 40,8% (elf) by 500 games
Elf < Orc, 41,55% by 1000 games (+/- 2,5%)
Human-Elf: 49,2% (human) by 500 games
Elf-Human: 48,1% (human) by 500 games
Human = Elf, 48,65% by 1000 games (+/- 2,5%)
Unit's power by statistics (500 games per unit):
Hero = 3.0
Footman = 1.0
Knight = 3.25
Monk = 3.5
Griffin = 5.0
Angel = 9.5
Guard = 1.15
Centaur = 3.1
Werewolf = 3.85
Wyvern = 4.7
Dragon = 8.7
Fairy = 1.2
Hunter = 2.4
Unicorn = 4.05
Pegasus = 5.2
Phoenix = 8.2
Overall:
Human = Elf
Orc > Human/Elf by 0.6 pawn
I think that there are two good ways to balance Orcs:
1) Orcish pawns promote only to Nightriders (special unit) but it seems as too big nerf, or
2) Orcish pawns promote only by simple turn (don't promote automatically)
In both cases I need to configure promotion at Fairy-Max.
Update rules:
Guards (Orcish Pawns) can promote only to minor pieces: Werewolves (Orcish Knights) and Harpies (Orcish Bishops).
Update statistics:
Human-Elf: 49,2% (human) by 500 games (+/- 3,5%)
Elf-Human: 48,1% (human) by 500 games (+/- 3,5%)
Human = Elf, 48,65% (human) by 1000 games (+/- 2,5%)
Human-Orc: 48,2% (human) by 500 games (+/- 3,5%)
Orc-Human: 47,7% (human) by 500 games (+/- 3,5%)
Human = Orc, 47,95% (human) by 1000 games (+/- 2,5%)
Elf-Orc: 50,3% (elf) by 500 games (+/- 3,5%)
Orc-Elf: 48,1 (elf) by 500 games (+/- 3,5%)
Elf = Orc, 49,2% (elf) by 1000 games (+/- 2,5%)
Update units' power:
King: Hero = 3.0
Queen: Angel = 9.8
Rook: Griffin = 5.0
Knight: Knight = 3.3
Bishop: Monk = 3.3
Pawn: Footman = 1.0
Queen: Dragon = 9.0
Rook: Wyvern = 4.8
Knight: Werewolf = 3.9
Bishop: Harpy = 2.9
Pawn: Guard = 1.1
Queen: Phoenix = 8.6
Rook: Pegasus = 5.1
Bishop: Ranger = 2.2
Knight: Unicorn = 4.1
Pawn: Sprite = 1.2
It was surprising for me, but as it has appeared, that a pair of Unicorns can ckeckmate a bare King without the help of the own King, like a pair of Werewolves. The demonstration of this: Unicorns
Update rules.
Remove next rule:
- Elvish Knights and Elvish Bishops are exchanged with starting places: Knights stay on the files "c", "f" and Bishops stay on the files "b", "g" (need to defend all Elvish Pawns)
This rule was introduced because of Elf-Elf mirror matchup, having 1. Qc3 move attacking g7 Pawn (and opponent must reply 1.... gf6 or ef6, because if Qe6 then 2. Bc4!).
But this rule has influence to Elf-Human matchup, having 1. Rh4 attacking h7 pawn (and if 1.... g6 or Nf6 then 2. Bd4).
So I think this questionable rule must be cancelled.
Now I start to get new statistics of mathups, with Fairy-Max auto battles:
- at 1000 ELO (0.6 sec per 40 moves)
- at 1400 ELO (6 sec per 40 moves)
- at 1800 ELO (1 min per 40 moves)
- at 2000 ELO (10 min per 40 moves)
How I get these ELO? I have ~95% winrate FIDE chess White vs Black when 1st White engine has 10 times more time than 2nd Black engine.
At low ELO I can get statistics very quick and modify rules to balance sides for it. But at higher ELO I can get statistics much slower, and can just check if balance is OK or not.
~10 000 games must be played for 1% accuracy (~100 games has only 10% accuracy - even equal sides may play 60-40).
I think the only things to be modified must be promotion rules. For example, introducing limitation of Orcish Pawns to promote only minor Pieces, lower Orcish winrate from 58% to 52%. Now I think that Elves and Orcs are a little stronger than orthodox Humans (~+2% winrate) and this point must be fixed.
Also, the most interesting thing is getting Pawns and Pieces values (at different ELOs). By statistics and changing start Pieces I can get only starting values. For example, starting values of orthodox Knight and Bishop are equal.
But there is also mid values which can be used at middle-game exchanges (theoretically, these mid values are best values for Fairy-Max engine, i.e. with these values Fairy-Max must have maximal winrate (vs engines with other values). For example, mid values of orthodox Bishop will be greater than orthodox Knight, because having less Pieces and Pawns at the board than at start.
Now I think that Guard (Orcish Pawn) must have promotion to Harpy (Orcish Bishop) only (earlier they can promote to Werewolf also). This is about 2% winrate nerf of Orcs.
Returning Rangers (Elvish Bishops) and Unicorns (Elvish Knights) to their natural starting positions ('c' and 'f' files for Bishops, 'b' and 'g' files for Unicorns) maybe is about 2% winrate nerf of Elves too.
In future, I will check update of race winrates (this will spend several days).
Hello!
I noticed a bug in the wyvern checkmate demo. For some time I even doubted that the Wyvern (ski rook) is a major piece, because there were some problems with the checkmating technique.
However, at the moment, these problems have been solved, the Wyvern (ski rook) is truly a major piece.
Here is a correct version of checkmate by the Wyvern (ski rook):
Buypoint Chess. Buy your fighting force - each piece costs a number of points.[All Comments] [Add Comment or Rating]A very interesting comparison of the ferz and the wazir.
Theoretically, the ferz should be weaker due to the color weakness.
However, in practice I would draw the following conclusions:
-
The color weakness does not matter at all as long as the piece's range of movement is low, like the ferz. What difference does it make that the ferz cannot reach 50% of the board squares if it cannot reach 90% of the board squares due to its slowness?
-
Slowness is the key parameter why the ferz is much stronger than the wazir, and why the wazir on 2 ranks is much stronger than the wazir on 1.
In my model, different ranks have different values. For convenience, consider the white pieces. The first rank will be worth 1 point, the second - 2, and so on, up to 8 - eight points. These numbers show that there is a much higher chance of capturing an enemy piece on the 7th and 8th ranks than on the 1st and 2nd, because they start on the 7th and 8th ranks, and they have a long way to go to 1st and 2nd.
While the wazir from the 1st rank will go to 4th, the ferz will have time to go from 1st to 6th.
Thus, the wazir from the 4th rank will attack 1 square of the 5th rank (5 points), 2 squares of the 4th rank (4+4 = 8 points) and 1 square of the 3rd rank (3 points), a total of 5+8+3 = 16 points.
While the ferz from the 6th rank will attack 2 squares of the 7th rank (7+7 = 14 points) and 2 squares of the 5th rank (5+5 = 10 points), a total of 14+10 = 24 points.
These numbers perfectly explain why the wazir on the 1st rank is worth 1 pawn, and the ferz is worth 1.5 (24/16), that is, 1.5 times stronger.
At the same time, the wazir on the 2nd rank will be 25% more valuable (1.25 pawns), because in the example above it will have time to reach the 5th rank instead of the 4th, and will score 6 + 10 + 4 = 20 points.
I predict that the ferz on the 2nd rank will also be stronger than on the 1st, and the difference will be the same 0.25 pawns (1.75 instead of 1.5).
It also follows from this model that a double pawn move (from the starting position) has a huge significance (up to 0.25), since it allows you to attack more valuable ranks earlier, compared to a slow single move.
According to my theory of ranks, the values for slow pieces like the Yawn or Maw are as follows:
The Yawn has almost the same activity as the Ferz in terms of reaching enemy ranks. Thus, it reaches the 6th rank as quickly as the Ferz. But from there, the Ferz attacks squares 7+7+5+5 = 24 points, while the Yawn attacks 7+7+5 = 19 points. Thus, the Yawn should be worth 19/24 of the Ferz, or 1.2 pawns.
The Maw is an improved Wazir that lacks its slowness. While the Maw reaches its best, the 7th rank, the Ferz will only end up on the 4th. On the 4th rank, the Ferz would be worth 5+5+3+3 = 16 points, while the Maw on the 7th attacks 8+7+7+6 = 28 points. Thus, the maximum value of Maw = 28/16 of the value of the Ferz = 28/16 1.5 = 1.75 1.5 = 2.625 pawns. The practical value of Maw will be slightly lower, since from the 4th rank the Ferz can improve its position further, and Maw on the 7th has already reached its best position. However, its value should be higher than 2 pawns (even in comparison with the Ferz on the 5th rank, Maw on the 7th will show 28/20 * 1.5 = 2.1 pawns). So I think Maw is about 2.1 pawns.
Also, my theory explains why the Queen is stronger than the sum of a Rook and a Bishop, compared to a Rook, the Queen occupies more active ranks much earlier, and thus the orthogonal squares attacked by the queen matter much more than the orthogonal squares attacked by the rook.
Similarly to the Queen, the Chancellor (Rook + Knight) is active in orthogonal directions much earlier than the rook (but the Knight is able to attack the most valuable squares later than the Bishop - thats why Queen is stronger than Chancellor).
As for the Archbishop (bishop + knight), there is maximum synergy, since diagonal moves allow the relatively slow knight to be strengthened as quickly as possible. To attack the 7th rank with a knight move, the knight needs 2 moves, while the archbishop does it in 1, with a simple diagonal move.
16 comments displayed
Permalink to the exact comments currently displayed.
I think that I need 10k games per unit.
My aim is the balance not far than 55%, such as 52 +/- 2% in each match-up. There are 5 different unit's types: queens, knights, rooks, bishops and pawns, so for each type accuracy must be +/- 0,8%. And it equals 0.05 pawn per type (if pawn = 16%). "Per type" means the full complect (for example, 2 bishops or 8 pawns).
Have you tested this values for orthodox pieces? This is no important for balancing (because of relative difference), but good to publicating absolute values. And I know that this is only statistics, real values are dynamical and positional.
I think that if the Orcs will be the imba, the best way to balance them is limiting promotion of their Guards, for example don't promote to a Dragon. But the next 2 candidates, a Wyvern and a Werewolf are very closed, so Fairy-Max "promoting to only Queen" (where the "Queen" is one of that pieces #7 or #9) will not be as good as for natural Queen.