Magician's Death Match: my invention (updated)

 Edit, 2-22-24 - This thread is way outdated!! The pieces and rules have been long updated since. The Prime Minister, Magician's Deathmatch Chancellor and Magician's Deathmatch Archbishop do not exist anymore!! Please disregard this thread and search for an updated .

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Magician’s Death Match: Chess VariantI – The Piece: the Magician

The magician much resembles the pawn in two ways: her moving power is different from her capturing one, and she can be promoted to any one of four more powerful pieces when a certain condition is met. (You will learn that in both the Magician and pawn's case, the required condition for promotion involves the pawn's advancement across the board! More on that in the "Promotion" section.)

 To play the Magician in Chess, a player switches out one of the Bishops and places her in his (the Bishop's) place. There’s also another possible way for the Magician to appear on the board that doesn’t require a Bishop: by pawn promotion. More of this is mentioned later on.

She may be used only once per player per game. Once switched in, she may not be switched out again for the Bishop in a later turn, remaining a Magician for the rest of the game. If she has been captured, the other Bishop, if still on the board, does not have the option to be switched out for her. Finally, the switch counts as one move; it’s now your opponent’s turn.

II – Powers 

a. Movement and Capture

The Magician can move in any diagonal direction (like the Bishop) over as many as two squares in range. When she captures, however, she can do so in any direction, crosswise or diagonally (like the queen) over two squares maximum.

(For clarification, she cannot land herself onto a square that's directly forward, backwards or sideways unless there is a piece for her capture! e. g. Standing in d5, if there isn't an opponent's piece on d6 for her to capture, she cannot move forward one square to d6; this is likewise so for d7.)

Because of her limited range, players might find her more useful as a defensive piece. On the other hand, what she lacks in mobility, she makes up in her special attribute.

 

b. Leaping Ability

The Magician is unique from the rest of the chess pieces in that there is a leaping ability specially characterized her. She can leap over any piece adjacent to her, yours or your opponent’s, to capture an opponent piece directly on the other side of the leaped piece. (Only to capture, though! E. g. Standing on D5, if a piece, yours or your opponent's, was on c4 and another piece, specifically your opponent's, was on b3, such as the knight shown in the left diagram, the Magician may capture the enemy piece on b3, regardless of the other piece standing on c4. On the other hand, if there was no piece on b3, as shown in the right diagram, she will remain blocked by the piece on c4; so long as there is nothing on b3 for her to capture.)

 

 

III – Promotion

(As mentioned earlier) The Magician has the potential to be promoted to one of four more powerful pieces after a condition's met; which of the four pieces becomes her promotion depends specifically on how it was met. The four promotional pieces are the following, listed hierarchically by power: 

1 - High-Priestess/High-Sorceress

a. Condition for promotion

One pawn must reach the 6th rank anytime the magician is in play; any pawn that is already on the 6th or 7th rank when the Magician was switched in does not count.

 The highest ranking major/minor piece of the opponent’s currently on the board upon the pawn’s reach of the 6th rank will determine which piece the Magician is promoted to. If the current most powerful enemy piece is a Knight, she is promoted to High-Priestess (HP); if it’s an enemy Bishop, she is promoted to Archbishop; and to Chancellor, if it’s an enemy Rook; and to Prime Minister, if it’s an enemy Queen.

Your opponent must have a major/minor piece in order for the Magician to be promoted. If, upon your pawn's 6th-rank reach, the most powerful opponent piece is a pawn or if no enemy piece is left in play (other than the King), she simply remains an un-promoted magician.

b. Their Powers 

1) The High-Priestess – Though the weakest of the four promotional pieces, the HP isn’t exactly weak. Her moving power goes in any direction over two squares; which is the same as the un-promoted Magician’s capturing power. Her (The HP) capturing power combines her moving power with that of the Knight’s, giving her a vast 5x5 area attack around her immediate location; whereas the Queen, Rook and Bishop have a line attacks.

 

(As another clarification, she can only capture like a knight, but can't move like one. E. g. Standing on D5, if there is no enemy piece on C3, E3, F4, F6, E7, C7, B6 or B4, which are all squares a D5 knight can move to or capture on, the Magician may not move to those squares.)

The leaping ability of the un-promoted Magician is still valid in the promoted stages.

2) The Archbishop, Chancellor and Prime Minister - The Archbishop's (AB) power combines that of the HP and the Bishop’s, giving him an unlimited diagonal line attack in addition to the HP's area attack. Likewise, the power of the Chancellor combines that of the HP and the Rook’s. Finally, the power of the Prime Minister (PM) combines that of the HP and the Queen’s; making him the most powerful piece on the board.

Archbishop -

Chancellor - 

Prime Minister - 

 When it comes to leaping over a piece to capture an piece, as a rule, they can only leap over a piece directly adjacent to their own in order to capture an opponent piece over two squares that direction. This is because a Magician can perform that maneuver, for the leaping occurs within her two-square range. Any capturing that occurs beyond that range will be dictated by the power of the Queen, Bishop or Rook in which the promoted piece is imitating; since none of these pieces leap but succumb to blocking, the promoted piece in question will so too be. (E. g. Even if white’s Archbishop can move infinitely diagonally, on b2, he can’t capture an opponent piece on g7 if there is a piece standing in between on c3, d4, e5 or f6. This is because a Bishop on b2 would be blocked by a piece on these squares every time. The Archbishop can, however, capture an enemy piece on d4, like black’s Bishop in the second diagram, even with a piece standing on c3. This is because the Magician in that position can execute this capture.) 

 

IV – Promotion by pawn-promotion

As stated earlier, the Magician can appear on the board through pawn promotion: if the Magician isn’t already on the board, she may be chosen as one of the pawn’s own promoted pieces; in this situation, both Bishops and she can be on the board at the same time. 

Instant promotion of the Magician to the High-Priestess, Archbishop, Chancellor or Prime Minister happens when she appears on the board through this method. In line with the regular condition of her promotion, the promoted piece she becomes depends on the highest ranking enemy piece at that time in play.

 

V – Checkmate

Check-mate by the (un-promoted) Magician alone is equivalent to a checkmate delivered by two knights and a king: while it’s definitely possible, it is most difficult! The short range of the Magician and the fact that she can only move diagonally will obviously make for a rather easy escape of your opponent’s King. Trapping the opponent's King at the edge of the board is possible, but the player would all too often rather resign.
If anything, checkmate should ideally be delivered in one of her promoted stages, since, as explained later, they can execute it so effectively. Among those things that are special to the Magician-promoted pieces are some of the unique (and rather dangerous) ways in which they can deliver checkmate –

1) By placing the Magician-Promoted piece on a square directly adjacent to the opponent's King anywhere on the board, if that adjacent square is protected by one of your other pieces; if the adjacent square isn't protected, the enemy king would merely be in check, in which case he could come out of it by capturing the Magician. (E. g. If the opponent's king is on f6, checkmate can be delivered on f5, e5, e6, e7, f7, g7, g6 or g5, assuming that another of your own piece is protecting that square.)

2) If the opponent's King is on a rank at the edge of the board (ranks 1 and 8 ), by placing the Magician-promoted piece directly two ranks inward on the exact same file; or one file over, to attack like a knight (e. g. If the opponent's king is on e1, checkmate can be delivered on e3; or on d3 or g3, attacking like knight.)

3) If the opponent's King is on a file at the edge of the board (files a and h), by placing the Magician-promoted piece directly two files inward on the exact same rank; or one rank above or below, to attack like the knight (e. g. If the opponent's king is on a5, checkmate can be delivered on c5; or on c4 or c6, attacking like knight.)

The following 5 diagrams are some of such positions of checkmate

(The red or green highlighted squares indicate where the checkmating Magician-Promoted piece can attack from its current position) -

 

One unfortunate thing about a King suffering from a Magician-Promoted piece's attack is that he can't escape by the typical block method, since it’s overridden by the Magician's ability to leap! (Consult the 2^nd and 5^th example.) Also, it might be interesting to note that once the opponent's King is in check by your Magician-Promoted piece, he is often times doomed, since driving him (enemy King) to the edge of the board through perpetual checking by consistently moving the Magician-promoted piece one consecutive square closer to him is a convenient and likely maneuver! As shown in 4 of these examples, checkmate happens while the enemy King is at the edge!

The Magician-Promoted pieces are unique from other chessmen in that they are the only pieces that can independently deliver checkmate with no direct help from other pieces necessary! (Even the Queen needs to collaborate with her own King to capture the other King.) .

 

VI – Chess notationIn recorded games, the Magician should be notated (as you saw in an earlier example) with a capital M. Key – 

VII – Discussing Material 

This is a tricky area open to debate. Currently, I put the magician at around 2.5 or 3 points of material: she’s more or less powerful than the Bishop and Knight due mostly to her fine ability to threaten pieces up-close but lack of mobility beyond a short diagonal line. The short range itself would make her worth 2 points, but the lost is made up by her crosswise attack and her ability to leap to capture.

The High-Priestess is probably a little more powerful than the Rook, placed at 6 points. While she too has weak mobility that can’t reach across the board like the Rook, she retaliates with a powerful area attack, which the Rook doesn’t have. Consider the following: if a knight is worth 2.75 or 3 points, the High-Priestess is double this, since she can capture like him (2 or 3 points) as well as capture and move in all directions as far as he can (another 2 or 3 points). In those positions where she can execute her leaping ability, she would be a little bit more at 6.5 points. (In the same way that certain positions make the knight worth more than the bishop by a slight.)

The Archbishop, Chancellor and Prime Minister are respectively set to 8.5 points, 11 points and 16 points. I need only discuss the Archbishop’s material points, since the Chancellor and Prime Minister’s grand powers don’t need a material point analysis to understand why they’re so powerful. (In other words, they win!) The AB's direct moving power is almost as powerful as the Queen, except for the fact that his crosswise movement and attack are pathetic compared to the queen’s absolute unlimited range in all directions. This alone would set him at around 7 points. Then, adding the capability to capture like the Knight redeems him 1.5 points (half the Knight’s material), placing him at 8.5 points. Finally, in those positions where leaping can occur, an additional half point might bring him up to 9 points.

One final note on material points: the very existence of the Magician would make a Bishop worth more, since he has the potential down the line to become a much more powerful piece. In this variant, the Bishop is probably 3.5 or 4 points because of this advantage. Thus, the Knight is no longer about as powerful as the bishop, because the Bishop here is more valuable!

VIII – Development of these variant Chess Pieces

This section explains why the Magician was created to move the way she does. Hell, why’s she even called the Magician? Where did the Archbishop, Chancellor and Prime Minister even come from?

a. The Original Idea behind the Magician

For a long time, witchcraft has generally been regarded poorly in Christian Europe society. Supernatural practitioners have been socially limited to cryptic venues or shamed/mocked in public. (Consider the way psychic people and ghost mediums of today are often regarded!) As such, the Magician’s range is only as good as two diagonal squares, whereas the holy Bishop’s range is unlimited. However, the King’s ignorance of her potential ability doesn't null its existence: she’s secretly aided troubled soldiers on the field, and battles were won with no concrete reason. These translate into her ability to attack crosswise and to leap over pieces, neither abilities of which the Bishop has. When it's realized that the King's sudden victories were owed to the her fore-unbeknownst aid, she would be regarded with a higher status. This concept became the magician's condition for promotion, where a pawn having reached an advanced rank would gain her the full ability to move in all directions (within her range) and attack like the knight. 

It may also be interesting to bear in mind, her presence on the board does seem to give pawns slightly more power: enemy pieces have to either work harder to capture them or prevent their advancement because of the havoc one of the eight might indirectly cause!

b. The Archbishop and Chancellor

In truth, I did not invent the Archbishop and Chancellor; at least not completely. I'm sure that many of you might have heard of Capablanca Chess, the famous Chess Variant created by Grandmaster Capablanca.  I had once read about a highly renowned player who created two pieces, respectively combining the powers of the bishop and knight and that of the knight and rook. The piece that had the combined powers of the Rook and Knight was called the “Chancellor”, and that which combined the powers of the Bishop and Knight was called the “Archbishop.”

It dawned on me that I could add my own variant version of these already-variant pieces, since, around this time, I realized that I needed to give the Magician a more "offensive" role: as mentioned in the beginning, her pathetic 2-square limited range likely renders her much useful only as a defensive piece. And, so, I created subsequent variant pieces that would become additional promotional pieces: they would have the same names as their Capablanca predecessors and would combine the powers of the High-Priestess and the Bishop and that of the High-Priestess and the Rook. (My version of the Chancellor and Archbishop do somewhat resemble these earlier variants created by Capablanca: Mine could capture like the Knight and Bishop and like the Knight and Rook.) Finally, the Prime Minister was added so as to have a piece that also combined the HP with the Queen; since there were already ones that each combined the other minor and major pieces. The historic governmental office of Prime Minister was not nearly as powerful as the King but was still a highly influential political position, much more so than the Chancellor's, and so, he became the official name for the last Magician-Promoted piece.

IX – Conclusion

I’ve always wanted to invent a new chess piece because of my grand love for the board game. The Magician has come a long way in development, and I believe that she is now decent for players to finally try her out.

In explaining the piece to a few people, one of two common criticisms I receive is either that she’s too powerful (This variance is dubbed “deathwatch” for a reason!) or that she sounds way too complex for one piece and, considering the ease of simplicity that defines the standard pieces, it might deter people from wanting to try her out. This is an understandable opinion. On the other hand, my compounded response to both these criticisms is this: If you’ve been playing the Queen in standard chess, you’ve already been playing a piece that’s “too powerful”. If you’ve been playing a Knight, what’s with its unorthodox move, you’ve already been acquainted with a “complex” chessman. If you’ve been playing the pawn by the standard rules, which are moving one square forward but capturing one square diagonally forward, you’ve already been acquainted with a “complex” chessman. (Why doesn’t a pawn capture the way it moves??) If you’ve been promoting a pawn to a Queen, you’ve already been exposed to a “complex” chessman that has the potential to be too powerful. People simply don’t realize that they don’t think anything of these chess things, because that’s what they’ve long been exposed to. What they’re really saying is that they don’t feel too fond of a new chessman interfering with the chess tactics that they’ve already learned. The magician isn’t “complex”. With the pre-existing rules of modern chess, which she was built on, she’s quite simple, really. The rules involving her are merely a lot to remember, more so than the other pieces; that, I do grant. But, again, if you’ve been playing chess this long, what’s the complaint?

There’s more analysis of her to be heard. Being nothing more than a fair chess player with a fair rating, I realized that there is a strong possibility that it might be heavily criticized (perhaps even mocked) by much stronger players than myself. Maybe they'll see it as nothing more than child's play. I guess I couldn't discount genuine opinions, so I have accepted this possibility long before it's actually so. However, I am content with myself for having put so much effort into developing her with the best of my logical abilities. Where the Magician will go in the end, I don’t know for sure. Maybe people will absolutely love her, and, if I'm completely absolutely optimistic, maybe she (or a variation of her) will even become an official variant in the far future. Maybe she’ll be nothing more than a fun or silly experiment of today, eventually to be discarded and moved on from. One thing is certain for the time being: I just won’t know until.

It seems to me you are significantly underestimating the value of the Magician. A piece that moves (and captures) diagonally 1 or 2 squares, with the ability to jump on both captures and non-captures in the latter case, is already as strong as a Knight (3). The only thing the Magician does not have of this is the jump-on-non-capture. Now non-captures are typically worth only half as much as captures, so that fact that you sometimes cannot make them because they are blocked hardly hurts (say 2.75).

As compensation the Magician has orthogonal captures, which endow it with mating potential. A piece that both moves and captures 1 or 2 squares (jumping) in all eight directions has a value of 7, i.e. the addition of the orthogonal moves adds 4. The captures would be responsible for 2/3 of this, i.e. 2.66. So the value of the Magician should be around 2.75 + 2.66 = ~5.4, i.e. significantly more than a Rook. And that is just its tactical value, not accounting for the promise of promotion.

BTW, checkmating a bare King with a Magician should be pretty easy. Even without the four distant orthogonal capture moves it would be able to force mate, in at most 29 moves.

Hi, HGMuller,

I want to thank you greatly for taking the time to read my full article (which I would think is difficult to do in just one day!) and thinking critically about the piece. I am excited that someone cares about my invention.

I really like the point you bring up in regards to the analysis. It seems I placed too much emphasis on range, while ignoring the potental that specific directionality and combinations of them had. I'm guessing that you feel I have shifted the distribution of points down one piece, where the magician is actually worth about as much as what I said the High-Priestess is worth and the High Priestess is worth as much as what I said the Archbishop is worth, etc.

On the other hand, my counter-response is this: when I was analyzing the piece, I was looking at my past games and games all around, taking note almost exclusively of the ubiquity in which players took advantage of long ranges; despite the fact that the Bishop can never leave the colored squares that he starts on, he is still a powerful piece because of his unlimited range. Still, this puts him only at 3 points. I figured the lowly 3 points had espcially taken into account his unlimited range, so I judged the movement and attacks of my own pieces in a likewise fashion. It takes the Magician and the High Priestess several moves to journey across the board to even be close enough to threaten pieces; in which case, the Magician herself usually becomes susceptible to threat herself, because the Queen and Rook can "see" her from far away. On the other hand, when I observed my games in which I played against my young cousins and those they played with each other(the three are age 7, 10 and 12 and are avid players for their ratings), more than half the time the Magician served great justice in protecting the King and the other major/minor pieces when they are in their "home territory". 

For example, the second diagram** in the examples I provided in explaining the Archbishop's limitation in leaping, which was an actual game played by my cousin Owen (black) against his sister Taylor (white), displays nicely the danger black's Magician poses for herself  if she were to venture too close into white's g4 Knight's line-of-sight by moving her maximum range. 

Had she had a longer ranger herself, she would have had many other options for tasks to perform and escaped the g4 Knight's threat; seeing that white's King, after all, being in danger would be the greatest advantage for Black. Rather, she is restricted by the Knight into ranks 6-8 of the A-D file; and then, her own pawn on a5 and the lesser indirect threat by the other white knight just a square below weren't helping her either. But, because of her combined diagonal and orthogonal attack, from where she (black's Magician) is,  Black's King is being shield from catastrophic checkmate by white's Archbishop****, since black's Magician controls b6 and c5; and c6; which are squares where white's Archbishop would have otherwise easily delivered checkmate in 2 moves.  At worst, black's King was checked and nothing more for several moves proceeding.

I can agree with how captures matter more than what one cannot do; it's something that I didn't consider before. However, one cannot honestly forget that level of easiness/difficulty in falling prey to capture finely aids in determining how many material points should be withdrawn. It's examples like this one that confirmed my presumption that she's mostly good as a "body guard" and little else; furthermore, people only switch the bishop out for her, sacrificing his long range, in hopes that they gain the Archbishop, Chancellor or PM down the (short) line. She's usually confined to the small space  that she started on, so it's hard for me to see her being worth as much as or a little more than the Rook.

 I'm sure you may have a follow-up rebuttal to this, but I also wanted to ask you: how many points do you think the promoted pieces should be worth if the unpromoted Magician is, in actuality, a little more powerful than the Rook?

**(I made two careless mistakes in creating this diagram: in the game, black's g7 pawn was actually out on g5; white's h-pawn should not have been as advanced on h4 and was, instead, on h3.)

****(This, on a sidenote - Needless to say, Owen (black) having moved his dark-squared Bishop onto  d4 was a major blunder to begin with. He figured that he could checkmate his sister by next moving the bishop to e3 in order to capture white's King, due to the lock performed by his Knight on c3. Sadly, the poor little dude not only forgot that moving his Bishop to e3 would have brought it to be captured by Taylor's g4 Knight, he forgot momentarily that Archsbishops could leap and that his having moved his Bishop onto d4 had exposed him to great danger. In epilogue, Taylor won the game in less than 10 white moves later.)

And, this is just for your resource. If you want to create a diagram to aid your any further response  in this dicussion, here is a photobucket page of the pieces and empty board that was prepared for that task:

http://s1298.photobucket.com/user/battlechessgn18/library/?sort=3&page=1

Well, without performing actual tests I can only compare the pieces to the closest similar things I did test. One of those was a piece that did move like the capturing power of of the HP, (moving and capturing) able to jump directly to any square in that 5x5 area. This was worth about one Pawn more than a Queen.

Values of short-range leapers with N (non-blockable) moves tend to cluster around (30+5/8*N)*N centi-Pawn (which for N=24 would indeed give 10.8). Your HP has the Knight moves only as captures, though, and that should count them as ~2/3 rather than 1, for an effective total of N=21.33. This would suggest a value of 9.25, but it would still lose a bit because the distant non-captures cannot be made as jumps. So my guess would be 8.75-9.00 for the HP.

Pieces like HP are very dangerous, because they have the power to drive an exposed King to checkmate all by themselves

The PM is very close to an Amazon (Queen-Knight compound), and the value for the latter tested as 13. Compared to the Amazon it does not have the Knight move as non-captures, but on the other hand it has the distance-two captures as direct jumps. This should approximaptely compensate, perhaps just suppress the value a little. So my guess would be HP=12.75-13.00.

To know it exactly it would have to be tested.

OK, I started some actual testing. To judge the Magician for its tactical value, I replaced the two Rooks of one side (alternatingly black or white) in the FIDE setup by non-promoting Magicians, and played a couple of hundred games with Fairy-Max (against itself) from that position, to see who was doing better. For technical reasons castling was only allowed to one side (K-side in half the games, Q-side in the other half), both with Rooks and Magicians.

The Magicians are winning this battle with a score of ~55%. I also played a match where there was an additional pawn-odds handicap for the Magicians, deleting f2/f7. The Rooks are then winning by ~63%. Apparently having an extra Pawn causes a score swing of 18%, which is what I also have observed in other positions (i.e. just deleting f2/f7 in FIDE causes a score of ~68%).

The advantage thus corresponds to about 0.3 Pawn, but that is for two Magicians. So a Magician is about 0.15 Pawn stronger than a Rook. Like I predicted, although slightly less than my guestimate of 5.4.

I also tested the High Priestess, by replacing one of the Queens by one. After some 300 games the HP is leading here by 57.5%, but in the first 150 games I had told the program HP was worth 9 (Q=9.5). When the score in those games (~59%) clearly showed the HP was actually stronger than a Queen, I corrected its assumed value to 10. This made the score in the following 150 games drop to about 55.5%. When I give the HP an extra Pawn-odds handicap, the Queen wins by about 63%.

So HP is actually slightly stronger than a Queen, 9.8 vs 9.5, rather than slightly weaker, as I had expected. Lacking the Knight non-captures is apparently a lesser handicap than I had assumed, probably because the piece already has so many other non-captures that it can still manoeuvre easily.

BTW, something was not clear to me from your rule description: when a Pawn reaches 6th rank, is the Magician upgraded that very same turn, or does it take an extra turn to do that? To determine what the higherst opponent piece is, are pieces that are captured by the moving Pawn counted or not? (I.e. do you take stock before or after the move?) What happens if the opponent's strongest piece is a Magician (or one HP, A, C, or PM)? Does the next-strongest piece then count, or do you not promote at all?

awesome

Did you use a computer program to do this, or were you simply playing against yourself, with the best knowledge of how black and white would have moved?

Either way, I can't thank you enough for taking so much time to analize my piece. Through a first read, I obviously have some minor trouble fully grasping such an advanced concept. I'll have to read it through a few times with my (old) chessboard and chess pieces with me to help me as to fully understand what these things are in regards pawn omitions and such. Once I am able to do this, I will update the material point analysis to reflect your findings: that the Magician is worth approx. 5.5 points and that the High-Priestess is worth 10 points. (I should assume, then, that the AB would be worth ~12, the Chancellor ~14 and the PM ~18. These new predicted points-worth are in accordance to your findings.)

In the meantime, I have great confidence in the conclusion that you arrived at: that, like the Bishop and Knight's material point comparison, the HP and  the Magician would be the equivalence to the Bishop where as the Queen and Rook would be to the slightly lesser Knight. 

Concluding, a thing to bear in mind when I was first analizing these pieces is, as I realized in the past few days when you first responded, I primarily understood their point-values through mobility and susceptibility of capture. This was probably a major flaw in my thinking, since all pieces are equally susceptible to capture, especially something as weak as the knight: even if they move in an unorthodoxed fashion, a lot of times they are still easily blocked by their own allied pieces; since they can only move a total of 8 possible squares. This doesn't stop them from being the grand 3 points (minus ~.25 points, to be slightly less than the bishop) that they are deemed to have.

It's not how easily they get captured. It's the fact that they could availably move to the squares they do in the first place.

BTW, something was not clear to me from your rule description: when a Pawn reaches 6th rank, is the Magician upgraded that very same turn, or does it take an extra turn to do that? To determine what the higherst opponent piece is, are pieces that are captured by the moving Pawn counted or not? (I.e. do you take stock before or after the move?) What happens if the opponent's strongest piece is a Magician (or one HP, A, C, or PM)? Does the next-strongest piece then count, or do you not promote at all?

Yes, upon the pawn's "achievement", the Magician gets promoted to _____ piece that very turn, so it is possible that a check/checkmate by the Magician could result from a pawn having reached the 6th rank. (This was a favorite tactic of Taylor's, the eldest sister of my cousins trio, whenever she could exploit it.)

The question regarding which enemy pieces get counted in the case of a pawn capturing one on the 6th rank is a very good one, and I wish I did clarify this beforehand. The verdict as to what the Magician gets promoted to is determined at the very exact moment in which the enemy pieces are judged. Since this happens after the pawn has captured a piece on the 6th rank, the enemy piece that was captured, if it was the strongest piece before capture, does not count. I feel that incorporating the captured piece that would have otherwise been the most powerful would give the Magician herself too much power: the captured strongest enemy piece is no longer on the board, why should the Magician be granted this extra privilege then?

In light of irony, this is the penalty applied for a pawn "being too smart"; even if this does contradict the original idea where a solder on the battlefield secretly having won because of the myseterious sorceress's aid would gain her a fuller officer's status. 

And, your last question was one that I have realized a long time ago and has left me in a deep quandary, even to today. Conscious of the existence of the enemy Magician and her promoted stages, the original rule was to only consider the four standard major/minor pieces (Rook, Bishop, Queen and Knight) of the enemy's to promote one's Magician. On the other hand, half of the time, that didn't make sense to me, and it still partially doesn't now: the AB, PM, HB and Chancellor are, after all, powerful pieces, and if a pawn has acheived the 6th rank while one of them is on the board, why shouldn't one's own Magician be promoted?

But, then again, to what should the Magician be promoted? The point of fact in considering the enemy Queen, Rook, Knight and Bishop is to gain a piece that is a more powerful version than the one that the Magician is imitating. (PM has the queen's power and more, Chancellor has the rook's power and more, etc.) How does one create a more powerful version of the PM, AB, HP and Chacellor?

I've always known that the original rule of considering only the standard major/minor opponents pieces could possibly be invalid. You've confronted a hole in my invention which I was trying to suppress. It's brought to the light and likely for a really good reason; since people would want a solid answer, and the one I provide ins't concrete and definitive.

Perhaps we should get chess citizens to vote on this; starting with those on chess.com.

I used Fairy-Max, which is a computer program. It is an engine where the moves of the pieces can be configured by the user, and I just added pieces that move like the M and HP to the description for normal Chess, so they could participate in the starting positions I set up with the material imbalance (HP vs Q or 2M vs 2R). I then just let it run all night, playing itself at 40 moves/min.

You probably overestimate the PM quite a bit; I once tested the Amazon (a Queen + Knight compound), and its value was just under 14. I don't expect the PM to be much different. It lacks the Knight non-captures, but can make the other distance-two captures as a jump, which should approximately compensate. It certainly wouldn't be worth 4 extra Pawns.

I would expect both A and C to be worth about 12. Note that in Capablanca Chess, where A and C are a simple Knight enhanced by B or R moves, they are also worth almost the same (A=8.75, C=9.0, Q=9.5). And here the piece you start from (HP) already does have the most important moves of R and B, so that adding the remaining moves of either B or R makes even less difference.

On 8x8 boards a range of two isn't that much of a disadvantage. It is important to centralize the piece, however, which is not the case for R or Q. In Fairy-Max you can configure if a piece must go for the center, and when you don't do that for pieces like HP, they perform significantly worse (about half a Pawn). It just doesn't use them effectively in that case. Even on the 4th Rank a HP is only one move away from being able to checkmate the enemy King on the edge or in the corner, if it gets a safe square. So it represents an extreme danger.

Thanks for the further analysis and testing. As I speculated, the way to optimally use the Magician and HP is to put her closer to the four center squares. I figured, however, that she wouldn't ideally be there most of the time because of the attacks and threats there that might be regularly caused by enemy long-ranged pieces who compete to get those positions; and who likely have a better chance at winning them. Since they (HP and M) are two squares in range, unless it's past mid-game, the 1st to 3rd rank are where I believe she would usually be the safest. As such, she's mostly good defending homeland pieces, but most especially the King; that is, until I extended the variance by inventing the AB, C and PM.  

I also checked out this Fairy-Max program when stumbling accross another variance, "Alpha-Omega Chess" (Not to be confused by Omega Chess, as invented by Dan MacDonald.) How exactly do you open/run the program? The Alpha-Omega .zip package came with the variance already configured and made, ready to use.

Fairy-Max is an engine for Chess variants that runs under the WinBoard GUI, and is included in the standard install of the latter (obtainable from WinBoard forum). Assuming you are running Windows the easiest way is to download the .exe installer from there, and run it. This will create items in the Windows Start menu to run WinBoard in various modes.

Fairy-Max will then be installed in a folder C:\WinBoard-4.8.0\Fairy-Max\ , and a text file fmax.ini in that folder contains the game definitions for it. A dozen or so Chess variants are already pre-configured there, but by editing the file you could also add your own. The file is 'self documenting', i.e. next to the game definitions it also contains an explanation for how to define a game. Unfortunately the format is a bit cumbersome: each piece has to be defined by giving a list of all the possible directions in which it can move, encoded as a single number, plus a code for what it is allowed to do in that direction (e.g. move, capture, hop, step, slide).

Now Fairy-Max' design goal was not to offer a platform that could be configured to play any conceivable Chess variant (the commercial software Zillions of Games does that), but to evaluate pieces with unorthodox gaits. So it has a lot of limitations in areas that do not interfere with that purpose. One is that the depth of the board should always be 8 ranks. Another is that only Pawns can promote (however they move).

So Fairy-Max cannot be configured for a full implementation of your Magician, due to the exotic promotion rule. It can, however, be configured for having pieces that move like the Magician, or its promoted forms, but do not promote themselves, participate in games.

What I did was not so much define a new Chess variant, but just add some new pieces to the definition of normal Chess. (Fairy-Max can handle 15 piece types in any variant, and normal Chess only used 9, so there was plenty of room for that.) Then I configured WinBoard 'by hand' to allow the use of two extra pieces in normal Chess, by typing the 'Additional option' -pieceToCharTable "PNBRQ..MHKpnbrq..mhk" in the Startup Dialog. This defined the extra piece types M and H as a crossed-swords symbol and a marshall star, respectively, and allows their use in FENs to setup a position. I had to make sure WinBoard's legality checking was switched off (in the General Options dialog) to allow these symbols to be used for the Magician/HP moves, as normally WinBoard would think they are the Capablanca A and C.

At the bottom of the definition of normal Chess in the fmax.ini file I then had to add lines to define M and H, by specifying their piece value, and giving a list of their moves. For Magician, for instance, this line would be:

m:460 1,5 -1,5 16,5 -16,5 2,5 -2,5 32,5 -32,5 30,5 -30,5 34,5 -34,5 15,53 -15,53 17,53 -17,53

* The 'm' specifies that this if for the piece called 'M', and is lower case to indicate the piece should be drawn towards the center

* 460 is the piece value the program will assume and base its trading strategy on. (For historic reasons Fairy-Max uses R=444 in normal Chess internally.)

* The next 4 number pairs describe the orthogonal steps +/-1 is sideway, +/-16 is forward/backward, and 5 means single-step (4), capture only (1).

* The 4 number pairs after that describe the orthogonal jump-captures.

* The next 4 number pairs describe the diagonal jump-captures

Then it gets really tricky, because the remaining moves (all diagonal, i.e. +/-15 and +/-17 for steps to the diagonal neighbor squares) are described as two-leg moves, starting as a slider that can both capture and move (code 3), but then on the next step toggles by 5 (hence 53), to change the 3 = 2+1 by 5 = 4+1, meaning the 1 bit is turned off and the 4 bit is turned on, so that the next step will have code 6, which is the code for a single-step non-capture. So this non-capture to the second diagonal square is only possible if the piece could slide over the previous square, i.e. if that was empty. As I promised, very cumbersome, but once you know it you only have to remember that code 53 describes a move that can do a second non-capture step in the specified direction if the first step (which could do anything) did not hit an obstacle.

For the HP the orthogonal neighbor captures (1,5 etc.) would have to be similarly upgraded to mode 53 (i.e. 1,53 etc.), and 8 capture-only Knight moves would have to be added (18,5 -18,5 14,5 -14,5 33,5 -33,5 31,5 -31,5).

For the other promoted forms, the best way to describe the moves would probably be to use plain slider moves (code 3) in the directions where they have those, supplemented by a hop-capture to the second square in the same direction. The latter would need code D8 (e.g. 1,D8 -1,D8 16,D8 -16,D8 for the orthogonal jump-captures).

The latest WinBoard version also has the nice feature it can allow the engine to tell it how the pieces should move, so that it can mark the possible target squares as soon as you pick up a piece. To trigger this from Fairy-Max you would have to write a few extra lines at the end of the game definition, in this case

#

# M& FmnAcWcD

# H& KmnDmnAcDcAcN

which for the M means "moves as Ferz, or non-captures as non-jumping Alfil, or captures as Wazir or captures as Dabbaba".

Unfortunately these are still completely different systems to describe the same moves, one used only by Fairy-Max, the other only by WinBoard (communicated to it by Fairy-Max). It would be nice if in future versions only the second description would have to be given, and Fairy-Max would derive the list of possible move steps and codes from it by itself, so that the user would not have to bother.

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