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Hello Kevin, Hello Fergus,

Actually I've noticed the camel issue on a 10x10 board in my own upcomming apothecary1 game, with the wizards being confident on exchanging favorably with black pieces. I currently don't know how to overcome this issue.Maybe enlarge the board.

It may be worth noting that in the case of variants where promotions occur, and then only on one rank (the last one!?), it would not be good game design to allow underpromotion to a given piece type, if there can never legally arise a position where the underpromotion would in some tangible way be a better move to play than promoting to a piece type of higher value. However, at the moment I cannot think of a game that would break this principle, assuming it's ever possible to do so.

I agree with this principle and believe it is indeed sometimes violated.  Take all the Capablanca variants.  They typically allow promotion to any piece (Queen, Chancellor, Archbishop, Rook, Bishop, Knight.)  The last three are pointless, however.  You might under-promote to avoid causing a stalemate, but if the Rook-move causes the stalemate you promote to an Archbishop.  If the Bishop-move causes the stalemate, you prmote to a Chancellor.  Otherwise you promote to a Queen.  David Paulowich first pointed this out and that's why his games do not include pointless underpromotions (and hopefully mine don't either.)

I once figured out that it was okay to underpromote to a B or N instead of an Archbishop, if other type(s) of promotion caused a problem for some legal position(s) I dreamt up, in the case of my 10x10 Sac Chess variant, even, which has 10 possible piece types to promote to(!). Unfortunately, I didn't record the positions I thought of. If I think of examples of any of them later, I'll try to get around to posting them. In the case of avoiding a Chancellor promotion, for example, both a R or N promotion instead might still cause some sort of a problem that underpromoting to a B would avoid (though not if an Archbishop).

I am encouraging promotion to weaker pieces on earlier ranks (technically not underpromotion I guess) but I am not sure why this principle does not catch steam :)! To me it seems extra choice and that is always good provided there are not clear inconviniences. And I see none :)!

And being at the topic of promotion, I'd like to bring a discussion from this topic on. In CWDA I'm quite uncounfortable with pawns promoting to pieces from both starting armies (where the case). That is because well then the armies are less "different". The reason given by Betza is very sound. The pawns are then different and that difference should be accounted for. True. But for future CWDA if they are on larger boards (normally with more pieces) there is more room to optimize so different promotions for pawns would not be an issue !

If promotion is only to captured pieces, as in Grand Chess, then underpromotion enables promotion when there are no captured compound pieces to promote to.

@Fergus,

In the era of computer chess promoting to captured pieces does not seem that relevant anymore. Your Gross chess idea on promotion is great. I had saw it once, but forgot the game and author and somehat use it in apothecary (the promoting to different things part not the captured pieces part). In the meantime I had read it again.

Here's a possible position from Seirawan Chess where White's best move is clearly 1.Pd7xc8=B, since promoting to an Archbishop instead would allow a possibe stalemate after 1...ab8-d7+, if White captured the enemy archbishop either way. Similar positions for other variants such as 10x8 Capablanca Chess could be dreamt up.

If your promote to a, after 1...ab8-d7 you can easily have 2.a c8-b7 with check and afterwards capture the enemy archbishop with your other one and then your are out of the woods :)!

After White's pawn takes the Queen and promotes to an Archbishop, Black has only four moves available. Two of these moves would expose it to capture without any significant consequence for White, and another would allow White to move the Archbishop to b8. The remaining move is to go to d7, checking the King. If White responds by taking the checking piece with either Archbishop, the resulting position is a stalemate. If White responds by moving the King, Black can take either Archbishop en prise. If White responds with a block on e6 from the Archbishop on e6, Black can exchange Archbishops. This might still be favorable for White. If Black takes the Pawn at b5 instead, White can still probably force an advantage. So, it looks like White could still win if the Pawn promotes to an Archbishop. The advantage of promoting to a Bishop is that White can win quickly and decisively. If the Archbishop moves to d7 for check, the Bishop can take it without causing stalemate. If the Archbishop makes its only safe move to c7, then the Bishop can safely check the King from b7, forcing the King to move to b8. The Archbishop can then move to d7 for checkmate.

I think I could have replaced the White A/f8 with a N in the diagram of my previous post, and still 1.Pd7xc8=B would be the best move, though I chose to be 'safer' by using an A just in case it mattered (not only that, but I got to use one more fairy chess piece, too).

Whether the White piece on f8 is an A or a N, a question might be whether the initial position could ever arise after some logical previous move(s) (i.e. a 'prequel' of some sort). At least the initial position could have legally arisen, even if it had to be via bad play at least on Black's part. Perhaps putting White's K on a different square on the h3-c8 diagonal at the start might allow for a logical prequel somehow, if it's necessary/possible. [edit: if a White N is initially on f8, perhaps having a Black R on c8 instead of a Q could better help in this regard]

Here's a possible position from Seirawan Chess where White's best move is clearly 1.Pd7xc8=N, since promoting to a bishop or archbishop instead is meet by 1...ab8-d6+ and if the archbishop is taken by a White archbishop then stalemate occurs.

@Kevin Pacey

Nice one!

Promote to a Chancellor

@ Greg: I thought of a way to underpromote to a Chancellor just this morning, but felt it was too easy and not what you were initially doubting was feasible in the way of a justifiable underpromotion. I'll see if I can remember what I thought of.

Meanwhile, here's another Seirawan Chess possible position, this time with an underpromotion to a rook (I feel I thought of some other example position that was more crystal clear long ago, though); White's easiest way to win (if nothing else) is 1.Pe7xd8=R since if White chooses a B, Archbishop or a Q instead then 1...ac8-g4+ allows Black to at the least bother White for a while, since taking the archbishop stalemates Black. If White chooses a Chancellor instead then 1...ac8-b7+ may prolong the struggle considerably since taking the archbishop with either Chancellor stalemates Black.

Here's a possible Seirawan Chess position showing underpromotion to a Chancellor (best option, though not the only way to win). After 1.d7xc8=C+ ka7-b7 2.Cc8-e7+ White mates in two more moves. This appears to be faster than if White chose an Archbishop or R, while choosing a Q would stalemate Black.

To complete my examples of justifiable underpromotions in Seirawan Chess, here's a diagram where the move 1.Pf7-f8=A+ is the only way to win, underpromoting to an Archbishop. Note that if Black's king were initially on a8 (for example) then underpromoting to a Chancellor would be the only way to win.