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Comment by beckerdo | Hacker News Reader

"They're all legal. That is, reachable from the starting position in a valid game of chess."

Help me out on the legality of some of these boards. I see excess pieces on many boards (for example, 2 or more queens, 4 or more knights of one color).

Are these considered legal by pawn conversion?

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The 10 queens situation is obviously impossible, but so is having 2 white queens and black has all of his pawns on the starting squares.

It's more difficult than you're thinking. If white has 6 dark squared bishops, they you know that he promoted at least 5 pawns on dark squares so one pawn must have taken a piece since it's promoting on a dark square instead of a white one. Not every board set-up will have enough missing pieces that 5 pawns can maneuver to get promoted on dark squares.

So assuming all pawns of one color are converted, I guess 9 queens or 10 knights would be a legal, if unlikely, board setting, but 10 queens or 11 knights are not?

Yes. If you only have eight pawns, then you can only get eight extra pieces as a result of promotion.

Yes. You do not need to choose a queen when the pawn reaches the opposite side.

Were redundant choices culled? No point in tracking all variations of pawn > queen/rook/bishop when one includes the moves of the others.

There is sometimes a point when you need to avoid giving stalement, like in the famous Savedraa study [1] or the vastly more intricate Babson task [2].

[1] https://en.wikipedia.org/wiki/Saavedra_position

[2] https://en.wikipedia.org/wiki/Babson_task

Sometimes the queen having both rook and bishop moves is a liability. There are positions (real positions from real games, not merely hypothetical ones) where promoting to a queen results in immediate stalemate, while promoting to a rook wins the game.

So those choices are not redundant.

There are even times when this is the right move. Sometimes you can put them in check by promoting to a knight, for example, where a queen would not. Common in beginner puzzles.

This is a very nice illustration of this, where a player had to turn off autoconversion to queen on the last seconds to win the game: https://youtu.be/HFG8pCInJKw

Your comment reminded me of this: https://www.youtube.com/watch?v=8wCJalNkTEI

Text: https://en.chessbase.com/post/solution-to-a-truly-remarkable...

Another situation where you would want to convert to something other than a queen is when doing so would result in a stalemate.

Pawn promotions are legal moves, yes.

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