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I'm very curious about games similar to alquerque, where all but one slots are filled.

Take the picture below. This appears to me (and maybe I'm wrong) that this gives an opening advantage to the second player. The moment the first player moves a piece to the center, it gets inevitably captured by the second player.

So, out of curiosity, do we know if Alquerque is a fair game with perfect play (meaning, both players with perfect play can force a draw), or if it is biased towards the first or the second player?

I don't find much in terms of game theory and research on this.

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  • Don't know the answer to your question, but it's certainly solvable considering that checkers is more complex from a search-space standpoint and is considered weakly solved.
    – DenisS
    Commented Sep 2, 2021 at 17:17
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    Part of the issue here is that there is not just one game under question. "Alquerque" is the name given to several variations of the game (use of Sultans, rules on Sultans, whether captures are mandatory, whether backtracking is allowed, etc.) So any "solve" would be for just one variation. But, as it is simpler than draughts (in most variations), it is solvable. To date, it has not been solved (cf: it is not on the list of solved games at Wikipedia)
    – L. Scott Johnson
    Commented Sep 3, 2021 at 11:52

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While I cannot find a formal proof, Alfonso X's "Libro de los Juegos" offers an anecdotal report that the solution to the game is a tie:

if both players known how to play it, they can both tie the game.

Alfonso X was king of Castile in the 1200's. One of his projects was a book on games called "Libro de los Juegos", which was a Castilian translation of an Arabic book on games. This book is the earliest (surviving) description of Alquerque. The above quote is from an English translation of this book (in this translation, the game is referred to as "Twelve Mans Morris"). The book also makes your point about the first player having a disadvantage in non-optimal play:

he one who plays first has a disadvantage because he is forced to play in that empty space

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