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Jeremy Lennert wrote on Fri, Sep 14, 2012 09:04 PM UTC:

The alibaba has similar qualities to a knight (leaping piece, similar range, same number of moves), but its movement pattern confines it to 1/4 of the board (similar to how bishops can reach only 1/2 the board, but moreso).

Betza suggested somewhere in this article on the Crooked Bishop that a non-colorbound piece would be 1.1 to 1.2 times more valuable than its colorbound equivalent, which means a colorbound knight ought to be worth ~87% of a knight. But the alibaba is colorbound "twice", which I would imagine warrants at least applying the penalty a second time, giving ~76% of a knight--a very good match for your estimate. (Though I wouldn't be surprised if "double-colorbound" turned out to warrant a greater penalty than that.)

However, Betza appears to have been talking about pairs of colorbound pieces on opposite colors (like the bishops in FIDE Chess), which are generally believed to be more than the sum of their parts. So that estimate is probably only good if you start with 4 alibabas, one on each "color"--they will be less valuable individually, especially in the endgame (when it becomes harder to find targets on your own "color").

Finally, if you are playing with bishops, rooks, and queens, I would guess that the knight is also benefitting from a "stealth" bonus, due to its ability to threaten these pieces without being threatened in return. The alibaba can only do this if there is another piece in the way (that it can jump over but the other pieces can't), and so I would guess that its true value would be a little bit lower again than the estimate above.

So, in summary, I would guess than 3/4 of a knight is close, but probably a little too high, and would expect the value to fall significantly in the endgame or if you don't get a complete set.


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