White's option of Qh3:
The stats on it's regularity are actually pretty easy to work out:
xxxxxQNN = 06
xxxxxQRN = 18
xxxxxQRB = 18
xxxxxQNB = 12
Therefore total probability = 54*2/960*100 ~ 11% ~ 10%!
But how often is Qh3 actually worth it, out of that total approximate possibility of 10% for Qh3 showing up on the board? Here is a subdivision of the above 10% of possibilities for Qh3, with a pin of the king on c8:
xxKxxQNN = 2
xxKxxQRN = 4
xxKxxQRB = 3
xxKxxQNB = 4
Therefore total probability = 13*2/960*100 ~ 3%!
The basic problem with Qh3 is not just that it is strategically dubious, but that it only ever shows up in one in ten games, and when it does, it probably is not a good idea for these reasons:
- To play Qf1-Qh3, g3/g4 must be played, but most likely, the only time that g3 is worth it is when a bishop is in the corner, but that only ever shows up in practice in roughly 6% of games. Even then, out of that 6%, there are probably no occasions where it is worth playing (see below).
- The queen can threaten to capture the edge pawn on h7, but that seriously misplaces the queen. Yes it is true that if the h7 pawn falls, black cannot castle g-side into safety and therefore black's strategy is disturbed, but the black king will be no closer to the area than e8 (otherwise h7 cannot be undefended), and therefore black will probably castle c-side into safety while white has wasted a lot of effort on the h7 pawn.
- The queen can threaten a pin on a king, but that is almost always parried. The only justification for Qh3 is if by pinning the king, black's development is disturbed. The question is though, will black be disturbed more than white sidelining the queen on h3?
- The queen can move from Qh3 across the third rank into a better position, but that costs a third tempo and usually the queens lateral movement is impeded because other pieces are sitting on the the third rank to block her.
- If a rook is on g1, then a pawn move g4 is a possibility, but again this only ever happens in roughly 7% of all Chess960 games. That said, pawn to g4 could well be good, but when would Qh3 ever be good to follow it with?
Chess960 insiders tip: If you want to play the opening quickly, you can almost totally disregard the move Qf1-Qh3 if it ever shows up as a possibility. This probably also applies to it's partner Qc1-Qa3.