NR****Q* & *Q****RN

One of my first games on Chesscube (see How I Spent My Free Day) began with the setup shown in the diagram (SP362 NRKRBBQN). I had the Black pieces and my opponent opened 1.f4, attacking the Pawn on a7 with the Queen.

It's not obvious how to defend the a-Pawn. The move 1...Nb6 cedes the center after 2.e4. This might be playable, but the rapid time control left no time to work out the nuances. The move 1...a6 has the same defect as the move 1...Nb6, without doing anything for Black's development. Ditto for 1...b6 with the additional disadvantage of blocking the best square for the Knight on a8.

SP362 NRKRBBQN

After 1.f2-f4

I decided to sacrifice the a-Pawn with 1...d5. It's not an important Pawn and if White captures it, Black gets some initiative with 2.Qxa7 Nb6 3.Qa3 Ra8, which is what happened in the game. After 4.Qb3, we continued 4...e6 5.a3 Bd6 6.Bf2 Nc4 7.e3 Na5 8.Qc3 Ng6 9.Nb3 Nxb3+ 10.Qxb3 Ba4 11.Qc3 f6 12.d3 Qf7. Although Black hasn't recovered the Pawn, the initiative and better development still offer some compensation. Now White made a mistake with 13.Rd2, giving up the option of castling O-O. After 13...O-O, I was happy with my game and eventually won.

Getting back to the sacrifice of the a-Pawn, I had already seen the tactical trick involving the Queen vs. the Rook & Knight in another game, but couldn't remember where. I wondered how many such positions there are in chess960, queried my database of start positions to find out, and discovered that there are 18 positions with the N, R, and Q on the a-, b-, and g-files. Since each of those positions has a corresponding twin (N, R, and Q on the h-, g-, and b-files), there are exactly 36 positions with a similar tactic, or 3.75% of all positions.

An analysis like I did in Introduction to Chess960 Geometry, would tell me why there are 18 positions of the type NR****Q*, but I'll leave that for another time. Right now I'd rather know the best way for White to play after the sacrifice of the a-Pawn in the game, and I'd like to know if 1...Nb6 is playable.

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Later: In fact, it's not difficult to derive that there are 18 positions of type NR****Q*. Of the five unassigned squares, one Bishop can be placed on three of them and the other Bishop on two. That leaves three squares to place the second Knight. The King and second Rook must then be placed according to the rules of chess960: King between the Rooks. The arithmetic is then 3 x 2 x 3 =18.