The coordinates above are incomplete! Solve the following puzzle to get the final coordinates.
Following the standard rules of chess. It's White's turn to move, and the right move will lead to checkmate on White's third turn.
Find the correct first move and move the game piece to that square. Take the number to the left of that square and call it XXX. Take the number to the bottom of that square and call it YYY.
Based on the piece you moved, select the multiplier from the following table and call it Z:
Multiply XXX by Z and add 9, and call the result LAT.
Multiply YYY by Z and subtract 7, and call the result LON.
The coordinates for the cache are N 37° 13.LAT W N 121° 46.LON.
Special Notes: Black pawns move from the top toward the bottom of the board; so if it were Black's turn first, Black would be able to capture White's bishop. If Black is unable to move but is not in check, the game is a draw, not a win.
The cache is a 35mm film canister. The original container came from Take and Place a Cache by Marky & Joani and contained a couple of Thai coins and a couple of San Francisco souvenir pennies.
Leprechaun convinced me that I should increase the difficulty rating to 4 (per the ClayJar rating system) because knowing how to play chess is "specialized knowledge"--you're welcome to let me know what you think the difficulty rating should be, and maybe I'll adjust appropriately based on feedback.
Thanks to targetdrone for being the first to solve the puzzle and verify my calculations.