Key idea. Count how many moves the game must contain.

1. There are \(10+15+20=45\) stones and initially three piles.

2. Splitting one pile into two increases the number of piles by exactly 1. It does not change the number of stones.

3. The game ends exactly when every pile has one stone. If any pile had more than one stone, it could still be split.

4. The final number of piles is therefore 45. Going from 3 piles to 45 takes exactly \(45-3=42\) moves, regardless of how the splits are chosen.

5. The first player makes the odd-numbered moves; the second makes the even-numbered moves. Move 42 is made by the second player, leaving the first unable to move.

Remember. Sometimes the number of moves is fixed, so no clever move can change the winner.