Capturing Races in Go (Semeai): How to Win Them

Sometimes neither of two groups can make eyes, and the only way for one to live is to capture the other first. You play Black.

Step 1 of 4

Count the liberties
Black's three stones on B9, B8 and B7 have no eyes and no way out. Their liberties are A9, A8 and A7. White's three stones beside them are just as stuck, with D9, D8 and D7, marked with stars. Whichever group runs out of liberties first is captured, and the other lives. This is a capturing race. Count both sides before you play.
Three against three
Three liberties each, and it is your move. Fill White's liberties one at a time while White fills yours. Moving first, you get there one move ahead.
Your move
Win the race: capture White's three stones.
Outside liberties first
Now the groups share a liberty, C9. It belongs to both, so filling it takes one of your liberties too. Your stones have A9, A8 and C9. White's have C9, E9 and F8. Fill White's outside liberties first, and leave the shared one for last.
Your move
Win the race against White's stones on D9, D8 and E8.
Who wins?
Black's stones have two outside liberties, A9 and A8. White's have three, E9, F9 and G8. They share C9. It is Black's move.
Question

What you learned

In a capturing race, count both groups' liberties before you play.
In an even race, the side to move wins.
Fill the outside liberties first. A shared liberty is one of yours too.
Count the moves each side needs to capture, with shared liberties counted for both.