Your dice are paired against your opponent's, from highest to lowest.

In the first pair, red's 5 beats blue's 3.
Blue loses its die.

In the next pair, red and blue are tied.
Both dice are kept for the next round.

In the final pair, red keeps its die.

In the second round, red has 3 dice, and blue has 1.

In the first pair, blue's 6 beats red's 2.
Red loses its die.

Red keeps this die for the next round.

Red keeps this die too.

In the third round, red has 2 dice, and blue has 1.
In this pair, red's 5 beats blue's 3.

Without any dice left, Blue loses the battle.