In Combat, whether it be single-contest or round-by-round, each party rolls their dice pool and adds together a number of dice equal to the smallest dice pool between all participants. Whoever rolls the highest total wins the round.
If there is a tie, the character with the smallest dice pool wins the round unless their opponent's dice pool is at least 4 times greater than theirs, in which case that character wins. If the dice pools are of equal size, the character who got the single highest die roll wins the round. If all characters' single highest dice are equal, look at the next highest, and so on until the tie is broken.
For example, if a Bumbling Barbarian Hero (4) swung their hammer haphazardly in the direction of a Scheming Dracolich (9), the dracolich would roll 9 dice, but only keep the highest 4, while the barbarian would roll 4 and add together all of their dice.
This mechanic significantly diminishes the gap between Cliché ratings while still giving the party with the higher Cliché a distinct advantage. In the example above, the Bumbling Barbarian Hero (4) has a ~10% chance of knocking the Scheming Dracolich (9) down a peg, whereas if the group was deciding combat by single highest die, they would have a ~57% chance, and under standard Risus combat rules, they would have a ~0.25% chance.