Alternity is an old game that was put out by TSR for science fiction roleplaying. The basic mechanic involved rolling a control die (a d20) and a situation die (some other dice). The results of each die were combined to determine the results. Here's how to apply this mechanic to Risus.

Note: This alternate mechanic somewhat levels out the differences between cliché levels. Some might like that, some won't. No one is forcing you to use this, but it will give you something to do with all of those funky dice you might have.

This mechanic works like this for Risus: Roll a d20 and a modifier die based on the rank of your cliché.
*Using this method effectively removes the When Somebody Can't Participate section of the rules. Everyone is given at least a d20 to roll.

Using this method does require a shift in the standard target number scale.
If you wan't to see how the probabilities break down, check out this file.

If you use this method, I recommend an agreed upon die to use for all pumping/double pumps (such as a d6). So, if you pump your Exiled Wizard King [4] cliché by 2 die (i.e. double pump one die), you'd roll d20 + d10 + 2d6 (at the end of the round, your effective cliché level would be Exiled Wizard King [3] and you'd be rolling d20 + d8 next round (assuming you won)).

If your cliché loses a die, you will end up rolling a smaller die for the next round (d8 goes down to d6, etc.). You still lose of you get to 0 (the 0 Rank is in the table above to handle conflicts where someone can't participate (if they lose one round, they are done)).

This option doesn't work very well with Funky Dice.

If you wish to increase the differentiation between cliché levels, feel free to change the control die to a d6 and change the target number scale back to the standard Risus scale.