Of Roshambo, Bram writes:

A tempting strategy is to make your bot 'wimp out' and start playing randomly if it isn't doing well. Tournaments play two programs against each other many times with no persistent information between runs to keep this strategy from being effective.

Going random when you're down sounds like a recipe for staying down. How about going random any time you get a modest lead, in the hope of keeping it?

Me, demoncrat, and another friend have had some ultra-simple Roshambo tornaments recently, with robots written in idel. The game is included in the Idel distro if you're interested in having a crack.

You can see demoncrat's first-generation champion to get the flavour.