To me (and my kids), there is no greater game than Roshombo, aka "Rock Paper Scissors."
Now I find that there is a whole Roshombo cult out there. Don't believe me? Just search and you shall find.
And presented here, the Advance RPS Rules.
I am a Gambit player, always have been, but now I know that there are names for the various gambits. Generally, I find something subtle like Fistful of Dollars works well against aggressive players, but my kids will nearly always fall into the trap of the Avalanche.