You could just play rock paper scissors three times and use the results as bits for d6? Maybe dropping 111 and alternating who is 1?

Edit, I realize you’d have to drop 111 and 000 to get 6, not sure what I had in mind in the original, either way it balances. It’s also nice because I don’t think you can intentionally lose rock paper scissors.

There actually are techniques to win (and presumably lose) rock paper scissors more frequently than random due to psychological factors that make player choices somewhat predictable.