I accomplished this by thinking of what I might want to throw, deciding that the computer would anticipate this and try to beat it. Factoring in a few levels of reverse-reverse-reverse psychology, and then picking the choice of the three that I thought of picking the least.
But really, I think even on expert mode, it largely comes down to luck.
I’d like it a lot better if you could see what the computer was thinking after you threw.
I did notice that repeating yourself to avoid fake randomness does not work on the full bot. Especially repeating yourself even after you lost. Those would be go-to strategies in the real game. I also note veteran mode doesn’t assume you will throw rock (and thus throw paper), as I would assume. That is the most common. But it seems to throw its first move randomly.