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Nothing Beats Rock


Earlier today, Aubrey Hesselgren linked to a Numberphile video about Rock, Paper, Scissors, with the tongue in cheek assertion that all competitive games “reduce” to RPS:

He went on to make it clear that he was being ironic, but admitted that the thought did haunt him a little:

…although, admittedly, it has been a thought that has haunted me. genuine nightmares. “oh my god! all games are same! This is what i am doing with my life? this is all there is? ahh!?”

I know how he feels. The fact that we are able to map the abstract structure of some games onto others is kind of spooky. For me, the nightmare lurking beneath the surface of every strategy game is Nim, the take-away game played by the tragic, existentially glamorous characters in Alain Resnais’ Last Year at Marienbad. (I may have gotten this nightmare from trying to read books that I’m not smart enough to understand.)

But, actually, watching that video had the opposite effect on me. And here’s why:

First of all, Numberphile is awesome. I like everything about it, but mostly I like the way they always write equations on big sheets of brown butcher paper using sharpies.

This particular video was about a paper from some Chinese game theorists who studied a large number of iterated R/P/S games. They observed that, on average, players don’t use the “perfect” strategy of randomly selecting a move. Instead, there are noticeable patterns based on the outcome of the previous round – there is a slight tendency to keep the same move after winning, and to pick a new move after losing (win-stay/lose-shift). This general tendency allows a savvy player to do better than average by assuming her opponent is playing win-stay/lose-shift and playing accordingly.

Sound familiar? Yes, this is basically Donkeyspace! Although neither the scientists nor Numberphile seems to recognize the larger implications.

What are the larger implications? Essentially, that the “fancy” strategy that takes advantage of the typical tendencies of average players is actually just level 1 of a virtually endless process of adaptive strategic responses. Yes, I can do better than average by assuming my opponent is playing win-stay/lose-shift. But I can do even better than that. Sometimes my opponent will be playing the strategy that beats w-s/l-s (let’s call it win-stay/lose-shift prime, or w-s/l-s’), I can change gears to take advantage of her (by playing w-s/l-s”) and the sooner I do, the better. Sometimes my opponent will notice that I’m playing w-s/l-s” and change gears back to perfect random (rnd). That’s ok, w-s/l-s” does fine against rnd (as good as possible in fact). But occasionally I’ll be up against an opponent who will notice what I’m doing and change gears to w-s/l-s”’. I need to be on the lookout for that.

My real goal is to efficiently discover what I’m up against – a complete fish who always plays rock, a standard donkey playing w-s/l-s, a medium sized shark playing w-s/l-s’ or a killer with the capacity of identifying my own gear-changing strategy and adapting to me.

This changes Rock Paper Scissors from a “solved” game with a known perfect strategy, to a very subtle game of reading my opponent. The first step of this reading is knowing the overall tendencies of the player population I am in (the local meta) as outlined in the paper. But this is just step one, because any particular opponent in this population might be a fish, a donkey, a shark, or a killer (or a killer camouflaged as a donkey.) The real game is how quickly and accurately I extrapolate from my opponent’s moves to understand her true strategy, which will sometimes include a gear-changing strategy based on her interpretation of me. (Hm – maybe we can develop an Optimal Meta Adaptation Response that will even give us an edge on the killers…)

You see where this is going, right? Even if all competitive games did ultimately reduce to R/P/S under the hood, we would still be at the bottom rung of a very tall ladder. (As long as we have the right kind of iterated, pair-wise tournament structure.)

But it’s even better than that. Because imagine this chaotic dance of mutual signal-processing and gear-shifting adaptation taking place around a core game that isn’t even solved – where, unlike R/P/S, you don’t have the base level of perfect-random as a starting point. That’s where competitive games reside, a turbulent swarm of moves and counter-moves, some random, some overloaded with meaning, some listening to hear the shape of the whole, the whole flock turning and turning, searching through problem-space, and searching through search-space, and beyond.