On Monday, Wade throws rock
Last updated 2/6/2024 at 11:17am
Just what is a game? Before I fully launch into my article series covering local games, maybe we should get that straight. For the past six years or so, Wade and I have played Rock, Paper, Scissors at Sisters Athletic Club to see who buys coffee, and it’s often a spectator sport, with the staff and regulars looking on as we stage our showdown. For the benefit of whoever misses it, the winner loudly praises the superior taste of that day’s coffee. And might even sip it loudly.
With savor. In the loser’s face.
You’re probably not impressed. How petty are we? And is Rock, Paper, Scissors even a game? After all, there’s no strategy, no skill.
Ah, but you see, Wade throws rock on Mondays… except when he remembers that I remember that he throws rock on Mondays, in which case, he throws scissors, but I know he knows that I know, so sometimes I throw rock on Mondays. My longest win streak against Wade is nine days in a row, the odds of which are 2 to the ninth power, or 1 in 512. But, wait, there’s more. Once, we played nine ties, before I won the tie-breaking tenth game that day. The odds of a tie are 1 in 3, which means the odds of nine ties in a row are 3 to the ninth power, or 1 in 19,683. At random odds, if we played every day, we would average a contest like that once every fifty-four years!
There must be some strategy and skill involved. Is there a pattern to Wade’s choices? Does he have a tell when he’s about to throw rock? (Do I?)
A game involves not only a system, which may lean one way toward pure strategy or the other toward chance, but also a player or players within that system. Human limitations make a game a game, just as much as the rules do. Consider Tic-Tac-Toe. Is that a game? For sure it is to young kids, but for those who’ve mastered it, the game always results in a tie — that is, the same activity switches from game to solved puzzle. Game developers widely recognize Rock, Paper, Scissors as the simplest form of a balanced game. If it had only two elements, then a rational player would always choose the winning one, so it takes that third element to put the contest in doubt.
In game theory, a strategy that maximizes a player’s expected payoff is identified by what’s called equilibria. There are a few ways to understand this concept. One is to compare equilibria to a set of social guidelines that people would generally follow even if they weren’t enforced by laws, like yielding at a stop sign. You don’t want to risk getting hit, and you assume the same attitude of other people. Cheating this system is generally a bad idea, given the risk of a collision stacked against the reward of saving a few seconds’ travel.
Equilibria are often explored through the thought experiment called the Prisoner’s Dilemma, where two accomplices to a robbery are caught by police and interrogated separately. Let’s say that if they both rat each other out, they will get three years in jail. If neither rats, they will each get a year in jail. And if one rats but not the other, the one betrayed gets ten years and the rat goes free. If the goal is to minimize collective jail time, then neither rats, resulting in a total of only two years served. However, mathematician John Nash observed that the stable unilateral strategy is to rat, because it maximizes your payoff no matter what your opponent does. In Tic-Tac-Toe, the Nash equilibrium is the set of moves that you mechanically follow until a tie results, because you must assume the right move is mutually obvious to you and your opponent.
Equilibria can help you understand the systemic aspect of games, but remember that games must involve people. The equilibrium state in Rock, Paper, Scissors is purely random play – within the abstract system of the game, there is no other strategy that can reliably improve your chances -- but that’s no fun, and what’s more, unless your opponent rolls dice or coins to determine what to throw, they may very well fall into an unconscious pattern, one that you might recognize.
Imagine a guy so transparent that he becomes a solved puzzle. Would you just go ahead and beat him over and over? It depends upon the game you’re playing. You can’t expect a guy to pay for coffee a hundred times in a row before bagging the whole thing. Sure I’d like to never pay, but over the course of a few years, I’ll take a thirty-percent discount — or even a bit less — over nothing.
Life is a game, so play it long.