The New York Times recently posted about an AI-backed Rock-Paper-Scissors game. I have written about it before and some have disagreed with me.
The AI version learns from past games and uses that data to predict future moves. There are two modes: “Novice” and “Veteran”. The former only learns from the rounds you’ve played with it, the latter draws from all previous games that have been played with it.
If you are someone, like my naysayer in the link above, that buys into the illusion that you can adopt any kind of real strategy in Rock-Paper-Scissors, the AI will smoke you. If you even pay attention to what the computer (or any opponent) does at all, you are buying into the lie and will become predictable.
As that page mentions, “[a] truly random game of rock-paper-scissors would result in a statistical tie with each player winning, tying and losing one-third of the time.” This is true assuming that both players are playing randomly, ignorant of one another’s choices. If one player adopts a random strategy (“plays irrationally”) while the other one plays with a strategy (“rationally”), the player with no strategy is unaffected, but the player with the strategy will be at a slight disadvantage.
A given choice in RPS is identical to the other possible choices — each one can win, lose, or tie the round with equal probability. The choices have no inherent value until the opponent’s choice is revealed. When both players play rationally, they attempt to out-think what their opponent will pick, and assign a weight value to the available choices based on that prediction. The thing to consider here is that the weight assigned is entirely based on the assumption that the opponent is selecting something on a rational basis. By selecting your choice randomly, you completely negate any advantage the other player would have gained through their strategy; not only that, but there is also a subtle cumulative penalty that they incur for as long as they believe you are still acting rationally.
When playing Texas Hold’em with some friends, a few years, ago, I realized that I was outmatched on skill and experience, so I instead adopted a completely irrational strategy – I would bet erratically, irrespective of what I was actually holding (unless I had a REALLY strong hand) and I ended up winning. Granted, my friends aren’t professionals, and that strategy would probably fail against real pros.
The fundamental difference between Poker and RPS is that RPS has no memory of previous rounds, unlike Poker. Each round in RPS may as well be a roll of the dice, a completely separate statisical event. You can play completely randomly and are not penalized cumulatively, like you would be with chips in Poker.
The screen-cap above is a small sample run I did against the computer, using a random number generator to make my choices. In a range of 1-3, 1 is Rock, 2 is Paper, 3 is Scissors. No matter what the computer plays, stick with the random protocol. You might as well just hide half of the screen, so that you aren’t tempted to make a “strategic choice.” After 40 rounds of random choice, my final record was 16W, 11T and 13L. Admittedly, the sample size isn’t very large, but I think it at least provides some good support to my argument: regardless of whether or not your opponent is using any kind of strategy, a random play is strictly better, and the more rationally they try to play the worse they do.
You do not get an advantage by playing random against a person who is using “
stradegystrategy.” If either person plays at random, the expectation for W-L-T will be 1/3-1/3-1/3. Why? If you choice is truly random, it is INDEPENDENT of their choice. The other person could pick rock every time and the distribution would still be uniform.jeff, I think you may be misunderstanding me.
Of course a random strategy should only ever yield a draw amongst two random players — the “edge” I’m talking about is more that you are depriving your opponent of whatever strategic edge they would be getting by doing some sort of “strategy”.
The idea that a random strategy gives you an advantage is predicated on the assumption that using a “rational” strategy (choosing a triplet based on reading your opponent) would give you an advantage otherwise. It’s a COMPARATIVE gain, not a statistical one.
For example: if you were a player with an obvious tell, you would be disadvantaged to your opponent because they would tend to pick better against you — but adopting a truly random strategy negates that advantage they had (thus increasing your chances of winning from sub-33% to 33%)
The bottom line from my OA is simply that it’s not possible to adopt a “strategy” in RPS that is more effective than 33% simply because the opponent can always choose to play randomly, which negates whatever edge you would have otherwise had.
There is no ‘slight disadvantage’ what so ever for adopting any strategy when facing a random opponent, it’s easy to understand how if you imagine that the strategic choice is made before the random choice. There is only a disadvantage for adopting a strategy if your opponent has a strategy that encompasses your strategy. Playing randomly is essentially ‘opting not to play’ – that way you can’t lose but you can’t win either.
Wow two comments within a week on the same post? did I get linked from somewhere?
The “slight disadvantage” I wrote about is the fact that you lose the vaporous advantage you PERCEIVED you had by adopting a strategy.
The fact that you don’t lose any REAL advantage by playing a strategy against an opponent playing randomly simply supports the idea that strategy in RPS is not actually possible.
Ignoring that most of the World RPS stuff is at least a little tongue-in-cheek, your claim that strategy in RPS is a waste of time is simply stupid. You are correct that random play results in 1/3 wins, ties, and losses, but as Dmytry said, at that point you’re opting not to play. If playing with a strategy puts you at a disadvantage, then how does this AI “smoke” you, unless it employs a strategy of its own?
If you check the AI’s logic, you note that it goes through your throw history, looking for what you’ve done in sequences. If you restrict yourself to the gambits, then yes, you are going to be stomped. RPS strategy is not solely about gambits, though, and far more about guessing what the opponent will do based on what you know about them. If you know that the AI will guess based on your past sequences, then you can form a counterattack based on that. Throw six Rocks in a row, and you’ve weighted the computer so hard into expecting you to follow up a Rock with another that you can easily punish their expected Paper on the round after you play ANY Rock, win or lose.
That ties back into the gambits. If you use, say, a RPP gambit frequently, then people will obviously expect that of you in your matches and play to counter it. But then, you know people will adapt to it, so if you throw Rock and then Paper, and they just know you like the gambit, you play a Rock as your third throw for a free win. And THAT is where the strategy of the game comes in.