Thread by @gengelstein

So this post engendered a lot of conversation yesterday. We laughed, we cried - but I'd like to delve into this a bit deeper.

Yes, I'm going to drop math on y'all.

(a thread)

https://twitter.com/gengelstein/status/1228714094808702978

First, I think that a lot of the differences of opinion are about terminology. Many of you said - no that's uncertainty, but it's not randomness.

In "Uncertainty In Games", Greg Costikyan argues convincingly that every game has uncertainty. If it doesn't - if the path and outcome of the game are known in advance - then it isn't a game. So just calling it "Uncertainty" is completely unhelpful.

mitpress.mit.edu/books/uncertai…

Costikyan classifies a variety of sources uncertainty like: Performative (flicking, or throwing a ball), Hidden Information, and Analytic complexity. He also includes Player Unpredictability and Randomness as two others, which sound like what we are looking at.

However, his "Player Unpredictability" examples are not what we're talking about. They include trading in Catan, or which role to choose in Puerto Rico. His category "Randomness" includes roulette, poker (card deal), and Magic: The Gathering card draws.

IMO Simultaneous Action Selection is closer to Randomness than Player Unpredictability in his taxonomy. The example I use is Rock/Paper/Scissors. RPS is a random result generator. Some argued that RPS isn't random because you can tailor your strategy based on your opponent.

Yes, that's true - humans aren't great random number generators. However, while software that takes advantage of these tendencies can perform better than chance, it's not that much better - they win 52% of the time instead of 50%. For all practical purposes it's random.

Others argued that the reason that RPS is random is that there's no situational information. Every choice is equally likely. In a game, if I'm picking between actions I need to consider the board situation. So you, as my opponent, can try to predict what I will do.

But this is a mirage. An example: Let's change RPS so that if you win with Scissors you score 2 points. If you win with Rock or Paper you score 1 point. This simulates having a choice that better advances your game position.

So does this add more psychological interest to the game? Maybe. Probably. But it doesn't change the fact that math can give you the answer. Game theorist John Nash developed the idea of the Nash Equilibrium. This is a strategy that cannot be exploited.

If either player moves away from their Nash Equilibrium, they will reduce their expected value.

en.wikipedia.org/wiki/Nash_equi…

For basic RPS, the Nash Equilibrium is 1/3R, 1/3P, 1/3S. In our modified game, you can work through the math and figure out the optimal strategy.

And for scissors being worth 2 points, its 50% Rock, 25% Paper, 25% Scissors.

So yes, it changes the texture of the game. But the optimal play is still to make a random choice, but weight the options. IT'S STILL RANDOM. Weighted randomness is still randomness. In SAS the best strategy will always be a weighted random selection between the choices.

This is related, by the way, to the fact that people cannot outperform the broad stock market indexes on a consistent basis by picking their own stocks.

Some will argue that people are not capable of making a random selection. And that's sorta true, but there are ways to do it.

Many poker books recommend that, for example, if you want to play a hand a different way 20% of the time, when the time comes to make your decision look at the second hand on your watch and use that as your RNG. You can (and probably should) do the same thing with SAS.

However I agree that psychologically SAS feels different than rolling a die. But rolling a die also feels different than flipping a card. However they are both random.

So I'm happy to try to come up with a name for this type of selection, to capture this difference in feeling. "Yomi" is the name for the feeling of trying to outguess your opponent, Princess Bride style. But I don't think it quite fits.

Maybe just keep things simple and call it "Simultaneous Choice Uncertainty".