Oh man this is an awesome talk, thanks for linking!

Quick excerpt:

> The player said “I lost a 2:1 battle, and I get that, I know I should lose that sometimes.”

> I said, okay, so what’s the problem?

> He said “well, I lost a 20:10 battle — what’s up with that?! 20 is so much more than 10!”

It seems reasonable to assume that's it's instead something like 10 simultaneous 2:1 battles, and you need to win a majority of them. That's very different odds than a single 2:1 battle.

He seems stuck on interpreting feedback through the lens of a linear-odds, one-shot model. The player feedback is that it shouldn't be linear, and there should be less randomness for larger numbers.

That all makes sense to me... and I suspect makes sense to him when he's not giving a talk for comedic effect.

What do you do when it's 15:7?

Then you probably want to calculate the attacks between two big blobs of units without separating them. But the result is still going to be "something like 7 simultaneous 2:1 battles", and not at all like 30% odds of upset.

Is that wrong? I don't know the logic of the game, but a 20:10 battle can very well have different odds than a 2:1 one.

They're talking about ratios of unit-strength, which correlate directly to odds of success in a battle, not to numbers-of-units or anything more fuzzy like that. Given which, 20:10 and 2:1 have identical odds of success.

Do they, though? It depends on how the combat works.

Suppose, for example, that each side has 5 hit points, and repeatedly you roll a 2:1 die to decide who gets 1 point of damage, until one side reaches 0 hit points. The chance of an "upset", where the weaker side wins, is not 1/3; I compute it to be roughly 14%. If both sides start with 10 hit points, I compute the chance of an upset to be 6.5%. The law of large numbers means that, the more die rolls the combat involves, the less likely an upset is.

Or. Suppose that, at each step, one side has N soldiers and the other has M, and repeatedly a random soldier gets a kill; so that's an N/(M+N) chance that the first side gets a kill, and M/(M+N) that it's the other side. This would make advantages compound within the battle. Then I compute that a 2:1 initial matchup has a 5/6 chance (83%) of victory, and a 10:5 matchup has a 98.8% chance of victory.

(edit) I guess you could say I'm challenging the idea that "unit strength", such that when strength A fights strength B it's decided in one step with probability A/(A+B), makes sense as an abstract concept.

  (defmemo meh (a b p)
    (if (is b 0)
        1
        (is a 0)
        0
        (+ (* p (meh a dec.b p))
           (* (- 1 p) (meh dec.a b p)))))

  (defmemo nub (a b)
    (if (is b 0)
        1
        (is a 0)
        0
        (+ (* (/ a (+ a b))
              (nub a dec.b))
        (* (/ b (+ a b))
           (nub dec.a b)))))

Sure, you could design a system where it's more complicated, but Sid Meier didn't. In the video he's talking about Civilization Revolutions, in which combat is just "attacker's Attack stat vs defender's Defense stat" to form a probability-of-success, which is then rolled to see who won the battle. There's no hit points or anything like that, just those stats.

More than "players don't understand math", this might be a UI or tutorialization issue. I.e. presumably it was unintuitive because people imagined more complicated ways it might be working behind the scenes, causing large absolute stat-disparities to feel like they should work differently despite being in similar ratios. It's a case where showing an explicit odds-of-success display might have helped, though XCom famously showed how that can backfire...

(Revolutions was a deliberate simplification of the Civ formula, so they could try to appeal to console / mobile gamers rather than the traditional hardcore PC audience.)

> presumably it was unintuitive because people imagined more complicated ways it might be working behind the scenes

I think this is exactly it. And then Sid Meyer calls his players stupid and irrational for assuming the game had more depth than it actually had. For assuming a celebrated game designer would put even a modicum of thought into making a combat system that was balanced, made sense, and felt good.

It's like selling a gallium spoon and then calling people stupid when it melted in their soups. Sure, if you know a lot about gallium, you wouldn't be so stupid and irrational as to put it in your hot soup. But it's a metal spoon that you bought from a reputable vendor. Spoons go in soup. They were being completely rational; it's just that they were tricked into assuming a product was less crappy than it actually was.

> I think this is exactly it. And then Sid Meyer calls his players stupid and irrational

I think this is overstating what Sid Meier says in the talk. His original goal was to make his simple combat stat system clear to users by describing its odds as odds conventionally are described.

> For assuming a celebrated game designer would put even a modicum of thought into making a combat system that was balanced, made sense, and felt good.

That's exactly what he did, through player testing! Through practice and player feedback seems to me like a perfectly reasonable way to uncover an intuitive notion of unit strength. It's not like he said 'they're odds, stupid! learn how to understand odds.'. He recognized that player intuition and fun was the real goal, and his team gradually made the combat system more sophisticated.

> His original goal was to make his simple combat stat system clear to users by describing its odds as odds conventionally are described.

Except that odds values don't add on to each other. It sounds like the numbers only worked like odds in a single way, and not in other ways. The system was inherently contradictory, and confusion is not irrational in that situation.

And it's easy to clarify something as odds by making it two opposing percentages out of 100.

1:3 (one to three) odds aren't the same as 1/3 odds (1 in 3 odds).

1:3 means the second outcome (that on the right-hand side of the ':' symbol) is 3 times as likely as the former outcome, which is true when the likelihood of the first outcome is 25% and the likelihood of the second outcome is 75%.

1/3 describes the chances only of one of the outcomes, and fixes it at 33⅓%. If there's only one other outcome, its likelihood is 66⅔%.

Is the 'addition' you're talking about just one of the readings of the first syntax, or did I miss something else in the video that made the initial presentation of those odds figures surprising?

Sorry if my terminology is off; it's been a long time since I did any stats

"Player psychology has absolutely nothing to do with rational thought ... the attacking unit has a strength of 1.5, and the defending unit has a strength of 0.5. So the attacking unit should win 3 times for every 1 time the defending unit wins. It's 3:1. That's just math. That's what the math says."

Wow, I liked Sid Meyer a lot more before I listened to that arrogant diatribe about how stupid his players are and about how his decisions are unarguable Math-God-Given conclusions that you'd have to be A Stupid Irrational Loser to disagree with. Fuck you, Sid. You can design your game any way you want. Don't blame shitty game design on math; math didn't make you decide that combat strength should map linearly to odds of winning. That's a shit-ass combat system and not any more mathematically pure than "biggest number always wins", or using a health system like later games did. The audacity to stand up in front of people and lament how he had to get his pure, beautiful game all dirty because of the irrationality of his stupid loser players who just want a game that doesn't feel like bullshit ... come on. So much respect was just lost for that man. Never meet your heroes, nor listen to them talk about how much smarter they are than everyone else.

Hey friend. He's not saying they're stupid. He's saying they're irrational. And he's right. Humans aren't rational beings and our expectations differ from simple mathematical probabilities. When making Civilization 3 in the years leading up to 2001, his team had to make changes to the game so that it felt better to the players. They improved game design as you say that they should have, but made it an internal change so that the presented numbers "felt" right. They learned from this experience and he's presenting this learning in a lighthearted presentation to an audience containing some of the very players he's talking about. They got the humor in the situation fifteen years ago and thanks to that, you, me, and other people making and playing games today expect better presentation in our games.

> He's not saying they're stupid. He's saying they're irrational. And he's right. Humans aren't rational beings and our expectations differ from simple mathematical probabilities.

He's right in that players are biased when it comes to rare player success versus rare player failure. He's not right that it's irrational to have different expectations from the "simple mathematical probabilities".

The simple math works when each side is trying to hit a single target that only needs to be hit once. It does not work for medium or large fights.

> He's saying they're irrational. And he's right.

No, he's not right. Humans only seem irrational when you myopically narrow your focus to one or two axes. This is something "smart" people do all the time: they're smart in one way, so everyone who acts in any way counter to what looks optimal from that narrow, simplified model is acting "irrationally". Economists will call humans irrational, but it's actually their over-simplified models that suck. Sid Meyer will call his players irrational, but it's actually his (originally) lame combat system that sucks. Rich MBAs will call lifelong employees irrational for not starting their own businesses, but they're ignoring a thousand factors that they took for granted. The people they are denigrating are incorporating more axes, more information, more context than their silly little models are.

There's a story I wish I could find about a young boy in India trying to answer his dad's math problems. His dad asks him questions like "A man wants 5 mangoes from a shopkeeper who is selling them for $4 each. How much money will he spend?" and gets increasingly exasperated that his child can't answer. But we see the child's inner thoughts, with things like "why would he spend $4 at this shopkeeper when they usually cost $2? Can't he just walk to a different shop and get them there? And what is he going to do with FIVE mangoes? He won't be able to use them all before they spoil!" etc. etc. Sid Meyer is the dad assuming his players are stupid (sorry, "irrational", meaning: stupid, losers, dumb, idiots, morons). They're not.

You might enjoy Gigerenzer's "Bias bias" paper. Discussed here: https://statmodeling.stat.columbia.edu/2019/07/14/gigerenzer...

Paper itself: https://www.nowpublishers.com/article/OpenAccessDownload/RBE...

Abstract: "Behavioral economics began with the intention of eliminating the psychological blind spot in rational choice theory and ended up portraying psychology as the study of irrationality. In its portrayal, people have systematic cognitive biases that are not only as persistent as visual illusions but also costly in real life—meaning that governmental paternalism is called upon to steer people with the help of “nudges.” These biases have since attained the status of truisms. In contrast, I show that such a view of human nature is tainted by a “bias bias,” the tendency to spot biases even when there are none. This may occur by failing to notice when small sample statistics differ from large sample statistics, mistaking people’s random error for systematic error, or confusing intelligent inferences with logical errors. Unknown to most economists, much of psychological research reveals a different portrayal, where people appear to have largely fine-tuned intuitions about chance, frequency, and framing. A systematic review of the literature shows little evidence that the alleged biases are potentially costly in terms of less health, wealth, or happiness. Getting rid of the bias bias is a precondition for psychology to play a positive role in economics."

Thanks, that paper is arguing something very different from what I'm used to seeing so that alone makes it worth a look. It's nice to see that not everyone is taking it as a given that humans are irrational.