[waterhouse]

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)))))

[kemayo]

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.)

[feoren]

> 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.

[pxc]

> 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.

[Dylan16807]

> 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.

[pxc]

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