Counter-hypothesis: these games' higher level gameplay loops demand a higher level of consistency; players' mismatched expectations come partially from a place

Counter-hypothesis: these games' higher level gameplay loops demand a higher level of consistency; players' mismatched expectations come partially from a place of "if that chance is actually 90%, then what you're asking me to do is impossible". Let me be more concrete. Take XCOM as the clearest example. On one hand, your troops level up with experience. A veteran soldier is more effective than a new recruit. So you need your them to survive, otherwise you'll be at a significant disadvantage on later missions. On the other, the developers want there to be some difficulty, to create a sense of tension (that you might not succeed) and make strategy matter. These two goals are diametrically opposed, given the genre. It is difficult-to-impossible to create a scenario where there is both a real risk of losing and where a player can recover from losing a nominally 90% roll. Maybe once per mission. To keep the gameplay balance intact, devs would need to raise the nominal chances to match the actual chances, not the other way around. The problem is, doing this would make it obvious to the player how much stronger they are than their opponents, in a game where you are supposedly vastly outgunned. So this type of fudging the numbers is more of a psychological trick by the developers, who want to have their cake and eat it, too. It's in the same class as shooters which prevent the AI from shooting you in the back or sniping you from offscreen, or horror games where the monster moves more slowly when you're not looking at them. An illusion to create a certain type of experience. Note: I don't dispute that people are bad at judging probabilities. But I also ask that you consider that players may use this reasoning (probably subconsciously): "The developer wouldn't set me an impossible goal. If I lose this battle, it will be impossible to reach the goal they have set. Therefore, my chance of winning must be 100%. The game says it is 90%. Therefore, when the game says 90%, it must actually mean 100%. Therefore, when I lose a roll that the game says is 90%, the game is cheating." They don't really mean the game is cheating, they mean the developer is setting them an unfair task, giving them the illusion that there is a chance at victory through smart play, when in fact there is none. I imagine you could test this hypothesis, or rather, how large of an effect it has, by taking the first 11 letters of the alphabet, randomizing their order, and then assigning them to probabilities 0-100% in steps of 10. Then have people play the game, showing only the letters. Then at the end, ask them to guess what each letter's probability is. This should show how much of the delta is the developer's fault vs player's. I think you'd want to do it with players whose perceptions have not already been poisoned by the lying of previous games, and use a less uniform distribution, so players can't guess the % just by figuring out the relative order.