so, here's the thing about probability
you have to remember that probability does not give a damn about your previous results. probability only cares about what is happening right now
yes, even in things like the x-com situation, where the percentage shown to you is slightly weighted from the actual calculation behind the scenes. if you missed 1 shot before at an 80% chance you are not going to magically get the next 4 shots just because that 80% is still there.
i bring this up because someone mentioned in a discord I'm in this whole thing about "isn't it weird that you can fail an 80% chance like 5 times in a row? that's weird" and someone else was like "yeah the way this works in [game x] definitely doesn't reflect reality", and even though i am not a math dev i think it is important to point out that probability does not give a damn about your previous results. probability only cares about what is happening right now. So it's not that you failed those crafts 5 times in a row despite a four-in-five chance that you wouldn't because the game schemed against you, it's because you literally lost the dice roll 5 times in a row even with the odds in your favor. It happens.
edit: as has been pointed out in the comments, i should note that this argument is different when you're talking about cards or any other system where you are actively removing or discarding elements from the overall set, so to speak--when discarding cards from a deck, for example, you are actually narrowing the possibilities down such that probability does have to care about previous results.
The chance of flipping tails 5 times in a row is 1 in 32. If most of what you're doing in a game is flipping coins, then you're absolutely going to run into a bizarre streak. It's just how randomness works.
The chances of missing 5 shots at 80% is 1 in 3125, or .0003125 percent chance. I haven't played much XCOM but I did watch a few let's plays and it looks like you would fire about 10 shots per 5 minutes of gameplay - more if you play faster. So about 2 shots a minute. The game takes about 27.5 hours to beat according to how long to beat, and assuming that ~80% of that is combat, let's do the back of the napkin math on how many shots one can expect to take in a single playthrough of XCOM:
27.5 * 60 = 1650 minutes
1650 * 0.8 = 1320 combat minutes
1320 * 2 = 2640 shots total
2640 / 5 = 528 five shot streaks of any kind
.0003125 * 528 = .165, or about 17%
Assuming that all of your shots had about an 80% chance of hitting (which actually seems high based on the gameplay I watched), then during one playthrough of XCOM, you have about a 17% chance of missing 5 of them in a row at some point. That's ~1 in 6.
Obviously this has a ton of unfounded assumptions about the game XCOM specifically. I'd need much more data than I have to get a good estimate. BUT I think it's a compelling argument that even seemingly unlikely things can happen with greater frequency than seems intuitive. Even if you didn't have a bizarre streak of misses, you almost certainly know someone who did. And if you're the kind of person who posts in Discord about XCOM, you've probably played waaaay more than 27.5 hours of the game and therefore shot many more shots.
For another fun illustration of how unintuitive probability is, check out this spreadsheet filled with random 0s and 1s:
I guarantee to you that that is random, but it sure looks like there are some patterned groupings in there. It doesn't look random even though it absolutely is. Like, look at that row of twelve zeroes near the bottom! That's a 1 in 4096 chance of occurring, but it's right there.
Brains just aren't wired for this stuff. We're naturally very bad at probability, so I always make an extra effort when probability shit comes up to actually try and think it through. Otherwise I make weird decisions and bad guesses.
