The game says 75% to hit. You miss. Then you miss again. You put the controller down and say something unkind about the developers.
Two consecutive misses at a genuine 75% happens 6.25% of the time. One mission in sixteen. Across a campaign you will see it constantly, and every single time it will feel like the game is cheating.
Which is why most games stopped using real randomness years ago. Not to cheat you, but because true randomness produces streaks that humans read as broken, and a system that feels broken is a worse system regardless of whether the arithmetic defends it.
The Bag That Fixed Tetris
Start with the cleanest example, because the fix is elegant and the problem is measurable.
Early Tetris picked each piece independently. One in seven for every tetromino, every time, no memory. Which means the chance of seeing no I-piece across twelve consecutive pieces is 15.7%, and the chance of a genuinely brutal drought is higher than anyone enjoys.
Modern implementations use a bag. All seven pieces go in, they come out in random order, then the bag refills. You can still get an awkward sequence, but you cannot be starved. The probability of no I-piece in twelve pieces drops from 15.7% to zero, because one is guaranteed inside every seven.
That is less random by any formal measure and unambiguously a better game. The bag preserves surprise while removing the outcome that makes people quit.
XCOM Adjusts and Does Not Advertise It
The most famous case, and the one that generated years of forum argument before it was confirmed.
On lower difficulties, the displayed hit chance is not the real hit chance. The game quietly improves your odds, and in some versions tracks consecutive misses to prevent a run that would end a campaign on variance alone.
Players insisted for years that the percentages lied. They were correct, and the reason was that a squad wiped by three consecutive 85% misses is a player who stops playing, regardless of how defensible the maths was.
Civilization made a related move, restructuring combat away from pure rolls after enough players experienced a technologically superior unit losing to something it should have flattened.
In both cases the design principle is identical: the displayed number is a communication device, not a specification.
Casino Games Are the Exception, by Law
Here is the category that cannot do any of this, and the contrast is instructive.
A licensed slot or table game must be genuinely memoryless. The previous spin has no bearing on the next one, there is no pity curve, no streak protection and no quiet adjustment toward the advertised return. Independent test houses certify exactly that property before a title reaches a regulated floor, and the published return figure is meaningful precisely because nothing in the machine is steering toward it.
Which produces an odd inversion. The industry with the worst reputation for fairness operates under the strictest independence requirement, while the games marketed as skill-based are full of hidden corrections nobody documents.
You can watch players work this out in real time. This reddit post is a fairly typical example of the genre, where someone asks a community to explain which systems can be relied on and what the numbers actually mean. Threads like it exist because the answer is genuinely not obvious from the outside, and because certification is one of the few places the question has a documented answer.
The Vocabulary Worth Knowing
Four mechanisms, and you will recognise all of them once named.
Pseudo-random distribution. Used in Dota and elsewhere. A stated 25% proc does not roll 25% each time. It starts lower and climbs with each failure, so the long-run average lands near 25% while the variance is compressed. Fewer droughts, fewer absurd streaks.
Bad luck protection. Explicit accumulating bonuses toward a rare drop. Diablo and its descendants use it openly, which is the honest version of the same idea.
Bag or shuffle systems. Tetris pieces, card draws, spawn tables. Guarantees distribution across a window rather than per event.
Pity timers. A guaranteed outcome after N failures. Common in gacha systems and increasingly disclosed rather than hidden.
Every one of these breaks independence deliberately. Knowing which you are inside is the difference between reasoning correctly and committing the gambler’s fallacy, and the fallacy is only a fallacy when the system genuinely has no memory. In video game systems, it frequently does.
When It Goes Wrong
Two failure modes, both real.
Undisclosed correction destroys trust when it surfaces. Players who suspected XCOM was adjusting were told for years they were imagining it. Being right after being dismissed produces a durable suspicion that outlasts the specific issue.
Correction that flatters the house is a different thing entirely. A system that smooths your losses and one that smooths its own are not equivalent, and without disclosure a player cannot tell which they are in. That asymmetry is the entire reason regulators mandate certification in the one category where money changes hands.
The gambler’s fallacy gets taught as a straightforward error, and it is, but only against genuinely independent trials. Apply it to a pity system and you are reasoning correctly. Apply it to a certified slot and you are not. Most people cannot tell the two apart because nothing on screen distinguishes them.
What to Take From It
The number on screen is a design decision before it is a fact.
A displayed 75% in a tactics game is a mood, tuned to produce the experience the designer wanted. A published return percentage on a regulated machine is a certified property with a test house behind it. Both are percentages and they are not the same kind of object.
Worth remembering next time a game misses three 90% shots in a row. It might be lying to you. It might be lying in your favour. And the only categories where you can be certain either way are the ones somebody was legally required to check.
