The Complaint Everyone Recognizes
A squad member lines up a shot that the screen says has a 95% chance to hit. It misses, the mission goes badly, and the player concludes that the game is cheating. Posts like this appear for almost every tactics game that shows its odds.
Sometimes the complaint is justified, because a game may use rules that differ from what the display suggests. More often the display is accurate and the feeling comes from how people handle probability. Both causes are worth understanding.
The Math of a High Percentage
A 95% chance of hitting is a 5% chance of missing, which is 1 in 20. That sounds rare, but a player does not take one shot. Take a campaign in which a player attempts 20 such shots. If each shot is independent, the chance that every one hits is 0.95 raised to the 20th power, about 0.358. The chance of at least one miss is therefore about 1 - 0.358 = 0.642, or roughly 64%.
Put differently, a miss at 95% is not a strange event across a whole campaign. It is the more likely outcome. The same logic applies to shorter sequences:
- Three consecutive shots at 90% all hit with probability 0.9 x 0.9 x 0.9 = 0.729, so about 27% of the time at least one misses.
- Ten shots at 90% all hit with probability 0.9^10, about 0.349, so about 65% of the time at least one misses.
- Two shots at 80% both hit with probability 0.64.
This is the multiplication rule applied to a sequence. Each shot looks safe on its own, but the combined chance falls quickly.
Why Misses Are Remembered
Memory does not record outcomes evenly. A miss at 95% is surprising, costly and usually happens at a dramatic moment, so it is remembered. Dozens of ordinary hits are not. When players recall their experience, they tend to overweight vivid failures. This is one of several cognitive biases that distort judgment about chance, and it can make a display that is perfectly correct feel dishonest.
Stakes matter too. A miss on a throwaway enemy is shrugged off. A miss on the shot that would have saved a favorite character is felt as an injustice. That feeling is attached to the situation, not to the odds, which were the same either way.
Related to this is loss aversion. The pain of losing a character or a turn is stronger than the satisfaction of an equivalent success, so a failure at 95% feels bigger than a success at 95% feels good.
Rounding, Hidden Rules and Real Differences
Not every case is psychological. A displayed percentage can differ from the true roll for legitimate design reasons, and it helps to know the possibilities.
- Displayed values may be rounded or capped. A game might show a figure to the nearest whole percent, which hides small differences.
- The roll may use more than one random number. Some games are described as averaging two rolls or otherwise shaping the distribution, which makes hits at high percentages more reliable and misses at low percentages less likely than the display suggests. Whether a given game does this depends on the game, so check its documentation or community knowledge before assuming.
- Hidden adjustments may exist. A designer may bias results to protect players from frustrating streaks, or the opposite. If a game does this, it is a design decision rather than a bug, though players disagree on whether it should be disclosed.
- The display may not include everything. Cover, flanking, abilities or status effects can change the real chance after the screen was drawn.
The upshot is that two games with the same displayed numbers can behave differently. A fair assessment needs the rules of the specific game.
How Designers Respond
Designers who care about trust tend to choose one of a few approaches. Some show exact numbers and stand by them, accepting that misses will still hurt. Some use qualitative labels instead of percentages, which reduces precise expectations. Some shape the odds so that very high and very low displayed chances are more reliable than they appear, aiming at the feeling players expect. Others limit the effect of a single miss through backup options or recovery moves, which lowers the stakes so the percentage matters less.
A related approach adjusts outcomes after streaks, which is the subject of pseudo-random distribution, though that is usually applied to chances such as critical hits and procs rather than shown hit percentages.
Reading the Display Better
A few habits make displays easier to live with.
- Treat a high percentage as a likely result, not a promise. A 90% chance should be expected to fail about once in ten attempts over a long period.
- Multiply the chances when a plan needs several shots to land. If your turn needs three shots at 90% to all succeed, plan for the roughly 27% case where one does not.
- Build in redundancy. A plan that survives one miss is stronger than one that depends on several hits.
- Judge a game’s honesty over many attempts, not one. Keeping a record over hundreds of shots and comparing it to the stated rate is a fairer test than a vivid memory, and the ideas behind that are touched on in the question of statistical significance for game data.
- When a miss happens, remember that it does not make the next shot more or less likely to hit. Expecting otherwise is the gamblers fallacy.
The percentage on the screen is a statement about the long run. Whether a single shot lands remains uncertain, which is exactly what makes tactics games tense.