Odds and randomness
Learning paths through this topic
How many kills until you hold five pelts, and what to tell the player?
A quest asks for several drops that fall with a modest chance, and the obvious division gives a number that most players will not reach in time. This shows how to work out a count you can honestly put on the quest, and how far off the obvious answer is.
Random level pieces must join up and must not stack the hardest ones
Gluing random pieces into an endless level produces steps the player cannot climb and runs of nasty sections with no breathing room. Both are fixed at the moment of picking, and there is one case where the rule has to bend or the game gets stuck.
Better loot deeper down, but blending two loot tables gives odd chances
Rarer items should become likelier as the player goes deeper. Blending an early and a late loot table sounds easy, but the tables are rarely written on the same scale, and the blend then favours the wrong one. A short step before blending avoids it.
Three luck bonuses stack and the drop chance goes past 100 percent
A charm, a potion and a campfire each promise better luck, and adding or multiplying them quickly gives chances that make no sense. This shows a way to combine any number of boosts so the result stays sensible and order never matters.
A drop that is guaranteed after ten misses still fails on the next try
Adding small chance bonuses again and again with ordinary decimals drifts by a hair, and a hair is enough to miss a guarantee or to break a promise like exactly a quarter. The cure is to count in whole units and compare in whole units.
Two players roll for a shared reward and tie: how often, and how to settle it fairly
When a group rolls for one item, ties are more common than most people expect once several players are involved, and rolling again for everybody is unfair to those who already lost. This shows how often ties happen and a fair way to settle them.
Pick who keeps watch each night without the same person twice in a row
Shuffling the crew every round is fair over time, but at the seam between two rounds the last person can come up first again, and fixing that by redrawing quietly makes some orders more likely than others. This shows a clean way to keep every allowed order equally likely.
Making noise near a sleeping camp: the chance that nobody wakes, and how many do
A clumsy step may wake some sleepers but not others, and guessing the group's reaction from one average distance gives a very wrong answer. This shows how to work out the odds of silence and the whole spread of how many wake up, so you can tune stealth.
How many raids hit your camp while you were away, with a cap on the losses?
When a player returns after hours away, the game must decide what happened in the meantime, and a limit on the damage changes the real odds in a way the plain average hides. This shows how to get the true spread of outcomes for the welcome-back screen.
An ore node regrows by chance each hour, so when is it really back?
Players ask when a mined-out spot will be ready again, and the average wait is a bad answer because many of them will still be standing there with an empty pickaxe. Here is how to give a promise that holds for nearly everyone.
Ore veins that grow with a chance per block: set the chance for the size you want
Letting a vein keep growing with some chance at each step gives natural sizes, but the chance you pick and the average size you get are not related the way people expect, especially once the vein must stop somewhere. This shows how to choose the chance from the size you want.
How likely is a typical player to hit a parry window of a few frames?
Designers pick a timing window by feel and then learn from reviews that it is either trivial or unfair. If you know how scattered players' timing is, the success rate follows from a bell curve and a half-frame correction that is easy to forget.