Odds and randomness
Learning paths through this topic
A weapon that does 3 to 6 damage almost never does 3 or 6
Turning a random number into a whole damage value looks trivial, yet the obvious way quietly halves the odds of the lowest and highest result. Players never see why their top hit is rare. This entry shows the conversion that treats every value alike.
At dusk the whole wildlife list changes in one second, so fade it instead
Switching to the night list at a set hour makes creatures pop in as if a switch was thrown, and blending two lists the obvious way lets the bigger list swallow the smaller one. This shows how to move between lists smoothly so every creature keeps the share you meant.
What is the exact chance that my attack roll beats the defender's roll?
Two players each roll a handful of dice and the higher total wins. Guessing the fairness from a few test rounds is slow and often wrong. This entry gives the exact winning, tying and losing chances, and shows how a flat bonus shifts them.
Where should the digger look next after two empty holes and a beeping detector?
Every empty hole and every signal tells the player something about where the treasure is, but a helper that forgets this digs the same places or trusts a signal too much. This shows how to keep the chances for every spot up to date after each clue.
A player says the drop rate is broken: how do you tell bad luck from a bug?
Every game gets reports of someone who killed hundreds of creatures and never saw the item, and some of them are just very unlucky while a few point to a real mistake. This shows how to judge a report fairly, taking into account how many players there are.
Who wins a shoot-out when both sides miss often and one is tougher?
Two fighters take turns, each hits with some chance, and one needs more hits to go down. The winner cannot be read off the numbers by eye, and the fighter who shoots first has a bigger edge than most people expect. This entry gives the exact winning chance.
Ambushes happen twice as often on a fast computer
A chance rolled on every screen update means the same walk through the same forest is far more dangerous for players whose screens refresh faster. This shows how to state the danger per second and still get the exact same odds on every machine.
Enemy reactions feel either robotic or impossibly instant
A fixed reaction time looks mechanical, and a uniformly random one lets enemies sometimes answer before a person could. A delay with a hard minimum and a tail of slower answers feels alive. One input edge makes the formula blow up.
Enemies always shoot the same player or decoy and the others are never touched
Choosing the nearest or the most threatening target makes one character a magnet while the rest of the team is ignored, and pure random ignores the tank role. A blend gives every target some attention and still rewards good positioning. The blend has a limit you must respect.
How many times will a player die in a level with and without checkpoints?
Where to put checkpoints is guessed far too often. Each section has its own chance of getting through, and the expected number of deaths follows from a short calculation that shows how much a single checkpoint saves and why long unbroken stretches hurt so much more than the sum of their parts.
Catching a chill while the weather keeps changing, rolled just once
Danger that rises and falls as the player walks through storms, cold nights and warm huts is awkward to roll step by step, and the results depend on how often you look. This shows a way to roll a single time and still get the right odds however the danger changes.
How wide must a cleared strip be so a grass fire does not jump it?
Fire that creeps from tile to tile with a chance each moment looks right until players build a gap and wonder if it will hold, and the answer depends on how long things burn as much as on the gap. This shows how to compute the chance of crossing and the narrowest strip that meets a goal.