Odds and randomness
Learning paths through this topic
Chance calculator
Exact answers to everyday odds questions: the chance of at least one success in a number of tries, how many tries you need to be fairly sure, how many on average, and how likely a run of bad luck is. The result comes with how it was worked out, so your AI can show you the sum as proof instead of guessing a number.
Real loot odds
Works out the real odds of a loot table that includes a bad-luck counter, exactly and without any random sampling. A counter means the chance you show is not the real one, and this tells you the real one, how many rolls players need and the most anyone can ever need.
Monte Carlo simulator
Plays a game rule thousands of times and reports what usually happens, how far results spread, and the worst cases it saw. It is for rules too tangled to work out by hand.
Markov chain
Randomness with a short memory: what comes next depends on what is happening now, so rainy days come in runs and moods drift instead of jumping. It also invents names that sound like your world.
Shuffle bag
Fair randomness with no long unlucky streaks: outcomes go into a bag, get shuffled and come out one by one. One win in four then really means one win in every four.
Roll twice and keep the better result: what are the real odds?
A good torch, a lucky charm or a steady hand lets a player roll twice and keep the better one, or the worse one when things go badly, and most people guess the effect wrongly. This shows the exact chances and how a flat bonus combines with them.
Drop the ammo the player is running out of, more often when stocks are low
Flat drop chances give full players ammo they cannot carry and starve players who are empty. A little shaping fixes both, but two details decide whether it feels helpful or like cheating, and one of them breaks when a weapon has no magazine limit.
Armor takes off damage but every hit still does at least one: the real average
Subtracting armor from a random damage roll and never going below a minimum makes the average hit larger than the simple subtraction suggests, so strong armor is worth less than it looks. This shows how to compute the true average and how many hits it takes to fall.
You asked for 20 percent desert and the generated world has almost none
Smooth landscape noise bunches its values in the middle, so cutting it at a round number gives far less of the extremes than the number suggests. This shows how to set the cut points so each kind of land covers exactly the share you planned.
A boss should vary its attacks without ever becoming a fixed pattern
Pure random makes the boss repeat one move four times and feels broken. A fixed rotation is solved in two fights. The middle road needs a weight that fades with repetition, plus a rule for what happens when the pick runs out of choices.
Random gaps in a bullet wall must always be reachable in time
A wall of bullets with a random hole is fun until two holes in a row sit too far apart to cross. Checking each pair of holes looks right and still lets an impossible row through. This entry shows what to track so every row can be survived.
Shots that miss the crosshair cluster in the middle instead of spreading evenly
A random offset for each bullet looks fine until you fire a magazine and see a dense knot in the centre and a thin ring outside. The cause is easy to miss, and so is the one-line change that makes the scatter honest.