IA ideas library
Simulation and Monte Carlo IA ideas: when the exact answer is too hard
Some questions are too messy to answer exactly: a queue with impatient customers, a board game with special rules, a disease spreading through a year group. A simulation answers them by running the random process thousands of times and measuring what happens. A Monte Carlo IA is strongest when it also does some exact mathematics, to check the simulation, or to find a simpler case where theory and simulation should agree.
You can simulate in a spreadsheet with RAND(), in a few lines of Python or on a GDC. Code is a tool, not the mathematics: explain in words and notation what each run does, and how many runs you need for the answer to be reliable.
Simulation & Monte Carlo methods ideas (8)
- One snake queue or a queue at every till? Simulating supermarket checkoutsAI SLAI HLAA SLAA HLSolid
- Estimating the area of a leaf with random pointsAA SLAI SLAA HLAI HLAccessible
- How far does a random walker get? Distance after n stepsAA HLAA SLAI HLSolid
- Why do buses come in bunches? A simulation of a bus routeAI HLAI SLAA HLAmbitious
- How many random numbers until the total passes 1? Finding e by chanceAA HLAA SLSolid
- Does the best team win? Knockout cups versus leaguesAI SLAI HLAA SLAA HLSolid
- What is a 'random' chord? Bertrand's paradox simulatedAA HLAA SLSolid
- Will the pension pot last? Monte Carlo savings with random returnsAI SLAI HLAmbitious
Also relevant (9)
- Are arrivals at the school canteen random? A Poisson model of a queueAI HLAI SLSolid
- Estimating π by dropping needles: how fast does the estimate improve?AA HLAA SLAI SLAI HLSolid
- How many shuffles does it take to mix a deck of cards?AI HLAA HLAI SLAmbitious
- Why does a random game draw the Sierpiński triangle?AA SLAA HLAI SLSolid
- Gambler's ruin: how long until someone runs out?AI HLAA HLAmbitious
- How likely is a voting paradox? Rock–paper–scissors preferencesAA HLAI HLAmbitious
- Secret Santa: how often does someone draw their own name?AA HLAA SLSolid
- How big should a school poll be? Sampling from a known populationAI SLAI HLAA SLSolid
- Counting a hidden population: capture–recapture at schoolAI SLAA SLAI HLAA HLSolid
Frequently asked questions
Is a simulation enough mathematics for an IA?
Not on its own. Pair it with exact calculation for a simple case, a probability distribution that explains the results, or an estimate of the simulation's error. The simulation then tests and extends the mathematics rather than replacing it.
Do I have to write code?
No. A spreadsheet with RAND() or RANDBETWEEN() can run thousands of trials. If you do write code, put it in an appendix and describe the algorithm in the body.
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