IA ideas library
Games and puzzles Maths IA ideas
Board games, card games, video games and puzzles are closed worlds with clear rules — which makes them perfect for exact mathematics. You can often calculate the answer precisely, then check it by playing or simulating.
Pick a game you actually play. Knowing the house rules, the tactics people use and the moments that feel unfair gives you questions no textbook asks.
Next step: shortlist ideas with the free IA topic explorer, which filters starting points by course, interest and how easy the data is to get. For feedback on your own draft, the IA package (€39 once) gives you 5 AI feedback credits and every annotated exemplar in full.
How games & puzzles explorations reach the top bands
Personal engagement (C)
Play the game, record your own games or simulate it yourself. Predict the answer as a player before you calculate it.
Reflection (D)
Compare your theoretical answer with real or simulated play and explain the differences (human choices, house rules, randomness).
Use of mathematics (E)
SL: Counting principles, tree diagrams, binomial probabilities and expected value, built step by step and checked by simulation.
HL: Markov chains with transition matrices, generating results for n, or combinatorial proofs.
An HL version
Model the game as a Markov chain and find expected lengths or steady states, or prove a counting result in general.
Games & puzzles ideas (11)
- How long does a game of Snakes and Ladders last?AI HLAA HLAmbitious
- Which Monopoly squares are landed on most often?AI HLAA HLAmbitious
- How big is White's advantage in chess, and does it depend on skill?AI SLAI HLAA HLSolid
- Can you beat people at rock–paper–scissors?AI SLAI HLAA SLAA HLAccessible
- What are the chances of rolling a Yahtzee in one turn?AA SLAA HLAI SLAI HLSolid
- How many attempts until the rare item? Drop rates and pity systemsAA SLAA HLAI SLAI HLSolid
- How many positions does a Rubik's Cube have?AA HLAA SLAmbitious
- How many different games of noughts and crosses are there?AA SLAA HLAI SLAI HLSolid
- How many shuffles does it take to mix a deck of cards?AI HLAA HLAI SLAmbitious
- What are the odds in a Risk battle?AA SLAA HLAI SLAI HLSolid
- Where should you build your first settlement in Catan?AA SLAI SLAA HLAI HLAccessible
Also relevant (5)
- How much does a small edge on each point matter in tennis?AA SLAA HLAI SLAI HLSolid
- How many packs does it take to finish a sticker album?AA SLAA HLAI SLAI HLSolid
- When should you stop looking? The 37% rule for choosing the bestAA HLAA SLAI HLAmbitious
- The Monty Hall problem when the host is forgetfulAA SLAA HLAI SLAI HLSolid
- Where should I aim on a dartboard?AI SLAI HLAA HLAmbitious
Frequently asked questions
Can I write my IA about a video game?
Yes, if there is real mathematics in it: drop rates and expected numbers of attempts, damage formulas, optimal strategies or map geometry. Check that the game's numbers are published or that you can measure them.
Do I need to write a computer program?
No, but a simulation (spreadsheet or a short script) is a strong way to check an exact calculation. Explain what the simulation does; include the code in an appendix if it is long.
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Related types of IA: Voting, fairness & game theory · Simulation & Monte Carlo methods
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