Card Nim
The classic 21-game. Take 1, 2, or 3 cards from the pile each turn. Whoever is forced to grab the last card LOSES. Out-think the AI with pure combinatorial game theory.
Pile of 21 real sports cards • AI goes first • Misère Nim • Strategy taught in every game theory course
New Game Setup
The Math Behind Card Nim
Call a pile "safe" if its size minus 1 is divisible by 4 — that is, sizes 1, 5, 9, 13, 17, 21. If you hand your opponent a safe pile, they are guaranteed to lose against perfect play.
The 21-pile is itself safe, which is why the AI (moving first) starts in the losing seat. Whatever it takes (1, 2, or 3), the remaining pile (20, 19, or 18) is not safe. Your job: subtract enough to hand the AI another safe pile.
The rule-of-thumb: if the opponent takes k, you take (4 − k). AI takes 1 → you take 3. AI takes 2 → you take 2. AI takes 3 → you take 1. Repeat. Eventually the pile reaches 1 and the AI has to take it.
This is the entire strategy. Once you internalize it, you should never lose an Expert match.
Card collecting connection: the same "parity counting" logic applies when you commit to a grading-submission schedule, a set-build order, or deciding which card of a pair to flip first. Discipline of counting multiples pays.