Everyone says a minimax Tic-Tac-Toe bot is “unbeatable.” I wanted a number instead of a vibe — so I benchmarked the exact engine that ships in my game. The code and the harness are open source; every figure below reproduces with node benchmark.js.
Three things I measured: whether it can actually lose, how much alpha-beta pruning really saves, and whether bigger boards crack it.
1. The proof isn’t a sample — it’s the whole game tree
On a 3×3 board, Hard mode runs a full depth-9 minimax search, so its reply to any position is deterministic. That means I don’t have to sample games — I can enumerate every reachable one: every move a human could make, answered by the AI.
Playing second, exactly as it does in the game:
- 569 reachable game lines → 386 AI wins, 183 draws, 0 losses.
Playing first:
- 73 lines → 71 wins, 2 draws, 0 losses.
Across all 642 possible 3×3 games, it never loses. On 3×3, “unbeatable” isn’t a claim — it’s the entire game tree.
2. Alpha-beta earns its keep
Minimax alone is wasteful: it scores branches that can’t possibly change the decision. Alpha-beta pruning cuts them the moment that’s provable. Choosing the opening move at full depth:
| Search | Node visits |
|---|---|
| Plain minimax | 549,945 |
| With alpha-beta | 36,528 |
That’s a 93% reduction — identical answer, ~1/15th the work. It’s why Hard mode replies instantly.
3. Does it break on bigger boards? I expected it to. It didn’t.
The engine caps its search depth as the board grows (9 → 7 → 5 → 3) and only needs 4-in-a-row past 3×3. A capped horizon should leave a crack. So I ran the Hard AI against random and greedy opponents on 4×4, 5×5, and 6×6:
| Board | vs random | vs greedy |
|---|---|---|
| 3×3 | 91.8% W · 8.2% D · 0 L | draw · 0 L |
| 4×4 | 72.5% W · 27.5% D · 0 L | draw · 0 L |
| 5×5 | 96.7% W · 3.3% D · 0 L | draw · 0 L |
| 6×6 | 100% W · 0 L | win · 0 L |
0 losses across 628 simulated games, on top of the exhaustive 3×3 proof. What actually changes with board size isn’t losing — it’s that forcing a win gets harder, so results drift toward draws.
Why it holds up: the engine always blocks an immediate threat before it searches, and 4-in-a-row stays defensible within the depth cap. The genuine fragility is theoretical — a player who can set up a fork beyond the AI’s horizon — which is exactly why the full game offers boards up to 10×10.
Takeaways
- If a game is small and its policy is deterministic, enumerate — don’t sample. A proof beats a big sample size.
- Alpha-beta’s payoff on real trees is bigger than the textbook “it helps” — here, 93%.
- Benchmark your own claims. I set out to find where “unbeatable” breaks and instead measured how it holds.
Engine + benchmark (run it yourself): github.com/lucian-devops/tictactoe-ai
Play it: lkforge.com/games/tictactoe
