Here is a fact about tic tac toe that sounds like it needs a computer to establish and does not: the second player can never have a winning strategy. Not in tic tac toe, not in Gomoku, not in Hex, not in any game of that shape.

You do not need to check a single position to prove it. The argument is a few lines long, it is completely rigorous, and it is one of the most elegant things in game theory.

The argument

Suppose, for contradiction, that the second player - call them O - has a guaranteed winning strategy. A strategy that wins no matter what X does.

Now let X do something cheeky. X makes an arbitrary first move anywhere, and then simply ignores it. From that point on, X pretends to be the second player and follows O's winning strategy.

Every time O moves, X responds exactly as O's strategy says the second player should respond. X is playing a winning strategy - the very one we assumed O had.

There is one complication. Occasionally the strategy will tell X to play on a square X has already occupied with that arbitrary first move. When that happens, X just makes another arbitrary move somewhere else and carries on.

So X wins. But we assumed O wins. Both cannot be true, so the assumption was false: O has no winning strategy.

That leaves exactly two possibilities for a game of this type - a first-player win, or a draw with perfect play. Second-player wins are impossible.

The hidden assumption

The argument depends entirely on one thing, and it is worth stating clearly because it is where the whole thing lives: having an extra piece on the board can never hurt you.

In tic tac toe that is obviously true. An extra X is either useless or helpful; it never actively damages your position. So the "wasted" first move costs nothing, and X can borrow O's strategy freely.

Change that assumption and the argument collapses immediately. Which is precisely what happens in the misère version of the game, where making three in a row loses - there, an extra piece can absolutely hurt you, strategy stealing does not apply, and the analysis has to be done the hard way. That is a separate story.

What it does and does not tell you

The result is what mathematicians call non-constructive. It proves a winning strategy for the second player cannot exist, and it tells you absolutely nothing about how to play.

That is a genuinely strange kind of knowledge. We know from this argument alone that tic tac toe is a first-player win or a draw - and it turns out to be a draw, but that fact required actual analysis of the game tree, not this proof.

The gap between "we know the answer exists" and "we know what it is" runs through a lot of game theory. The draughts family is the clearest example: it was proven a draw under perfect play in 2007 after roughly eighteen years of computation, which is a completely different kind of achievement from a three-paragraph argument. In Checkers, you are playing a game whose final answer is known but whose winning technique still has to be learned move by move.

Where else it applies

The argument works for any game where these hold: two players alternate, extra pieces never hurt, the board is symmetric between the players, and there are no draws by exhaustion that favour one side.

The most famous application is Hex, where John Nash used exactly this reasoning in the late 1940s. Hex cannot end in a draw - someone must complete a connection - so strategy stealing proves the first player wins outright. And still, on a large board, nobody knows the winning strategy.

It applies to Gomoku on an unbounded board, and to many variants of tic tac toe on larger grids. It does not apply to games where pieces move rather than accumulate, because there the "wasted move" is not free - moving a piece changes your position rather than simply adding to it.

That distinction is worth holding onto. Games where you place pieces and games where you move them behave differently at the deepest level. Play Reversi and pieces are placed but they also flip, so having more of them mid-game is frequently a disadvantage - which breaks the assumption completely, and is exactly why Reversi cannot be analysed this way.

What this means at a 3x3 board

Practically: if you are going second, you cannot force a win against a competent opponent. Your realistic best outcome is a draw, and your entire job is to secure it.

That is not defeatism, it is accurate. Going second in tic tac toe is a defensive assignment, and playing it well means:

  • If X takes the centre, take a corner. Taking an edge loses against correct play.
  • If X takes a corner, take the centre. Anything else loses.
  • If X takes an edge, take the centre - or an adjacent corner, both of which hold.
  • Then block forks, not just immediate threats. Most second-player losses come from blocking a line while allowing a position where two lines complete at once.

Bigger boards, and where it gets interesting

The 3x3 game is solved and drawn, which is exactly why the larger boards are where the interest lives. On 4x4 and 5x5, the question of how many in a row are needed changes everything - and the general family of these games, where you specify board dimensions and a target line length, has been studied extensively without being fully resolved.

The pattern is roughly that small targets on large boards are first-player wins, and large targets on any board tend toward draws because the defender always has time to interfere. Strategy stealing tells you second player never wins in any of them, which narrows the question usefully before any analysis begins.

Give it a go

Play a few games on hard mode going second and confirm for yourself that a draw is the ceiling - the engine will not let you win, and it will punish any deviation from the responses above. Then try 5x5, where the extra space genuinely reopens the game.

The how to win guide covers the forcing patterns, the maths page goes further into the game-theory side, and the rules cover the variants. The main game is where to practise, and two-player mode lets you test the second-player defence against a human.