Pentago

How to win at Pentago

Pentago is five-in-a-row with a twist that is never optional. The board is a 6x6 grid split into four 3x3 quadrants, and every turn has two halves: place one marble on any empty cell, then rotate any one quadrant a quarter turn, left or right. Five of your marbles in a straight line, horizontal, vertical, or diagonal, wins. The rotation is what separates this from Gomoku or Connect Four: a row you patiently assembled can be swung apart, and a scatter of marbles nobody was watching can snap into five. Beginners play the board in front of them. The only board that matters is the one after the twist.

Marbles that do not move

Each quadrant spins around its own center cell, and that center never goes anywhere. Those four cells are the board's bedrock, which is why strong openings usually start on or beside them. There is a subtler stability worth knowing too: three in a row through a quadrant's center survives any rotation of that quadrant, because a quarter turn maps the middle row onto the middle column. The trio stays intact; only its direction swings. Notice also where the board's two long diagonals run: each one passes through two quadrant centers. Diagonal attacks anchored on center cells are the hardest threats in the game to dismantle, and a large share of wins against good opposition arrive on exactly those lines.

Threats that survive the spin

Any line of five must cross at least two quadrants, so every plan is exposed to at least one hostile rotation. The answer is the double threat: build toward two different five-lines at once, ideally sharing marbles, so that no single defensive twist covers both. Better still, arrange to win by rotation. Place a marble that looks harmless, then turn a quadrant so two of your groups swing into one straight five. Rotation wins are genuinely hard to see coming, because spotting them means checking all eight possible twists every single turn, and human attention runs out before eight.

A worked example makes the idea concrete. Suppose you hold the entire middle row of the bottom-left quadrant, and two of your marbles sit on the middle column of the bottom-right quadrant. On your turn, place your marble anywhere quiet, then rotate the bottom-right quadrant a quarter turn: its middle column swings onto its middle row, and suddenly five of your marbles run straight across the board's fifth row. Nothing about the position looked urgent one move earlier, which is the point. Set up trios and pairs on the cross lines through quadrant centers, and let a single twist do the assembling.

There is also a quiet trick hiding in the rules. Rotating an empty quadrant changes nothing, and neither does rotating a quadrant whose only marble sits on its center. When every meaningful twist would improve the computer's position, spinning a dead quadrant is a legal way to pass, and close games regularly hinge on who still has a harmless rotation in reserve.

Habits of strong Pentago players

• Before committing, picture the board after your rotation, then after each twist the computer could answer with.
• Check all eight rotations for an immediate five, yours and theirs, every turn. Most lost games trace back to one skipped check.
• Open on or next to quadrant centers, and route your main threats through them.
• Prefer two slow threats to one obvious row that a single twist dismantles.
• Keep a dead quadrant in mind as your emergency pass.

A Mensa winner, fully solved

Pentago comes from Sweden, created by designer Tomas Floden and published by Mindtwister in the mid-2000s. The tactile pleasure of physically twisting the quadrants helped it win a Mensa Select award and spread around the world, and larger multiplayer editions followed. Then in 2014 the mathematician Geoffrey Irving settled it: running the game on a Cray supercomputer and working through on the order of three quadrillion positions, he proved the first player wins with perfect play. Nobody plays perfectly, so the practical lesson is about initiative: moving first carries real weight, and if you move second you should lean harder on double threats and dead-quadrant passes than on racing. The computer opponent here punishes lazy rows quickly, so treat every placement as half a move, and remember that the half you finish with, the twist, is the one that decides games.