Red connects left to right. Blue connects top to bottom. Claim a hex each turn — first to link both of your sides wins.
Each cell borders 6 neighbours. Red is trying to build an unbroken chain of red cells from the left edge to the right edge; Blue is trying to connect top to bottom.
Players alternate placing one stone per turn on any empty cell — there's no capturing, stones never move once placed.
A quirk of Hex: the game can never end in a draw — it's mathematically impossible for both a left-right and a top-bottom connection to be blocked at the same time on a filled board. Someone always wins.
Pick a side. The computer always takes an immediate winning move and always blocks an immediate one-move loss. Beyond that, it decides between moves by randomly finishing out the game many times per move and seeing which move wins most often — a real technique used by strong Hex-playing programs, since it naturally favours moves that keep multiple ways to connect rather than committing to one fragile path. On Hard, it also looks one move further ahead, weighing candidates against the opponent's best likely reply rather than just the position before that reply.