A game of chance is played on a gaming machine controlled by a processor in response to a wager. The game includes an array of locations displayed on a video display and individually selectable by a player and the processor. The player and the processor make alternating selections of unoccupied ones of the locations in the array for placement of respective first and second symbol types. The probability of using a winning strategy for the selections by the processor increases with successive ones of the selections by the processor so that the processor appears to become more intelligent as the game progresses. A payout is awarded to the player based on an outcome of the game.