The Onin game is a minigame in Jak II given by Onin. In the mission "Beat Onin game", Jak had to beat Onin's final test to acquire the last piece of the Seal of Mar. He needed 400 points to beat the task.
Onin will summon four different symbols (corresponding with the face buttons on the controller; , , and ). She will continuously summon them at a faster rate as well as higher amounts at once as the mission progresses. Generally the types of waves can be divided into those where a lot come all at once (mass), many after each other (speed) or at a more steady rate and in couples.
You start with twenty allowances: missing a symbol or pressing a button without a corresponding symbol on-screen results in the loss of one point. It is unknown if the game actually has a limit or if it goes on until it becomes impossible to continue.
The key to winning and earning points is by activating the same symbol in succession. You receive one point for every symbol, however if you press square twice in a row then the second square will return one extra point for the combo. This combo point also increases by one for every extra symbol pressed and most importantly is awarded for every succeeding symbol pressed, not at the end of the combo.
Taking this into account, activating two squares (for example) results in 1 + 1 (+ 1 combo point). Add another square and it becomes 1 + 1 (+ 1 combo point) + 1 (+ 2 combo points) which equals six total points. If you were to add another you would have ten points, then fifteen, twenty-one, twenty-eight, thirty-six, forty-five, fifty-five and so on. Take note that the combo only ends when a different button is pressed, not when all on-screen symbols have been activated.
You can also pause the game by pressing the select button on your controller; this gives you time to think about what buttons you're going to press next.
You earn three Precursor orbs for reaching the target score. The orbs will be awarded immediately once the score is reached, but note that you can only get the reward once. The target is 1000 points