Math Hap!

In this game, two players attempt to find "haps" — valid mathematical equations — in a grid of numbers.

There are 9 rounds to this game. At the start of each round, a grid of 9 unique numbers is revealed. Players take turns, having 30 seconds to call a valid "hap." In Math Hap!, a hap is defined as a set of three numbers that can form a valid mathematical equation using one of the four operators plus, minus, multiply, or divide and the equal sign. For example, 3, 4, and 12 form a valid hap because 3*4 = 12, but 1, 2, and 5 do not form a valid hap because there is no way those numbers can form a valid mathematical equation using the four standard operators. During the 30 seconds, a player will earn a point if they call out a valid hap that has not been called out before, while they will lose a point if they call out an invalid hap or call out a valid hap that has already been called. You may also call 'gyul': if you call 'gyul' when there are no more new valid haps available to be called, you will earn 3 points. If you call 'gyul' incorrectly, you will lose a point. After you call a hap or a gyul, the turn passes to your opponent, who will then have 30 seconds to do the same. A round ends after a successful gyul.

The DMO, @Anon, may choose if he wants to go first or second in the first round. Every following round, the player who did not call gyul correctly goes first.

After 9 rounds, whoever has the most points will win the Death Match and advance to the Finals of Exordium. If the points are a tie, a tiebreaker round will be played. If the points are still a tie after the tiebreaker round, whoever earned the least amount of penalties (from incorrect gyuls and haps) will win the Death Match. If even that is a tie, @Anon, as the DMO, will win the Death Match.

Clarification: A hap consists of 3 different numbers. Looking at the example in #dm7-examples, 1 x 1 = 1 and 2 - 1 = 1 are not valid haps.