To Win or Not To Win

Playing games in Math classes can be fun and enjoyable, but also can be a way of learning. In class the other day we played a game much like master mind in the sense that you have to try to match your sequence to your opponents. This game differs from master mind by the way you play. Player 1 is given a 6x6 array in which to start the game, Player 1 chooses a sequence of 1's and 0's to fill in the first row of the 6x6 array. After this is done, Player 2, in their 1x6 array, fills in a single 1 or 0. This process continues until Player 1 fills in the 6th row of their array and Player 2 fills in their last square. The goal, much like master mind, is for Player 1 to end with the same sequence that Player 2 creates, allowing Player 1 to win. For Player 2 to win, they must ensure that Player 1 does not match their sequence.


Through activities such as these in the classroom, students become more engaged in the material. Even more so engaged if the game is actually fun. In this game, most groups found the logic behind it right away. Most groups still, however, continued to play in order to gain a better insight into what worked and what didn't. We took what we had concluded about the game and tried to figure out if it worked in various cases. One such case my group did was having Player 2 choose the same digit in certain spaces. This allowed for Player 1 to have a better chance at winning but did not ensure victory. To see the strategy behind the game, you can look below, otherwise try your best to figure out what works and why.














*Game Spoiler*
















While this game at first may seem fair in the sense that both players have an equal opportunity to win on their own accord, this is not exactly the case. Player 1 can have all of the strategy in the world to win, but all that matters is what Player 2 does. Because Player 2 goes second, to ensure a victory every time, all they have to do is pick the opposite of what Player 1 chose (if Player 1 picks a 1, Player 2 chooses a 0) for each row. This, in the end, shows the opposite of the diagonal of Player 1's array. (i.e. (1,1) is the opposite of the first spot in Player 2's array, (2,2) is the opposite of second spot in Player 2's array, etc.) Albeit not the only way for Player 2 to win, it is the easiest way.