## Multiplication table game

I wrote this because I was running a “stations” day in my AIMS class (seniors who haven’t passed the standardized test to graduate yet) and I wanted them to practice making a multiplication table but add some spice.

It’s based on a card game, Goofspiel. I haven’t come up with a name for it yet, so suggestions are appreciated.

It seems worth a go even outside of math class, due to the balance risk/reward and the possibility of outwitting the psychology of the opponent.

Supplies: Two dice, paper.
Players: 2 optimal, can be done with 3 or 4.

Before starting: each player needs to fill out a multiplication table, 12×12.

On each round:

1. Roll the dice.

2. Each player secretly picks a number from the row indicated by the dice, and writes it down covered by their hand.

3. Players reveal their numbers simultaneously.

4. The player with the higher number wins the number of points they wrote down. If there is a tie no points are won.

5. After a player uses a number from a particular column that column can no longer be used by that player in the game.

(Since the rows used are determined solely by the rolls of the dice, they can repeat.)

After 11 rounds the game is over and the highest score wins.

It’s easiest for the players to write their number picks directly on the scorecard, then cross them out if they lose or tie a round.

Rule #5 is very important: it is what makes the game interesting. Does one go for broke with the 12 column early (especially if it is on a high die roll), or does one save it? Should one be mostly random to confuse the opponent, or try to optimize based on the dice rolls (leading to potential ties if the opponent runs the same strategy)?

### 6 Responses

1. Is a different row required each time, too, or can rows repeat?

2. Ok, so I guess you answered this in the last paragraph, but I was curious about how large the table is.

But now I’m wondering if strategy would be to always just go for the largest number remaining in the respective column?

So if we roll a 6, I’d think both players would pick the highest remaining multiple of 6 on the table.

• I changed the rules to be clear about the 12×12.

Let’s say Ann is playing with your strategy, and Bob is doing his own thing.

ROUND 1: Dice comes up as 6.
Ann goes for column 12, 6 * 12 = 72
Bob goes for column 1, 6 * 1 = 6. Ann wins 72 points.

ROUND 2: Dice comes up as 12
Ann goes for column 11, 12 * 11 = 121
Bob goes for column 12, 12 * 12 = 144, Bob wins 144 points.

Ann gets no points for round 2, so Bob is winning, 144-72.

3. Neat. I’ll tuck it away, and if the opportunity presents itself…