The River Game

Introduction

In today's lesson, you will device a strategy to beat your classmate at the River Game.

You need: 2 dice, 24 counters (12 each of 2 different colours), a classmate and this game board (PRINT ME)
Put your 12 counters behind the numbers along your side of the river. You can put 1 or more counters behind a number or none at all.
Take turns to roll the dice and add the 2 numbers together to get your score. If there is
a counter behind the stone with that number, move it across the river. You can only move
1 counter in each turn.
The winner is the first person to move all their counters across the river.

Play the game several times. What is the best strategy to win this game?

Support

Here are some prompts to help you work out a strategy:

You may wish to record your total each time you throw the dice on this template (PRINT ME). What have you noticed?
Which number or numbers are hardest (or impossible) to get? What are the theoretical probabilities of getting these? How do you work these out?
Which numbers seem to be easy to get? What are the theoretical probabilities of getting these? How do you work these out?
To work out the theoretical probabilities, can you draw a table that sets out all the possible scores (dice totals)? Hint: here.
Put your theoretical probabilities on this template and add the experimental frequencies on as you play more games.
At the end, calculate the experimental probabilities. How do they compare with the theoretical ones? For a refresher of experimental and theoretical probabilities you learnt in year 7, click on the hyperlink.

Further Questions and Challenges

Can you design a pair of dice that will give the counters behind any of the 12 stones the same chance of crossing the river?

How would your strategy change if you throw one 12-sided die instead? What if you throw three 4-sided dice instead? Play the game with a friend and test your theories.

Further Practice

Some of the essential skills introduced in this lesson are theoretical and experimental probabilities of combined events. Practise these relevant skills on DrFrostMaths, CorbettMaths, MyiMaths and Eedi. Watch any video and/or go through any online lesson as you see fit.

Transum

For more goodies on Probability on Transum, click on the hyperlink.

Extension

Can you adapt what you learnt in the lesson to come up with the best strategy to win the following games?

Snail Race
Two Dice Bingo
Skunk Game
Best Dice - this puzzle is more challenging!

Page updated

Report abuse