Random number generation in a programming language

What you'll learn

• What random number generation means in a program.
• How to generate a random integer within a chosen range.
• How to use random values with variables, selection, loops, and lists.
• How to avoid common range and off-by-one mistakes.

Why programs use random numbers

Most programs follow exact instructions, so they normally behave predictably. Sometimes, though, you want a program to make an unpredictable choice: rolling a die in a game, choosing a quiz question, generating a secret number, or simulating an event.

At GCSE, you are expected to use random number generation in programs. You are not expected to explain how the computer creates pseudo-random numbers.

Prerequisites: variables, assignment, and integers

A random number is usually stored in a variable so the program can use it later.

For example:

score ← 0
name ← USERINPUT

Most GCSE random-number tasks use integers, which are whole numbers such as 0, 1, 2, 3, and so on.

Generating a random integer in a range

A range is the set of possible values a random number can have. The lower bound is the smallest possible value, and the upper bound is the largest possible value.

In these notes, we will use AQA-style pseudo-code like this:

randomNumber ← RANDOM_INT(lower, upper)

This means: generate a random integer from lower to upper.

The diagram shows how the lower and upper bounds control the possible outputs.

Example: counting possible outputs

Storing and using a random value

A random number is most useful when you store it and then use it in a calculation or decision.

For example, this creates a secret number guessing game:

secretNumber ← RANDOM_INT(1, 10)
guess ← USERINPUT

IF guess = secretNumber THEN
    OUTPUT "Correct"
ELSE
    OUTPUT "Not correct"
ENDIF

Example: creating a dice game turn

The pseudo-code could be:

dieOne ← RANDOM_INT(1, 6)
dieTwo ← RANDOM_INT(1, 6)

IF dieOne = dieTwo THEN
    OUTPUT "Double"
ELSE
    total ← dieOne + dieTwo
    OUTPUT total
ENDIF

Using random numbers to choose between outcomes

You can map each possible random value to an outcome. For a fair coin toss, there are two possible outcomes, so you only need two possible random values.

coin ← RANDOM_INT(1, 2)

IF coin = 1 THEN
    OUTPUT "Heads"
ELSE
    OUTPUT "Tails"
ENDIF

Example: choosing a fair outcome

Choosing a random item from a list

A random number is often used as an index into a list or array.

If a list has 5 items and uses indexes starting at 0, the valid indexes are 0, 1, 2, 3, and 4. So the random index should be from 0 to 4.

index ← RANDOM_INT(0, 4)
OUTPUT questions[index]

Example: choosing a random question

Using random numbers inside loops

Iteration means repeating instructions. Sometimes you want a new random value each time a loop runs.

For example, this keeps rolling a die until a 6 appears:

attempts ← 0

REPEAT
    roll ← RANDOM_INT(1, 6)
    attempts ← attempts + 1
UNTIL roll = 6

OUTPUT attempts

Example: stopping when a random value appears

Python 3 version

In Python 3, you need to import the random module before using randint.

import random

dice_roll = random.randint(1, 6)
print(dice_roll)

For a guessing game:

import random

secret_number = random.randint(1, 10)
guess = int(input("Enter a number: "))

if guess == secret_number:
    print("Correct")
else:
    print("Not correct")

Testing programs that use randomness

Random programs are harder to test because you cannot predict the exact output every time. Instead, test whether the output is always sensible.