Dice Race

Beep and Pixel are racing! Each turn they roll a dice and zoom ahead by that many squares. The first one to reach 20 wins. You will not even need to type anything, because the computer plays both racers. This is called a simulation: a program that pretends to be something real so we can watch what happens.

What you need

• A computer with Python 3 and IDLE
• A real dice, if you would like to compare the program with real rolling (optional)
• About 45 minutes

A dice in Python

A real dice has six faces. In Python we can write random.randint(1, 6) to get a whole number from 1 to 6. It can be 1 and it can be 6, and each number is equally likely.

We also need a way to remember where each racer is. A variable is a labelled box that holds a value. We will use beep and pixel for the positions, and turn to count the turns. They all start at 0.

The race

Each time round the loop is one turn. Beep rolls first. We add the roll to Beep’s position, print what happened and check for a win. If Beep has not won, Pixel gets a go.

The loop starts with while True:. Since True is always true, this loop would go on forever, so we need a way out. The word break means “stop the loop right now”. We use it as soon as somebody wins.

The program has random.seed(7) so that the race is the same every time and you can check your work. Delete that line to get a different race each time.

import random

random.seed(7)
beep = 0
pixel = 0
turn = 0

while True:
    turn = turn + 1
    roll = random.randint(1, 6)
    beep = beep + roll
    print("Turn", turn, "- Beep rolled", roll, "and is on", beep)
    if beep >= 20:
        print("Beep wins the race!")
        break
    roll = random.randint(1, 6)
    pixel = pixel + roll
    print("Turn", turn, "- Pixel rolled", roll, "and is on", pixel)
    if pixel >= 20:
        print("Pixel wins the race!")
        break

Turn 1 - Beep rolled 3 and is on 3
Turn 1 - Pixel rolled 2 and is on 2
Turn 2 - Beep rolled 4 and is on 7
Turn 2 - Pixel rolled 6 and is on 8
Turn 3 - Beep rolled 1 and is on 8
Turn 3 - Pixel rolled 1 and is on 9
Turn 4 - Beep rolled 5 and is on 13
Turn 4 - Pixel rolled 1 and is on 10
Turn 5 - Beep rolled 3 and is on 16
Turn 5 - Pixel rolled 5 and is on 15
Turn 6 - Beep rolled 1 and is on 17
Turn 6 - Pixel rolled 5 and is on 20
Pixel wins the race!

That was a close one. Look at the last two lines of the race. Beep was on 17 and Pixel rolled a 5 to reach exactly 20, just in time. Notice we wrote >= 20, which means “20 or more”. That way a racer who rolls past the finish line still wins.

Here are the new ideas:

Is going first fair?

Beep always rolls first. Does that help? In a race to 20, the first player might just get there a little sooner. Let us ask the computer to run 1000 races and count how often the player who goes first wins. The for race in range(1000) loop plays the races, and the while loop inside it plays one race.

import random

pixel_target = 20
beep_wins = 0
for race in range(1000):
    beep = 0
    pixel = 0
    while beep < 20 and pixel < pixel_target:
        beep = beep + random.randint(1, 6)
        if beep < 20:
            pixel = pixel + random.randint(1, 6)
    if beep >= 20:
        beep_wins = beep_wins + 1
print("Beep won", beep_wins, "of 1000 races")

There is no seed this time, so the number is a bit different each run. Your output might look like this:

Beep won 618 of 1000 races

If the race were perfectly fair, you would expect about 500. Beep usually wins somewhere around 600. That is a big advantage just for taking the first turn, and it is good to know before you make a game!

Challenges

import random

pixel_target = 18
beep_wins = 0
for race in range(1000):
    beep = 0
    pixel = 0
    while beep < 20 and pixel < pixel_target:
        beep = beep + random.randint(1, 6)
        if beep < 20:
            pixel = pixel + random.randint(1, 6)
    if beep >= 20:
        beep_wins = beep_wins + 1
print("Beep won", beep_wins, "of 1000 races")

What you learned

• random.randint(1, 6) works like a six-sided dice.
• A variable remembers a score or position while the game runs.
• while True: with break repeats until something happens that you choose.
• A simulation lets the computer play a game many times to test it.
• Going first can be an advantage, so a good designer checks that a game is fair.