Flip a Coin or Roll a Die

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Problem to Solve

My code needs to randomly pick or decide something.

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Background Knowledge: Pseudorandomness

Computers are deterministic rule-following machines, and can't do things truly randomly. However, we can make them follow a sufficiently complex set of rules that are sufficiently sensitive to initial conditions that the outcome, is, for all practcal purposes, random. This is called pseudorandomness.

A deep dive into that is coming later in this course. For now, we just need a way to "flip a coin" (perhaps a biased one) or "roll a die" in order to write code that can make effectively-random decisions.

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Recipe: Flipping a (Biased) Coin

Goal: Simulate the probabilistic outcome of flipping a coin that comes up "heads" with probability \(p\) and "tails" with probability \(1-p\). (If \(p = 0.5\), we say that the coin is "fair". If \(p \neq 0.5\), we say that the coin is "biased".)

For the convenience of computer code, we'll represent "heads" as True and "tails" as False.

Python's random module has several useful functions. One of them is random.random(), which returns a (pseudo)random floating-point number in the range \([0, 1)\). (That notation means "from 0 to 1, including zero but not including 1".) We can use this to simulate a coin flip by returning True if the random number is less than \(p\) and False otherwise.

import random
def flip_coin(p=0.5):
    return random.random() < p

Easy, no? It's barely even worth wrapping up in a function.

example: sequential flips

How many times in a row must I flip a fair coin to get 3 heads in a row?

heads_in_a_row = 0
flips = 0
while heads_in_a_row < 3:
    if flip_coin():
        heads_in_a_row += 1
    else:
        heads_in_a_row = 0
    flips += 1
print(flips)

Recipe: Rolling a Die

Goal: Simulate the probabilistic outcome of rolling a fair \(N\)-sided die.

The random module also has a function random.randint(a, b) that returns a (pseudo)random integer in the range \([a, b]\). We can use this to simulate a die roll by returning a random integer in the range \([1, N]\).

import random
def roll_die(N=6):
    return random.randint(1, N)

example: rolling two dice

How many times in a row must I roll two fair dice to get a sum of 7?

sum_is_seven = False
rolls = 0
while not sum_is_seven:
    if roll_die() + roll_die() == 7:
        sum_is_seven = True
    rolls += 1
print(rolls)

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