# Can You Cut The Perfect Pancake?

A FiveThirtyEight Riddler puzzle.
mathematics
Riddler
Published

April 23, 2021

## Riddler Classic

Riddler Nation’s neighbor to the west, Enigmerica, is holding an election between two candidates, $$A$$ and $$B$$. Assume every person in Enigmerica votes randomly and independently, and that the number of voters is very, very large. Moreover, due to health precautions, $$20$$ percent of the population decides to vote early by mail.

On election night, the results of the $$80$$ percent who voted on Election Day are reported out. Over the next several days, the remaining $$20$$ percent of the votes are then tallied.

What is the probability that the candidate who had fewer votes tallied on election night ultimately wins the race?

## Computational Solution

The probability that the candidate who had fewer votes tallied on election night ultimately wins the race is approximately $$\bf{14.82}$$.

using Distributions
runs = 100000
frac_day = 0.8
frac_mail = 1 - frac_day
num_total = 1000000
num_day, num_mail = trunc(Int32, frac_day*num_total), trunc(Int32, frac_mail*num_total)
succ = 0
for i in 1:runs
print(2*succ/runs)