The Chance Of Schwarzenegger’s ‘F*ck You’ Acrostic Being Random: One In A Trillion

The likelihood that Gov. Arnold Schwarzenegger’s (R-CA) recent vulgar hidden message was inadvertent is about one in a trillion, according to a Wonk Room analysis. In a recent message announcing a veto of a bill sponsored by Assemblymember Tom Ammiano — who had earlier told the governor to “kiss my gay ass” — the first letters in each line of the two paragraphs spelled out “Fuck You,” with that capitalization. The governor’s press secretary claimed it was just a “weird coincidence“:

Schwarzenegger’s press secretary, Aaron McLear, insisted Tuesday it was simply a “weird coincidence.” He sent us veto messages the governor sent out in the past with linguistic lineups such as “soap” and “poet,” which he said were also unintended.

Ignoring the likelihood of the paragraphs breaking into the correct 4-3 lines necessary for “Fuck You” and the likelihood of the capitalization being inadvertently correct, the probability of that particular phrase is approximately one in a trillion.

This is considerably smaller than the likelihood of the vulgarity appearing if the distribution of first letters were even, which is 1 in 10 billion (26^-7 = 1.25e-10).

If word distribution were based on the frequency of first letters in a common word dictionary [3esl.txt], then the likelihood of randomly spelling out the particular phrase would be one in a trillion (1.19e-12).

However, that ignores the distribution of word frequency in speech — words beginning with “t” (e.g. “the”, “that”) appear much more often than any other. Calculating first-letter frequencies from a 30,000-word concordance of recent speeches by Schwarzenegger (removing instances of “Thank you”), we still find the likelihood of the phrase in question randomly appearing to be one in a trillion (8.8e-13), in line with our less well-designed estimate.

Now, the likelihood that some phrase would be spelled out? Ignoring letter distribution, there’s about a 0.3% chance any four letter string is a common English word, and a 3% chance any three letter string is a common English word. The specific likelihood of the words “soap” and “poet” appearing, for example, given the Schwarzenegger speeches, is one in 100,000 — much greater than the one in 10 million shot of “fuck” appearing.

As letter distribution would make the appearance of common words more likely (e.g. “teas”), the probability of some two-word combination appearing is on the order of two percent. The likelihood of it making any sense, of course, is smaller. A more accurate estimation is left to the reader.

How likely is one in a trillion? To give a sense of scale, one trillion is about 10 to 20 times the number of human beings who have ever lived on the planet. For a person to speak a trillion words, you’d have to live for 400,000 years. About 20 trillion words are spoken every day on the planet. You would need to search through about the number of books in seven Libraries of Congress to find a book that randomly had Schwarzenegger’s phrase going down one of its pages.

Still, that means there’s a chance.

First-letter distribution
Common English words Schwarzenegger speeches
s: 11.57%
c: 9.29%
p: 8.14%
a: 6.04%
d: 5.91%
r: 5.43%
b: 5.25%
m: 5.22%
t: 5.02%
f: 4.92%
i: 4.88%
e: 4.15%
h: 3.99%
g: 3.52%
l: 2.99%
w: 2.93%
o: 2.56%
u: 2.24%
n: 2.06%
v: 1.43%
j: 0.91%
k: 0.60%
q: 0.43%
y: 0.33%
z: 0.12%
x: 0.05%
t: 17.44%
a: 12.74%
i: 8.62%
w: 7.84%
o: 5.96%
s: 5.83%
c: 4.66%
h: 4.55%
b: 4.28%
p: 3.06%
f: 3.06%
g: 3.00%
m: 2.97%
d: 2.42%
l: 2.42%
y: 2.15%
n: 2.07%
e: 2.01%
r: 1.93%
u: 0.81%
k: 0.74%
j: 0.72%
v: 0.68%
q: 0.03%
z: 0.01%
x: 0.00%