Anagrams - Combinatorial Probabilities

July 27, 2013
Posted by Jay Livingston

Maybe you’ve just taken a course in advanced probability.  Here’s a problem. Consider the following tweet*

What is the probability that someone else within the next day or two, coincidentally and without any knowledge of this tweet, would tweet a message that is a perfect anagram of this one? 

I have no idea even how to start thinking about it. The tweet has 29 letters, probably the more frequently used letters.  How many groupings of them form words, how many of those groupings make sense, and so on.  I give up.  But here’s one answer.

Second question.  What is the probability that someone would create a program to cull the Twitter universe, extract anagrams, and post them to a Tumblr page?  I’m not sure how to calculate that one either, but when you see the site, you might well think the probability approaches 1.0, i.e., “It had to happen.”**

This Tumblr has been up for less than a week, and so far there are about thirty examples, most of them short. It’s possible that the pool of matches has been edited to include only those that sound like they might be a conversation.  Like this:

Or this conversation between hooker_225 and FutureShrink:

You can find the entire collection at Anagramatron (here).

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* Ignore whatever else Victoria and Larry, with their interesting @ might be doing. Focus on the letters in the message.

** UPDATE:  My advanced probability informant tells me that it can be done with a fairly simple algorithm. Take two phrases, strip out everything but letters, sort alphabetically, and check to see if they are identical.  For the 400 million tweets in a single day, your computer has to do only about 80 trillion such comparisons.