MONTE CARLO TEST OF "THEODOR KAZNSKI" in 340 CHARACTER ZODIAC CIPHER Abstract I compute the probability that the first line of the 340 Character Zodiac cipher contains a "close match" to the ciphertext THEODORE purely BY CHANCE to be roughly 0.1 %, while the probability that the last line of the 340 cipher contains a "close match" to the ciphertext KACZYNSKI is computed to be roughly 0.08 %. The probabilities depend on what is meant by "close match", so different definitions of "close match" are explored. The odds that a pure coincidence is responsible for the first and last lines of the 340 Cipher "closely matching" the first and last names of THEODORE KACZYNSKI are computed to be somewhere between 100,000 to 1 and 20 million to 1. INTRODUCTION Since the late 1990's the possibility that confessed UNABOMER suspect Theodore Kaczynski was responsible for the Zodiac crimes has been discussed. The strengths and weaknesses of such a theory, based on psychological profiles, technical skills, physical location of the suspect and other factors will not be discussed here. One intriguing possible connection is the supposed appearance in the 340 cipher of near matches to the suspect's first and last names THEODORE & KACZYNSKI. The purpose of this discussion is to determine how likely it is that this supposed connection was in fact due to pure chance. The 1st line of the cipher contains 17 characters which include THER. It also includes a reversed D and two different circular symbols which are be taken by those wishing to support this connection to represent "O". If allowance is made for reversed letters and the "O"'s, then the 17 characters of the first line then contain the characters THEODOR. This is 1 character away from matching THEODORE. Similarly, the last line of the cipher contains the letters: KAZINS, and also a reversed "K", spelling KAZNSKI, which is TWO characters away from matching KACZYNSKI. In both cases, seven characters are matched. Note that the last line also contains, ZOAI, 4 of the 7 characters in ZODIAC. If we take a solid triangular symbol to represent "D" and if we change the letter "K" to its homophone "C", AND if we switch the location of the A & I, this sequence forms the killers epithet: "ZODAIC". It is interesting that in order to find "ZODIAC" in this last line, 2 substitutions and 1 letter switch must be made, (but no major anagramming); yet everybody would agree that these alterations are "required", that this "near match" to ZODIAC could not possibly have happened by chance. I will attempt to answer the following questions: 1.) What is the probability that a 17 character line of text, randomly drawn from the cipher will provide a near match to "THEODORE" ? 2.) What is the probability that a 17 character line of text, randomly drawn from the cipher will provide a near match to "KACZYNSKI" ? MAKING THE CIPHERTEXT READABLE TO answer these questions we need first to define which non-alphabet symbols (like half filled 0's) represent actual letters (like "O"). The more such correlations we make, the easier it will be to spell what we want. For purposes of this discussion, I will make the MOST correlations I can think of, that is, I will make it as EASY AS POSSIBLE for the ciphertext of the 340 cipher to spell names BY PURE CHANCE. (This is the most conservative approach to take, ie it allows pure chance the best possible opportunity to be the explanation for the matches we find). I make the following assignments: -All reversed letters = their forward counterparts -All 6 Circle characters = O -All 3 triangle characters = D (As suggested by ZO"D"AIK) -Zodiac symbol = Z -Upsidedown T = T DEFINING "CLOSE MATCHES" Using these assignments the string "THEODOR" appears in the first line of the code. In one sense this is a perfect match to "THEODORE" because every letter of THEODORE is found there. I will call this a (Perfect) Type 1 Match. Alternatively, to get a perfect match we could require that every letter be present in the code AT LEAST AS MANY TIMES TIMES as it is present in the name. I will call this a Type 2 Match. In this stricter sense, "THEODOR" is not perfect match; it is one letter away. Depending on how many letters off we are willing to tolerate, we can define "Close Match" to be a match of type 1 or type 2 which is, say either 1 character off or 2 characters off. Of course the more characters we are willing to tolerate being off, the more likely it is that any random string of text will "closely match" the name we're considering. Using these definitions, the last line is 2 letters off from being a Type 1 match to KACZYNSKI, and also 2 letters off from being a Type 2 match because both "C" and "Y" are missing. MONTE CARLO METHOD To answer the questions above, I randomly draw characters from the 340-cipher, 17 at a time, then check to see if that string provides a close match, as defined above, to the given "matchword", ie "THEODORE" or "KACZYNSKI". After a large number (~10,000) draws are made, the number of matches divided by the number of draws is reported as an approximation to the probability that the close match occured BY CHANCE. This process can be repeated several times to see if the results are consistent. The average (mean) of five such "runs" is reported below, for matchwords "THEODORE" and "KACZYNSKI", under Type 1 and Type 2 matches, along with the variance (standard deviation) between the runs. PROBABILITY OF MATCHES Match Tolerance Draws Mean Match Variance Matchword Type (# Letters) per run Fraction over 5 runs THEODORE 1 0 10,000 0.11 % +-0.04 % KACZYNSKI 1 2 10,000 0.91 % +-0.06 % THEODORE 2 1 10,000 0.10 % +-0.03 % KACZYNSKI 2 2 10,000 0.08 % +-0.04 % COMBINING PROBABILITIES To summarize these results, I find that the probability that RANDOM 17 Character lines of the 340 Cipher contain as "close matches" (Type 1) to BOTH THEODORE and KACZYNSKI as the actual text does to be: 0.11% * 0.91% = 1 * 10^-5 = 0.001 %, ie one in 100,000 The probability that random lines match BOTH "THEODORE" & "KACZYNSKI" in the stricter sense (Type 2) to the same degree as the actual Cipher is found to be: 0.10% * 0.08% = 0.00008 % or one in 1.2 million. It might be added that there is another type of "match" here. In the 340 Cipher, the FIRST and LAST lines are the ones which match the FIRST and LAST names of THEODORE KACZYNSKI. Since there are 20 lines in this cipher, perhaps the probabilities above should be multiplied by 20. CONCLUSION Using the Monte Carlo method of random draws, I showed that the probability that the Zodiac 340 Character cipher contains close matches to both THEODORE and KACZYNSKI by PURE CHANCE can be estimated at somewhere between 100,000 to 1 and 20 million to 1. If random chance is not the reason that this name "appears" in the cipher then this name must have been consciously inserted into the code by the author of the cipher. It should be added that close match of KACZYNSKI in the last line might not come as a surprise, since most people assume that the match to ZODIAC in the last line is not a coincidence. Even if we do not consider the KACZYNSKI match in the last line significant, the odds of the first line matching THEODORE are still about 1,000 to 1. Also this question can be turned around. The probability that the killer's name and/or opening phrase "This is the Zodiac Speaking" nearly match THEODORE KACZYNSKI, merely by chance, must be similar to the odds calculated above.