# John Kerrich Coin-flip Data

Can anyone suggest where to obtain the results of the 10,000 coin flips (i.e., all 10,000 heads and tails) performed by John Kerrich during WWII?

• Given that he was locked up in a Nazi prison at the time, I do wonder if he had enough paper to record all 10k results, or if he only actually wrote down the summary values. Nov 15, 2013 at 17:00
• @Corone 10K results could easily be recorded on one standard sheet of paper using, say, a dot and bar code (as in ||||..|....||.|..||. etc). This can be compressed using (for instance) hexadecimal. In the previous example, letting | be 1 and . be 0, the hex representation is f21a6. By writing small but visible characters I can easily fit 50 such characters in one line of writing and 50 lines on a sheet, thereby representing a sequence of 50*50*4 = 10K outcomes.
– whuber
Nov 15, 2013 at 17:08
• @whuber haha, yes I started pondering similar things after my comment. I'm doubtful that in the pre-computer era hexadecimal would have sprung to mind as it does now, although octal would still give you a chance. Still I gave it a go and dots and dashes alone I could get more like 100 across a sheet, so if he used both sides 10K would just about fit. Maybe that's why he stopped at 10K! Nov 15, 2013 at 22:19
• A Nazi prison, yes, but in Denmark, it was not an extermination camp ... Mar 17, 2015 at 21:13
• @kjetilbhalvorsen - actually a Danish prison camp in Hald with Danish guards etc. to protect the internees from the Germans Aug 16, 2018 at 17:34

I hadn't heard about Kerrich before-- what a bizarre story. The Google book scan (shared by reftt) of "An Experimental Introduction to the Theory of Probability" doesn't seem to include the body of the text. Feeling a little old-fashioned, I checked out a copy of the 1950 edition from the library.

I have scanned a few pages that I found interesting. The pages describe his test conditions, data from the first 2000 coin flips and data from the first 500 of a series of 5000 equally implausible-sounding urn experiments (with 2 red and 2 green ping pong balls).

Text recognition (and some cleanup) using Mathematica 9 gives this sequence of 2000 tails (0) and heads (1) from Table 1. The head count of 1014 is one more than 502+511=1013 in Table 2, so the recognition was imperfect, but it looks pretty good--at least it got the right number of characters! (Sharp-eyed readers are invited to correct it.)

Here is a graphical summary of this random walk, followed by the data themselves. The accumulated difference between head and tail counts proceeds from left to right, covering all 2000 results.

00011101001111101000110101111000100111001000001110
00101010100100001001100010000111010100010000101101
01110100001101001010000011111011111001101100101011
01010000011000111001111101101010110100110110110110
01111100001110110001010010000010100111111011101011
10001100011000110001100110100100001000011101111000
11111110000000001101011010011111011110010010101100
11101101110010000010001100101100111110100111100010
00001001101011101010110011111011001000001101011111
11010001111110010111111001110011111111010000100000
00001111100101010111100001110111001000110100001111
11000101001111111101101110110111011010010110110011
01010011011111110010111000111101111111000001001001
01001110111011011011111100000101010101010101001001
11101101110011100000001001101010011001000100001100
10111100010011010110110111001101001010100000010000
00001011001101011011111000101100101000011100110011
11100101011010000110001001100010010001100100001001
01000011100000011101101111001110011010101101001011
01000001110110100010001110010011100001010000000010
10010001011000010010100011111101101111010101010000
01100010100000100000000010000001100100011011101010
11011000110111010110010010111000101101101010110110
00001011011101010101000011100111000110100111011101
10001101110000010011110001110100001010000111110100
00111111111111010101001001100010111100101010001111
11000110101010011010010111110000111011110110011001
11111010000011101010111101101011100001000101101001
10011010000101111101111010110011011110000010110010
00110110101111101011100101001101100100011000011000
01010011000110100111010000011001100011101011100001
11010111011110101101101111001111011100011011010000
01011110100111011001001110001111011000011110011111
01101011101110011011100011001111001011101010010010
10100011010111011000111110000011000000010011101011
10001011101000101111110111000001111111011000000010
10111111011100010000110000110001111101001110110000
00001111011100011101010001011000110111010001110111
10000010000110100000101000010101000101100010111100
00101110010111010010110010110100011000001110000111

• You're welcome. I superimposed a plot of these data on your scanned image, hoping it would make any discrepancies obvious, but I'm unable to find any differences at all. Either there are no errors and Kerrich miscounted or I just cannot find the error, but in any case the data posted here are an accurate text rendering of his Table 1.
– whuber
Nov 20, 2013 at 18:16

This presentation shows the data for set intervals of tosses. It also references the primary source from Kerrich.

• The source of the (summary) data in that presentation is Freedman, Pisani, & Purves Statistics (any edition). It is, however, only a summary, not an account of all the results requested here. Kerrich published his results in 1946 in a small book; Google has digitized it.
– whuber
Nov 15, 2013 at 16:35
• Like I said, it has data for "intervals of tosses" and the presentation references Kerrich's monograph where he published his results. I don't know if Kerrich published his a list of every single toss. Figured this was at least more helpful than just the overall proportion.
– user31668
Nov 15, 2013 at 17:20
• @whuber: yes, that was the monograph referenced in the presentation. it seems to have limited availability. has anyone found a pdf?
– user31668
Nov 15, 2013 at 17:24

There's another Kerrich reference in the book "Chance encounters: A First Course in Data Analysis and Inference" by Chris Wild and George Seber which says in chapter 4 (can download supplement from this page) that the data are published in Kerrich [1964] and Freedman [1991, Table 1, p. 248]. The Kerrich book is probably An Experimental Introduction to the Theory of Probability, and Freedman is the same textbook already mentioned. I doubt that the 1964 monograph would contain more data than the 1946 one though.

That book of Kerrich can be bought used from Amazon, but the quoted price is rather stiff!

A better option is https://openlibrary.org
You need to make an account there, then install Adobe Digital Editions for reading the book. (seems like no other program will do, the downloaded book have DRM, digital restrictions management). Then you can download ("borrow") the book. I am reading it just now. I guess I can take a screen copy of the pages with the results, and use ocr on that. For later ...

(No I have gone fast through the book, it seems that only the first 2000 tosses are given individually, but there are many diverse tables with summaries of the throws. There are also tables for some other experiments, such as drawing balls from an urn, in the same spirit.

• It's not clear whether you have noticed that the first 2000 individual results are already available in this thread at Bill Bradley's answer. The book appears in Google books; I provided a link in another comment. Currently Google links to other booksellers, in addition to Amazon, where the quoted price (including shipping) is considerably cheaper.
– whuber
Mar 17, 2015 at 22:11
• Thanks, I noted the 2000 tosses where available above, but hoped I could find more in the book itself. Seems not. I am not able to read the book via google books, maybe that access depends on geography? By the way, I now returned my loan from openlibrary, so others can try ... Mar 17, 2015 at 22:20
• I attempted the same thing when this thread appeared, with the same negative results. :-( I did not mean to intimate that we can actually read the version on Google books: it is only sort of searchable. GB's main value (at least until Google's policy changes) is in providing links to places where we might purchase it.
– whuber
Mar 17, 2015 at 22:23

I came across this when doing some background research on Kerrich. I took the data from Bill Bradley's answer - really appreciate that the data was digitized! I've added the data to the R package that I use for teaching, which is available on GitHub.