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A Probability Theorist Writes #13 and #62

Updated: Feb 24, 2022

Being an occasional series in which our resident Probability Theorist Bown T'Appen answers frequently asked questions.

NB In a freakish coincidence, contributions numbers 62 and 13 were found to be identical and, given the improbability of this, we have taken the unusual decision to reproduce them both here.

Probability Theory and Gambling are ancient cousins. Roman probability theorist Julius Caesars-Palace wrote the first known treatise containing the famous dictum: "No matter how often you blow on your dice or your wife kisses your balls, the house always wins" - a sentiment as true today as it was all those years ago.

As a probability theorist I am often asked: what are the chances of winning the Dorset Lottery and are odd socks bad luck? Such questions arise - interestingly enough - from what we probability theorists call "categorical confusion" or sometimes "a confusion of categories" or even, more judgementally, "category errors". In any event it should be clear from the outset that the first half of the question rests, quite properly, in the field of expertise known as probability theory, whereas the second, more metaphysical inquiry, lies in the area generally designated "nonsense, superstition, old wives' tales", and - more colloquially - "tommyrot". It is, therefore to the first part of the question that I will devote the majority of my not inconsiderable attention.

The "chance" of winning something [or more generically of a "given event" "happening"] might be better expressed as the "probability of a specified event occurring within a timeframe plausibly construed as that allowed for the event to occur or not occur according to the satisfaction/definition of the inquirer" or, more succinctly, "when they expect it". So, to take this specific example: what are the chances of six balls each marked with a specific and unique number being drawn from a set of balls [via a random selection process or machine] next Saturday evening at approximately 8pm [give or take a few unspecified and inconsequential moments] matching the set of numbers previously selected by a given individual [eg myself] at some unspecified moment prior to the draw? Thus specified any probability theorist worth his salt can answer exactly: virtually none!

[I should add, to avoid confusion, that whether the lottery entrant wears matching or odd socks either at the time of purchase or at the time of the draw, has little or no significance and can to all intents and purposes be disregarded in any probability calculation.]

Still from the Threadbone Studio's The Seventh Man. The probability of a remake is, says industry expert, Rex Gaumont, very unlikely.

The exact congruence between six ball numbers and a set of previously selected numbers can properly be called a co-incidence [note the importance of the stress] though may not always result from coincidence. Co-incidence can, of course, result from coincidence [if you believe in such a phenomenon as opposed to say providence, fate or pre-determination] but it may equally result from design, manipulation, engineering or - as we say in the lottery trade - rigging. This is another matter entirely and outwith the purview of the Probability Theorist per se. I shall put it aside for the present purpose

Featuring a redesigned cover, Hornimint Records are hoping the coincidence of the Threadbone Studio's Anniversary and the CD's release will bolster sales beyond the 36 copies sold on first release.

That said it was intriguing to read - both as a Probability Theorist and as a film buff with a strong interest in the music of master technician Addinsell Threadbone, that in the very week that Threadbone Film Studios celebrated its 150th Anniversary, Hornimint Records should re-issue in its Movie Series the outstanding disc of film suites he composed for some of the studio's most famous feature films. Featuring the TPO Concert Orchestra under its indefatigable former Artistic Director, Russian maestra Irina Legova, the disc is a delight from start to finish.

Is the timing of these two events coincidental or might a Probability Theorist take a different view? Professional speaking this is very hard to say and I would add only that I would probably put the odds at about 50:50.

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