Ancestors

Written by Stuart Langridge on 2025-01-04 at 09:35

Maths people, help!

In "Scarne on Cards", John Scarne discusses the odds for a game. He says this:

"The chances are 12220 to 9880 in their favour. [These numbers are definitely correct -- sil] That is, the percentage in their favour is 10-1/123."

Where's he getting that percentage from? How's he doing the calculation? I can't end up at that number, so I must be doing something wrong...

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Written by Stuart Langridge on 2025-01-04 at 18:43

Ok, our conclusion to this little puzzle is “Scarne did the calculation wrong”. The number is 2340/22100, which is an edge of about 10.58%, not “10-1/123” (which is about 10.081%).

This being an error is bolstered by further research: in his later Scarne’s Complete Guide to Gambling, he relates the same game (with a different story about it), lays out the same calculation, and comes up with an answer of 10 1/17% which isn’t right either!

Still, be tolerant: life is hard pre-calculators.

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Written by Stuart Langridge on 2025-01-04 at 19:02

it's not all that hard, though. Admittedly he's doing this in the context of writing a big long book, but didn't they have editors in the 50s? I -- no aficionado of long division -- just spent all of five minutes doing the calculation on paper and there it is, ~10.58%.

(I don't even know how you do this division to end up with a fraction rather than a decimal. Someone who was doing maths by hand in the fifties (and presumably learned to do so in the 1910s) will have to tell me (by ouija board).)

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Toot

Written by Alex Russell on 2025-01-04 at 19:03

@sil TFW your Gell-Mann Amnesia is flaring up again.

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Descendants

Written by Stuart Langridge on 2025-01-04 at 19:06

@slightlyoff what, me mistakenly trusting a gambling expert to get the maths right, or you mistakenly trusting me to get the long division right? :-)

the first two minutes were spent trying to divide 117 into 1105 instead of the other way around and being baffled as to why the answer began with a 9 when I knew in advance it ought to begin in a 1. Long time since I did any maths on paper :)

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