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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Written by Colin Watson on 2025-01-04 at 22:54

@sil You're dividing one integer by another - it's already a fraction! Just need to multiply by 100 to turn it into a percentage, then reduce by common factors.

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Written by Stuart Langridge on 2025-01-04 at 22:57

@cjwatson sure, if you want it as a fraction you do the (long) division, get the remainder, put the remainder over the dividend, cancel. But then you get a fractional part which looks like something over 22100, which in no way is ever going to cancel to something over either 17 or 123, hence my puzzlement :)

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Toot

Written by Stuart Langridge on 2025-01-04 at 23:01

@cjwatson and since you've gotta basically do the long division anyway to get the integer part, why would you not carry on doing it to get a decimal part? I have polled a couple of Old People (to whom I happen to be related) and they said yeah, doing long division at school, you'd either report the answer as a decimal, or as 8 remainder 62 or whatever. Nobody seems to have even been taught a procedure which gives you an answer in the form 8 62/1317ths, or whatever. (I can see how to do it!)

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Descendants

Written by Stuart Langridge on 2025-01-04 at 23:01

@cjwatson maybe it was different in the US, though (and pre-war, which my family aren't old enough to have been taught in :))

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Written by Colin Watson on 2025-01-04 at 23:18

@sil I sort of feel the transformation from "8 remainder 62 after division by 243" to "8 62/243" is obvious and just a matter of how you choose to spell it, though. But I agree the original author seems to have done something screwy, at a quick glance - almost as if they copied it down and mistranscribed the denominator or something.

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Written by Stuart Langridge on 2025-01-04 at 23:18

@cjwatson that’s fair comment, now that you say it like that, yeah!

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