I’m a fan of early 20th century humorist Robert Benchley. You might not be yourself, but it’s rather likely that among the humorists you do like are a good number of people who are fans of his. He’s one of the people who shaped the modern American written-humor voice, and as such his writing hasn’t dated, the way that, for example, a 1920s comic strip will often seem to come from a completely different theory of what humor might be. Among Benchley’s better-remembered quotes, and one of those striking insights into humanity, not to mention the best productivity tip I’ve ever encountered, was something he dubbed the Benchley Principle: “Anyone can do any amount of work, provided it isn’t the work he is supposed to be doing at the moment.” One of the comics in today’s roundup of mathematics-themed comics brought the Benchley Principle to mind, and I mean to get to how it did and why.

**Eric The Circle (by ‘Griffinetsabine’ this time)** (September 18) steps again into the concerns of anthropomorphized shapes. It’s also got a charming-to-me mention of the trapezium, the geometric shape that’s going to give my mathematics blog whatever immortality it shall have.

Bill Watterson’s **Calvin and Hobbes** (September 20, rerun) dodged on me: I thought after the strip from the 19th that there’d be a fresh round of explanations of arithmetic, this time including imaginary numbers like “eleventeen” and “thirty-twelve” and the like. Not so. After some explanation of addition by Calvin’s Dad,

Spaceman Spiff would take up the task on the 22nd of smashing together Mysterio planets 6 and 5, which takes a little time to really get started, and finally sees the successful collision of the worlds. Let this serve as a reminder: translating a problem to a real-world application can be a fine way to understand what is wanted, but you have to make sure that in the translation you preserve the result you wanted from the calculation.

It’s Rick DeTorie’s **One Big Happy** (September 21) which brought the Benchley Principle to my mind. Here, Joe is shown to know extremely well the odds of poker hands, but to have no chance at having learned the multiplication table. It seems like something akin to Benchley’s Principle is at work here: Joe memorizing the times tables might be socially approved, but it isn’t what he *wants* to do, and that’s that. But inspiring the desire to know something is probably the one great challenge facing everyone who means to teach, isn’t it?

Jonathan Lemon’s **Rabbits Against Magic** (September 21) features a Möbius strip joke that I imagine was a good deal of fun to draw. The Möbius strip is one of those concepts that really catches the imagination, since it seems to defy intuition that something should have only the one side. I’m a little surprise that topology isn’t better-popularized, as it seems like it should be fairly accessible — you don’t need equations to get some surprising results, and you can draw pictures — but maybe I just don’t understand the field well enough to understand what’s difficult about bringing it to a mass audience.

Hector D. Cantu and Carlos Castellanos’s **Baldo** (September 23) tells a joke about percentages and students’ self-confidence about how good they are with “numbers”. In strict logic, yes, the number of people who say they are and who say they aren’t good at numbers should add up to something under 100 percent. But people don’t tend to be logically perfect, and are quite vulnerable to the way questions are framed, so the scenario is probably more plausible in the real world than the writer intended.

Steve Moore’s **In The Bleachers** (September 23) falls back on the most famous of all equations as representative of “something it takes a lot of intelligence to understand”.

Joe could be my sons, except instead of poker odds they know baseball stats! Multiplication table? Not real good :) Thanks.

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The various statistics tables I can find show that those stats are in the ballpark (within the margin of error allowed for most probability tables being given in percentages instead of ratios). I’m just bored enough to work them out. For all hand counts I’ll assume the cards have been sorted in some order, so permutations don’t matter.

There are 52!/(47!5!)=2598960 possible hands.

Royal flush: 4 possible hands = 649740:1

Straight flush (assuming ace can be low): 40 hands, of which 4 are also royal flushes, so 36 hands = 72193:1

Four of a kind: 13*48=624 possible hands = 4165:1

Full house: I am having a surprisingly difficult time working this one out in a way that matches any of the probability charts I’m finding.

Flush: 52*12*11*10*9/5! – 40 = 5108 hands = 509:1

I suspect the cartoonist’s persistent off-by-one errors are a sign that he’s removing the 1 from the odds, forgetting that 1:1 odds is the same as 100% (and not 50%).

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Thank you for the work put into this! And I suspect that you’re right about the off-by-one errors, although that makes me wonder why he has got it wrong then. If Detorie had been used some reference book listing card odds, why would the book have gotten it a little wrong? But if he’d worked it out himself, why go to that much work?

I wonder if he got it from a probability textbook that used the card problems as a good natural problem. The textbook writer could have made the one-off mistake from not understanding the odds notation, and the writing could easily not be read by someone who’d catch the error before publication.

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Baldo’s joke is a variation of the classic ‘There are three kinds of people – those who can count, and those who cannot!’.

It’s interesting what you said about humor – true… often old movies and dated books that most likely were intended to be funny just strikes us odd. So I guess humor is always constructed in relation to what is important and ‘serious’ at a certain point of time.

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You’re right about Baldo’s joke, yeah.

Trav S D — Travalanche, on WordPress — has a magnificent book about the history of Vaudeville (No Applause, Just Throw Money: The Book That Made Vaudeville Famous) which points out that a major shift in American humor, at least, came from radio and talking pictures adapting the vaudevillian style of comedy and then trimming it way down. Part of this was that the performers didn’t have to worry about being heard and understood even in the way back seats (so they could speak quicker, and more punchily, and didn’t have to repeat setups quite so much as they could be more sure people heard them the first time), and this did a lot for the pacing of comic writing.

The process, like all processes, was surely more complicated than that. But it is, typically, a lot easier to see why something written as comedy in (say) 1935 was funny than something from 1915. (Though not slapstick; that stays nice and clear and easy to understand.)

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