Card Games

Suppose your dog eats the ace of spades and you’re forced to play poker with a 51-card deck. Does this make it more or less likely that you’ll be dealt a two-pair hand?

The answer is not immediately clear. The loss of the ace means that fewer two-pair hands are possible, but the total universe of possible five-card hands is also reduced.

Surprisingly, the probability is unchanged. “[T]he probability of getting a Two-Pair hand in the 51-card deck with the missing Ace of Spades is exactly the same as for a 52-card standard deck,” notes George Mason University mathematician D.M. Anderson. And “[i]t turns out that this seemingly magical result for a deck with a missing Ace of Spades is not limited to Two-Pair hands. Indeed, examining the traditional hierarchy of 5-card poker hands, we find an analogous result holds for One-Pair hands, Three-of-a-Kind, Full Houses and Four-of-a-Kind.”

(D.M. Anderson et al., “Not Playing With a Full Deck?”, Recreational Mathematics Magazine 11:18 [March 2024], 51-63.)

Dammit I’m Mad

Demetri Martin composed this palindromic poem as part of a project for a fractal geometry class at Yale in spring 1993. The first two and last two lines are palindromes, the middle line (“Be still if I fill its ebb”) minus its last letter is a palindrome, and the entire poem is a palindrome:

Dammit I’m mad
Evil is a deed as I live.
God, am I reviled?
I rise, my bed on a sun, I melt.
To be not one man emanating is sad. I piss.
Alas it is so late. Who stops to help? Man, it is hot.

I’m in it.
I tell.
I am not a devil.
I level “Mad Dog”.

Ah, say burning is as a deified gulp
in my halo of a mired rum tin.
I erase many men. Oh, to be man, a sin.
Is evil in a clam? In a trap?
No. It is open.
On it I was stuck.

Rats peed on hope.
Elsewhere dips a web.
Be still if I fill its ebb.
Ew, a spider … eh?
We sleep.

Oh no!
Deep, stark cuts saw it in one position.
Part animal, can I live? Sin is a name.
Both, one … my names are in it. Murder?
I’m a fool. A hymn I plug,
Deified as a sign in ruby ash – a Goddam level I lived at.

On mail let it in. I’m it.
Oh, sit in ample hot spots.
Oh, wet!
A loss it is alas (sip). I’d assign it a name.
Name not one bottle minus an ode by me:
“Sir, I deliver. I’m a dog.”
Evil is a deed as I live.
Dammit I’m mad.

Hand to Hand

https://www.reddit.com/r/interestingasfuck/comments/1cte4kg/during_the_battle_of_saunders_field_in_virginia/

An odd incident from the memoir of Lt. John Worsham of the 21st Virginia Infantry — during the Battle of Saunders Field in May 1864, two opposing soldiers found themselves in a gully and agreed to a fistfight to decide which had captured the other:

Then they decided that they would go into the road and have a regular fist and skull fight, the best man to have the other as his prisoner. When the two men came into the road about midway between the lines of battle, in full view of both sides around the field, one a Yankee, the other ‘a Johnny,’ while both sides were firing, they surely created a commotion! This was true in our line and I suppose in the enemy’s line, because both sides ceased firing! When the two men took off their coats and commenced to fight with their fists, a yell went up along each line, and men rushed to the edge of the opening for a better view! The ‘Johnny’ soon had the ‘Yank’ down, who surrendered, and both quietly rolled into the gully, where they remained until night, when ‘the Johnny’ brought ‘the Yank’ into our line. The disappearance of the two men was the signal for the resumption of firing!

This type of story is common, and I haven’t been able to confirm this one, but it’s certainly striking. “Such is war!”

Double Duty

These verses can be interpreted to support either the Stuarts or the Hanovers, according as they’re read. If each is addressed separately, from top to bottom, they’ll seem to support the Hanoverian regime; read together, right across the page, they declare for the Stuarts:

https://books.google.com/books?id=KbJ1dbG0XjYC&pg=PA170

From Reuben Percy, Relics of Literature, 1823.

Square Meal

https://commons.wikimedia.org/wiki/File:Missing_square_edit.gif
Image: Wikimedia Commons

In this conundrum by Mitsunobu Matsuyama, when four congruent quadrilaterals are rotated about their centers, their area seems to increase. What has become of the red square?

The answer is that each side of the large square is slightly shorter after the rotation. If θ is the angle between two opposing sides in each quadrilateral, then the ratio of the areas of the two large squares is sec2 θ, about 0.8 percent when θ is 5°.

Local Talk

“Improprieties in pronunciation” among the people of New England in 1808, collected by Caleb Bingham and published in The Child’s Companion:

afraid:          afeard
apron:           apun
audacious:       outdacious
bonfire:         burnfire
brittle:         brickle
cards:           cairds
caught:          cotch
coin:            quine
cucumber:        cowcumber
dictionary:      dixonary
drain:           dreen
earth:           airth
fanciful:        fancical
five pence:      fippence
gown:            gound
grasshopper:     hoppergrass
jaundice:        janders
musician:        musicianer
poplar:          popple
quart:           quairt
quotient:        coshun
sassafras:       saxafax
turtle:          turcle
tutor:           tutorer
umbrella:        amberrillar
Vermont:         Vermount
walnut:          warnut
watermelon:      watermillion

“It is not to be supposed that they are all in common use in every part of New England. Some of them are local. In general, however, they are used more or less in all the New England States.”

C Change

How can we make sense of this passage, composed by Willard R. Espy?

The Optic Reed has a Haste Harm. It Hose, one assumes, not to be Lever; it neither Heats the Ripple, nor Hides the Razed sinner for his Rude Rime; it is not Old. Then Leave to it; ere thy grave Loses, thou mayst find here the Hart to the Rest thou Ravest to Limb.

Click for Answer