Vagueness and the Aftermath - A sporadic diary

[doubleup]

nah, before we look at any of the cards we have 104 unknown cards giving us 52 pairs, each of which is 51 to 1 to be a match

to simplify your objection lets take the 2 decks and strip out 50 of the cards leaving us with just the    s and the  s

shuffle them up and half the time both pairs will match, half the time neither so on average one pair matches from each 2, it's 50/50

your objection

if your deck rolls the Ace of spades the first card and it's in the second position in my deck, try as I might, I can't get there

while completely true has no bearing on the odds. we're dealing with unseen cards, not peeping at some of them first

at least I think that's right

right, I got the pen and paper out and had a bash.... I'm pretty sure this is right.

we need to basically solve (for n=52)

p = 1 - [1/2! - 1/3! + 1/4! - 1/5! + . . .1/(n-1)!]

that series (after the 1-) converges really quite quickly and approximates to 1/e (it's a McLauren (sp?) series expansion for e^-1, as I remember from school) and so the chance is 37% that there is no pair (1/e) and 63% that there is a pair. (approx)

The reason for this is that, since my deck (A) is shuffled, whether yours (B) is or not is wholly independent and you could just have all the cards in order -> so we can label them 1 to 52.

So basically, for there to be no match, we're looking for the probability for all n 1-52 that A(n) =/ n -- this turns out to be a regular nCk problem (how many ways can we deal two decks) which summises to:

n! − nC1 · (n−1)! + nC2 · (n−2)! + ...  nCn · (n−n)!

or

n! − n!/1! + n!/2! + ... (−1)n

which for n=52 gives the first 53 terms of the MacLaurin series for e^-1 as above.

that make sense?

[david3103]

ffs, had hoped that was going to be really quick to read as I have to go out, I'll read it later

assume it means I'm wrong. were you right?

it actually makes quite a lot of sense empirically that it should be less than 50% when you start to think of examples

like I always wondered why secret santa draws don't constantly end with someone buying for themselves

Surely Secret Santa draws get redrawn if you pull yourself out of the hat/bag/whatever?

[kinboshi]

ffs, had hoped that was going to be really quick to read as I have to go out, I'll read it later

assume it means I'm wrong. were you right?

it actually makes quite a lot of sense empirically that it should be less than 50% when you start to think of examples

like I always wondered why secret santa draws don't constantly end with someone buying for themselves

Surely Secret Santa draws get redrawn if you pull yourself out of the hat/bag/whatever?

Especially if you bought some cheap tat.

[gatso]

ffs, had hoped that was going to be really quick to read as I have to go out, I'll read it later

assume it means I'm wrong. were you right?

it actually makes quite a lot of sense empirically that it should be less than 50% when you start to think of examples

like I always wondered why secret santa draws don't constantly end with someone buying for themselves

Surely Secret Santa draws get redrawn if you pull yourself out of the hat/bag/whatever?

yeah, but I was wondering why this doesn't happen often

Surely Secret Santa draws get redrawn if you pull yourself out of the hat/bag/whatever?

Especially if you bought some cheap tat.

surely you wait and see who you've got before you buy?

[tikay]

I'll be honest, Tom, you have disappointed me.

There I was, all day yesterday, pressing F5, awaiting a Post or two from you to mark the special occasion, & you posted NOTHING.

Yoor credibility as the Diary of Culture is shot to pieces.

[tikay]

So, for those disappointed that Tom never marked the occasion, yesterday was "Burns Night", or "Burns Supper" as I think it is supposed to be called. You may enjoy this. I doubt anyone else will.

Basically, the Scots celebrate a poet by eating a haggis.

http://en.wikipedia.org/wiki/Burns_supper

Address To a Haggis  

Fair fa' your honest, sonsie face,
Great chieftain o' the puddin-race!
Aboon them a' ye tak your place,
Painch, tripe, or thairm:
Weel are ye wordy o' a grace
As lang's my arm.

The groaning trencher there ye fill,
Your hurdies like a distant hill,
Your pin wad help to mend a mill
In time o' need,
While thro' your pores the dews distil
Like amber bead.

His knife see rustic Labour dicht,
An' cut you up wi' ready slicht,
Trenching your gushing entrails bricht,
Like ony ditch;
And then, O what a glorious sicht,
Warm-reekin, rich!

Then, horn for horn, they stretch an' strive:
Deil tak the hindmaist! on they drive,
Till a' their weel-swall'd kytes belyve,
Are bent like drums;
Then auld Guidman, maist like to rive,
"Bethankit" hums.

Is there that o're his French ragout
Or olio that wad staw a sow,
Or fricassee wad mak her spew
Wi' perfect scunner,
Looks down wi' sneering, scornfu' view
On sic a dinner?

Poor devil! see him ower his trash,
As feckless as a wither'd rash,
His spindle shank, a guid whip-lash,
His nieve a nit;
Thro' bloody flood or field to dash,
O how unfit!

But mark the Rustic, haggis fed,
The trembling earth resounds his tread.
Clap in his wallie nieve a blade,
He'll mak it whistle;
An' legs an' arms, an' heads will sned,
Like taps o' thristle.

Ye Pow'rs wha mak mankind your care,
And dish them out their bill o' fare,
Auld Scotland wants nae skinkin ware
That jaups in luggies;
But, if ye wish her gratefu' prayer,
Gie her a haggis!
 

 

[tikay]

PS - What a load of tosh.

[RED-DOG]

PS - What a load of tosh.

I agree.

If you're going to do culture, do something decent.

[RED-DOG]

While we're marking occasions, tomorrow is Holocaust Memorial day.

[gatso]

I was going to go to the pub last night for haggis but decided against it in the end. good call as it turned out as apparently they ran out rather early

[mulhuzz]

I was going to go to the pub last night for haggis but decided against it in the end. good call as it turned out as apparently they ran out rather early

weirdly, the morrison's in gibraltar has been FULL of haggis for the past week....don't understand the connection - there certainly aren't enough Scots here (including halfscots like me who will happily cook a haggis for burns) to justify the close to 1k haggis' I saw in the chilled section.

very weird.

[Rod Paradise]

At least quote a decent poem by him....

A Man's a Man for A' That

By Robert Burns, 1795

Is there for honest poverty
That hings his head, an a' that?
The coward slave, we pass him by -
We dare be poor for a' that!
For a' that, an a' that!
Our toils obscure, an a' that,
The rank is but the guinea's stamp,
The man's the gowd for a' that.

What though on hamely fare we dine,
Wear hodding grey, an a' that?
Gie fools their skills, and knaves their wine -
A man's a man for a' that.
For a' that, an a' that,
Their tinsel show, an a' that,
The honest man, tho e'er sae poor,
Is king o men for a' that.

Ye see yon birkie ca'd 'a lord,'
Wha struts, an stares, an a' that?
Tho hundreds worship at his word,
He's but a cuif for a' that.
For a' that, an a' that,
His ribband, star, an a' that,
The man o independent mind,
He looks an laughs at a' that.

A prince can mak a belted knight,
A marquis, duke, an a' that!
But an honest man's aboon his might -
Guid faith, he mauna fa' that!
For a' that, an a' that,
Their dignities, an a' that,
The pith o sense an pride o worth,
Are higher rank than a' that.

Then let us pray that come it may
(As come it will for a' that),
That Sense and Worth o'er a' the earth,
Shall bear the gree an a' that.
For a' that, an a' that,
It's coming yet for a' that,
That man to man, the world, o'er
Shall brithers be for a' that.

[AndrewT]

Burns night happens very close to the Chinese New Year - this is where we get Chinese burns from.

[mulhuzz]

Burns night happens very close to the Chinese New Year - this is where we get Chinese burns from.

i know that the chance is like super slim, like, really really, really thin. but I so want this to be true.

[b4matt]

Burns night happens very close to the Chinese New Year - this is where we get Chinese burns from.