Here's some perspective

[Rushmore]

I posted this in the Probabilty Forum, but I figured it would get more play here.

http://www.pokerpages.com/articles/archives/hench33.htm

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[brad]

52! or 51!

something like that?

of course for a lot of card games a lot of the cards dont matter (ie, when the dealer drops the deck at end of hand those cards).

so for a lot of games the ,er, functional whatever would be equivalent to 15! or 20! or something i would guess.

[cferejohn]

There are roughly 80,658,175,170,943,878,571,660,636,856,404,000,000 ,000,000,000,000,000,000,000,000,000,000 combinations.

Lets see now, some math nerd must have a website that will give us a name for that number...aha (knew I could count on the nerds):

Ahem.

"A fifty two card poker deck can be arranged in roughly Eighty unvigintillion, six-hundred-fifty-eight vigintillion, one-hundred-seventy-five novemdecillion, one-hundred-seventy octodecillion, nine-hundred-fourty-three septdecillion, eight-hundred-seventy-eight sexdecillion, five-hundred-seventy-one quindecillion, six-hundred-sixty quattuordecillion, six-hundred-thirty-six tredecillion, eight-hundred-fifty-six duodecillion, four-hundred-four undecillion different ways."

Damn calculator rounds off or I'd be more specific about the decillions, nonillions, octillions, septillions, sexillions, quintillions, quadrillions, trillions, billions, millions, thousands, and, umm, ones.
Someone put that to music and we've got a hit song on our hands.

Why, what do *you* do at work?

[whiskeytown]

should be 52! - (technically, though...the last card is decided)

basically...there's a 1/52 chance of a card being first - then there's a 1/51 chance of a card being 2nd...

so let's say you want the Ac Ah as cards one and two...that's 52*51 for 2652 -

so yeah...do that 50 more times....big ass number...sorta like the story of the guy who made a bet to give rice away...he put one grain on the first square of the chess board, 2 on the second, 4 on the 3rd, 8 on the 4th, etc, etc...

If he had gotten to the 64th square, the mass of rice would have been so great it'd have caved in on itself and then caused a black hole...LOL - exponential and factored numbers get big REALLY fast /images/graemlins/wink.gif

RB

[cferejohn]

If he had gotten to the 64th square, the mass of rice would have been so great it'd have caved in on itself and then caused a black hole...LOL - exponential and factored numbers get big REALLY fast

I call hyperbole. 2^64th = 18,446,744,073,709,551,616 grains of rice. Figuring 10 milligrams per grain, that's 184,467,440,737,095,516 kilograms. The weight of the earth is roughly 5,980,000,000,000,000,000,000,000 kilos, so in fact a black hole is really quite out of the question.

Still a lot of rice though.

[cferejohn]

Oops. I should be adding 2^64th to 2^63rd, 2^62nd, etc. So really that's 36,891,236,343,310,450,687 grains equals ~368,912,363,433,104,500 kilos. Still pretty small relative even to the weight of the earth, and definitely not in the black hole range.

Now, give him a go board, and you've got yourself a cosmological event.

[brad]

what do u think about most of the deck not mattering though?

i mean say holdem 10 handed thats 20 cards plus 5 for board, and the rest dont matter, so

effectively

how much variation is there? more than 25! because you know but far less than 52!

like (choose 25 from 52)! or something i have no idea.

but it could be pretty low if you lump all trash hands together (ie, 72 == 73 )

just a thought

[rigoletto]

Not even a teeny weeny modest black hole? I'm disappointed.

[cferejohn]

Well, perhaps if you actually put all that rice into a space the size of a chessboard. However, one of the things about solids is they don't change volume under pressure. I suppose if you squeeze them hard enough there is some term for what happens when they become super-impacted, but I have no idea what it might be. So, if you could find a way to get several quadrillion pounds of rice into a 1'x1'x1/4" area, perhaps a small black hole would appear. Try it and see... /images/graemlins/grin.gif

[whiskeytown]

I think that's the concept -

most astronomers thing Black Holes are created by the collapsing weight of a White Dwarf star - we're talking stuff like a cubic inch of it weighs a ton...

so if you could compress that much rice into a chessboard square - by golly, you COULD possibly start a black hole.

If I get some time this weekend, I'll test the theory /images/graemlins/grin.gif