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anyone good at probability / maths?

Started by zombie no.one, December 04, 2023, 04:55:14 AM

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zombie no.one

little problem I'm trying to work out

if a standard deck of 52 cards is randomly shuffled, and then dealt out to 4 people (13 cards each), what are the odds that one person will end up with a 'straight'

i.e.

A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K

(of any suit... don't all have to be the same suit)
Quotethe movie was cringe, corny, cheesy and "what the biscuits" is with this atrocious acting and childish corny thing of a movie???

Alex

Hail to thyself
For I am my own master
I am my own god
I require no shepherd
For I am no sheep.

zombie no.one

haha, way over my head but thanks anyway... those clearly math-y guys don't even seem to agree on how to answer that OP's question. think this might be a more complex problem than I hoped.
Quotethe movie was cringe, corny, cheesy and "what the biscuits" is with this atrocious acting and childish corny thing of a movie???

Trevor

Quote from: zombie no.one on December 04, 2023, 04:55:14 AM
little problem I'm trying to work out

if a standard deck of 52 cards is randomly shuffled, and then dealt out to 4 people (13 cards each), what are the odds that one person will end up with a 'straight'

i.e.

A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K

(of any suit... don't all have to be the same suit)

No, sorry: I was so bad at math at school I thought 2 + 2 = 22  :buggedout: :wink:
We shall meet in the place where there is no darkness.

zombie no.one

Quote from: Trevor on December 04, 2023, 08:31:30 AM

No, sorry: I was so bad at math at school I thought 2 + 2 = 22  :buggedout: :wink:

well I'd say there's definitely an argument that it does... depends how you look at the question really.

I mean, we take it for granted that 10 รท 2 = 5... but where in the question does it state that the 10 has to be divided equally?

Quotethe movie was cringe, corny, cheesy and "what the biscuits" is with this atrocious acting and childish corny thing of a movie???

Rev. Powell

This may be both an approximation and cheating, but...

https://en.wikipedia.org/wiki/Poker_probability

Odds of a straight are 0.3925%. But that excludes straight flushes so you need to add them in: 0.00139% and 0.000154% for a total probability of 0.394044%.

Assuming the chances of any player drawing a straight are absolutely independent of the others, that's 4 chances to draw a straight at 0.394044% so multiply the probability four times for = 1.576176%.

Now, if your example specifies that one and only one person draws a straight, it's a little bit less than that because you have to remove the unlikely multiple straight scenarios. I think 1.5% chance is a fine approximation, though.
I'll take you places the hand of man has not yet set foot...

zombie no.one

 thanks Rev  :thumbup:

actually I could've specified at least one person gets a straight...

1.5% seems a little high but then again I don't know, and I trust your working more than my instincts :smile:

an interesting thing to note is the odds of 3 people getting dealt a straight are exactly the same as 4 getting a straight, because if 3 have one, the only other remaining combo of cards is another straight, which the 4th person must have.
Quotethe movie was cringe, corny, cheesy and "what the biscuits" is with this atrocious acting and childish corny thing of a movie???

Rev. Powell

Quote from: zombie no.one on December 04, 2023, 11:53:13 AM
thanks Rev  :thumbup:


an interesting thing to note is the odds of 3 people getting dealt a straight are exactly the same as 4 getting a straight, because if 3 have one, the only other remaining combo of cards is another straight, which the 4th person must have.

Not at all.

Person 1: 2C-3D-4H-5S-6C
Person 2: 2D-3H-4S-5C-6D
Person 3: 2H-3S-4C-5D-6H
Person 4: 7C-7H-9D-KD-AD

for example.
I'll take you places the hand of man has not yet set foot...

zombie no.one

#8
I'm talking about a straight of all 13 cards...from Ace all the way to King

if 3 people get dealt that configuration, the 4th must also have it

- to be clear, this is what I meant in my original question... what are the odds of one (or more) people getting dealt a straight of all 13 cards from Ace to King
Quotethe movie was cringe, corny, cheesy and "what the biscuits" is with this atrocious acting and childish corny thing of a movie???

Rev. Powell

Quote from: zombie no.one on December 04, 2023, 02:16:13 PM
I'm talking about a straight of all 13 cards...from Ace all the way to King

if 3 people get dealt that configuration, the 4th must also have it

- to be clear, this is what I meant in my original question... what are the odds of one (or more) people getting dealt a straight of all 13 cards from Ace to King

Oops! I totally misread your question---I thought we were talking about standard 5-card poker hands.

I probably could have solved your problem years ago when I was in college, I aced statistics. But today I'd have to do some research to remember the proper formulas.
I'll take you places the hand of man has not yet set foot...

Rev. Powell

I believe the number of combinations of 13 cards dealt to four people from a 52 card deck is

52!/(52-13)13!=635,013,559,600

https://www.calculator.net/permutation-and-combination-calculator.html?cnv=52&crv=13&x=Calculate

Now, we just need to find out how many of those are 13 card straights (a much thornier question), and we're golden!

Maybe tomorrow...
I'll take you places the hand of man has not yet set foot...

zombie no.one

haha, no worries - I actually didn't word my question that well, reading it back... that looks more like the kind of number I'd expect

Quote from: Rev. Powell on December 04, 2023, 06:34:24 PM
I aced statistics. 

I see what you did there  :teddyr:

I'm not terrible at maths but I have a certain 'cut off point' where it becomes gobbledygook
Quotethe movie was cringe, corny, cheesy and "what the biscuits" is with this atrocious acting and childish corny thing of a movie???

lester1/2jr

I got a 440 on my math SAT so no not at all

Rev. Powell

#13
Possible number of straights might be simply 13!, or 6,227,020,800.

In that case 6,227,020,800/635,013,559,600=0.0098061225714967, or about a %0.9 chance (9 in a thousand hands) for any one player to get a straight. If chances of any player getting a straight are independent (not sure if they are or not) then multiply by 4 chances for a %0.4 for any player to get a straight.
I'll take you places the hand of man has not yet set foot...

zombie no.one

ok nice so it's about somewhere between a 1/100 and 2/100 chance of getting dealt the full 13 card straight?
Quotethe movie was cringe, corny, cheesy and "what the biscuits" is with this atrocious acting and childish corny thing of a movie???