Good At Maths? Help Me Out!

n99 · Post by **n99** » Thu Aug 12, 2004 6:55 am

OK here's the deal. I did all this in high schools, but after years of sitting on my arse, it got a bit rusty. I'm talking about chance calculation. Setting: a 'fictional', 5 color deck of cards, each color having (the standard) 13 cards. Game is poker, but then of course with five colors instead of four. You take 5 random (of course) cards from the deck. What are the chances of getting the following combinations:

[standard poker combo's]
a pair (duh)
two pair (2 different pairs)
triple (three-of-a-kind)
straight (five cards, in order)
flush (five cards, in a single suit (card color))
full house (a pair and a triple)
carre (four-of-a-kind)
straight flush (five cards, in order, in a single suit)
royal flush (10-to-Ace, in a single suit)

[new combinations]
'rainbow' (one of each color)
'straight rainbow' (one of each color, in order)
'rainbow royale' (10-to-Ace, in 5 different colors)
'poker' (five-of-a-kind)

Ok, got it? Help? Suggestions, I actually need it before monday night, and giving the calculations themselves would be even better.

Common, there must be some wizkid who loves doing this.

n99 · Post by **n99** » Thu Aug 12, 2004 9:49 am

The Land of the Rising Sun Needs You!

IBA · Post by **IBA** » Thu Aug 12, 2004 6:49 pm

not really hard, do it as a tree

n99 · Post by **n99** » Fri Aug 13, 2004 10:13 am

yah the how part came back to me today as well. Unfortunately, the straight rainbow tree is gonna be gigantic.

anesthes1a · Post by **anesthes1a** » Sun Sep 05, 2004 7:16 am

Well.. Im not very good at math.

But gl!

gegoj · Post by **gegoj** » Sun Sep 19, 2004 12:37 pm

Quite a problem You have (had q: ) there, but I think I've 'cracked' it:

pair: 1 x 4/64 x 60/63 x 59/62 x 58/61 = 0.053857873...
You take one card for what you have (if not lame) a chance of 1 (100%). The next card is of the same value, and since there are only 4 such cards between the remaining 64 in deck, You have a chance of 4/64 to get it. The next 3 cards can have any value BUT the first card, so You must take any card but one of those 3 remaining.

two pairs: 1 x 60/64 x 4/63 x 4/62 x 57/61 = 0.003588426...
One card and another of different value, one of the same value as first, one as the value of the second and one that is completely different.

tripple: 1 x 4/64 x 3/63 x 60/62 x 59/61 = 0.002785752...
First three cards of same value, last two of any other.

straight: 1 x 5/64 x 5/63 x 5/62 x 5/61 = 0.000040986...
First card is any card, other card bust be of value that follows.

flush: 1 x 12/64 x 11/63 x 10/62 x 9/61 = 0.000779066...
First card followed by any of the same colour remaining.

carre: 1 x 4/64 x 3/63 x 2/62 x 60/61 = 0.000094432...
Four of a kind followed by one different.

straight flush: 1 x 1/64 x 1/63 x 1/62 x 1/61 = 0.000000065...
First card is random, others are exactly defined by those before them.

royal flush: 5/65 x 1/64 x 1/63 x 1/62 x 1/61 = 0.000000005...
First card MUST be one of the aces (or 10s if You are counting other way), thus a 5/65 chance to pic it. Others are defined by the first card.

rainbow: 1 x 13/64 x 13/63 x 13/62 x 13/61 = 0.001872972...
First one followed by one of each colour.

straight rainbow: 1 x 4/64 x 3/63 x 2/62 x 1/61 = 0.000001573...
First one followed by card of next value, with number of available colours reducing at each draw.

rainbow royale: 5/65 x 4/64 x 3/63 x 2/62 x 1/61 = 0.000000004...
Same as abowe, but the first card MUST be one of aces.

poker: 1 x 4/64 x 3/63 x 2/62 x 1/61 = 0.000001578...
First card is any card, others must be of the same value.

multyply with 100 if You need a % values.
I hope it's not too late q:

...but please, tell us, why would You need this calculated? Planing on some kind of hazard's revolution? q:

n99 · Post by **n99** » Sun Sep 19, 2004 1:03 pm

gegoj wrote:Quite a problem You have (had q: ) there, but I think I've 'cracked' it:
straight rainbow: 1 x 4/64 x 3/63 x 2/62 x 1/61 = 0.000001573...
First one followed by card of next value, with number of available colours reducing at each draw.

rainbow royale: 5/65 x 4/64 x 3/63 x 2/62 x 1/61 = 0.000000004...
Same as abowe, but the first card MUST be one of aces.

...but please, tell us, why would You need this calculated? Planing on some kind of hazard's revolution? q:

Well I wanted it for my interview of the course I wanted to get in, and I succeeded while omitting this. So I no longer need it. (Look at the post date.) Anyway, i'm still interested in this, and I think you already pointed out the flaw in your own design (I think the rest is pretty good, skimmed through the other parts) See, when your playing standard poker, first card doesn't need to be the ace at all, can be the king first, and then the ace. Or whatever. Same with 'next value' - there is no need normally, if u have, for instance, a two and a three of spades and hearts and throw the other three crap card out and pull first a five of diamonds you can still pull it off... Anyway, fave fun with it if you want. I'm letting it all go

gegoj · Post by **gegoj** » Sun Sep 19, 2004 1:21 pm

I've only used phrases as 'first' and 'next' for better understanding and easier explanation,but the order of the cards is not included in the calculatoins as it is (as You said) irrelevant.

I didn't noticed the date thouhg, I just saw that you (had) need(ed) it till monday, and presumed that the topic was new, as it was at the top, but it looks like someone needed to bring it back from it's eternal rest q:

so OK, let's drop it...

n99 · Post by **n99** » Sun Sep 19, 2004 5:03 pm

Sorry bout that gegoj, I appreciated your effort though, I had not even seen the post anethesia made. He has been digging up dusty threads like mad and doesn't seem to get the hints...

'Drop the hammer' indeed.