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Thurbane
2008-11-15, 06:45 PM
Not sure if this is the right part of the fourms, but...

OK here goes - I'll try to explain this as simply as possible, but my explanation is going to be quite awkward.

Assume a standard deck of cards (52, no jokers) and that each card has a number value equal to it's pips (Ace=1, 2=2, 10=10) with a Joker=11, Queen = 12 and King = 13.

Now, assume a new type of hand is allowed in a poker game - a Fibonacci. This is where you have a sequence of 5 cards, where the sum of the next card equals the previous two card values added together. Examples:

A 2 3 5 8
A 3 4 7 J
2 3 5 8 K
A A 2 3 5
2 2 4 6 10

Now, if I'm working that out correctly, there are only 5 possible combinations (updated as per advice below).

Still with me? OK, my question is basically what is the statistical chance of getting one of these hands, compared to say a straight, flush, full house or 4 of a kind? And what are the chances of getting a Fibonacci Flush - where one of the above sequences are all of the same suit?

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

http://en.wikipedia.org/wiki/Flush_(poker)#Flush

...cheers - T

Lord Lorac Silvanos
2008-11-15, 06:58 PM
What about combinations that involve two of a kind to start off the series?

Such as:

A A 2 3 5
2 2 4 6 10

Thurbane
2008-11-15, 07:03 PM
Good point, I hadn't thought of that! Yes, those would certainly count!

Charlie Kemek
2008-11-15, 07:09 PM
just use the probability of each card, multiplied by the chances of the next card, so it's 4/52*4/51*4/50*4/49*4/48*3/1 (last fraction number of possibilities there are, see below), or (simplifying) 1/13*4/51*2/25*1/49*1/3*3/1 (or however many possibilities there are, will look up soon), or 8/812,175 aka 8 times out of 812125 times. yeah.

Edit: if you have the first two numbers are the same, then it is 4/52*3/51*.... or 24/2436525 times the number of possibilities

UglyPanda
2008-11-15, 07:25 PM
There are (52*51*50*49*48)/(5!), or 2,598,960, possible hands in stud poker when you ignore order.

Ignore suit:
A 2 3 5 8 - 4^5 versions of this hand, or 1024
A 3 4 7 J - Ditto
2 3 5 8 K - Ditto
A A 2 3 5 - (4*3/2)*(4^3), or 384
2 2 4 6 10 - Ditto

Flushes:
A 2 3 5 8 - 4
A 3 4 7 J - ditto
2 3 5 8 K - ditto
A A 2 3 5 - impossible
2 2 4 6 10 -impossible

Personally, I don't see the value of adding this, unless you're trying to outgeek your pals. It's inelegant, for lack of a better word, it just doesn't fit with the other types of hands. The odds are so low that it's just not good strategy to try to get one, and most occurrences of these hands would be purely by accident.

fractic
2008-11-15, 07:25 PM
There are 52 over 5 = 2.598.960 possible 5 card hands. We just have to figure out the number of fibonaci hands and divide to figure out the odds.

Possible series with number of hands with this series

A A 2 4 6
2 2 4 6 10
both 4*3*4*4*4 = 768 hands

A 2 3 5 8
A 3 4 7 J
2 3 5 8 K
all have 4*4*4*4*4 = 1024 hands

grand total is 4608 hands giving a chance of about 0.177%.
There are 5108 (non-straight) flushes and 3744 possible full houses so it would fall inbetween there.

There are exactly 12 fibonaci flushes which is even rarer then a straigth flush but less rare then a royal flush of course.

Thurbane
2008-11-15, 07:34 PM
Thanks for the replies - yes, I know it's a pretty odd excercise, but it did come up at our poker game last night, and the guys were pretty interested in working out the odds...

herrhauptmann
2008-11-16, 01:34 AM
Where's Eldariel?
Everytime someone disagrees with him he announces how he's smarter because he's a math major, and whoever he craps on like that just always takes it, so it must be true. :smallamused: If he can't answer your question, NO ONE can.

Lord Lorac Silvanos
2008-11-16, 03:54 AM
Well fractic already answered the question correctly.:smallsmile:

Eldariel
2008-11-16, 05:16 AM
Where's Eldariel?
Everytime someone disagrees with him he announces how he's smarter because he's a math major, and whoever he craps on like that just always takes it, so it must be true. :smallamused: If he can't answer your question, NO ONE can.

I was sleeping. Sorry. Luckily there seems to be a good number of people knowledgable in basic probability calculus, so I'm not really needed either. And unfortunately, I can't use that particular line anymore since I now Major in Linguistics. I could start saying "I'm the former math major!" though.

fractic
2008-11-16, 07:18 AM
Well fractic already answered the question correctly.:smallsmile:

Actually I got it wrong! That'll teach me to do math at 1:30 in the morning. The I counted the fibonaci series with two of the same cards double. The correct total would be 3840 so it's still inbetween a flush and a full house allthough the gap is much smaller.

And BTW I'm a mathematics student (nearly graduated too), so even those make mistakes ;)

Lord Lorac Silvanos
2008-11-16, 07:36 AM
Actually I got it wrong! That'll teach me to do math at 1:30 in the morning. The I counted the fibonaci series with two of the same cards double. The correct total would be 3840 so it's still inbetween a flush and a full house allthough the gap is much smaller.

And BTW I'm a mathematics student (nearly graduated too), so even those make mistakes ;)

Ahh I did not see you did not divide with 2 like UglyPanda.
Apparently I was unable to do simple summation. :smalltongue:

Artanis
2008-11-16, 01:47 PM
I was sleeping. Sorry. Luckily there seems to be a good number of people knowledgable in basic probability calculus, so I'm not really needed either. And unfortunately, I can't use that particular line anymore since I now Major in Linguistics. I could start saying "I'm the former math major!" though.
How the HELL do you go from math to linguistics?

Eldariel
2008-11-16, 04:24 PM
How the HELL do you go from math to linguistics?

Long story.