Re: [DL] 5 Deck of Cards - PS This will be long folks...

["Jeff Tolle" <jwtolle@hotmail.com>]

Brian,

IANANDIPHOTV, but here is my statisitcal reasoning.  BTW, not only am I not 
Alan, I am not a statistician.  But I have played one in a role playing 
game, (actually it was a protocol droid, but thats another system and story) 
and I love to dabble.  So here goes.

You are correct that adding a card changes the chances of drawing any one 
card.  The formula to calculate the probability of drawing AT LEAST ONE 
Joker is thus:

D = Deck Size: Them fine folks at PEG toldja size wuz important
T = Number of target cards in the deck
H = Number of Cards drawn in the poker hand

P (X) = 1-((((D-T)!)-((D-T-H)!))/((D!)-((D-H)!)-1))

If you like I can justify this formula, but in the interest of brevity (yeah 
right Jeff, why start now) I will save it for private E-mail if you are VERY 
curious.  Here's a hint tho - think about the probability of not pulling the 
jokers, and start with a Hand of 1.

So if, in our original state we have 54 (52 + 2 Jokers) cards, and we pull 5 
cards.  (Bad roll Mr. Huxter)

P(J from 54)= 1-((((54-2)!)-((54-2-5)!))/((54!)-((54-5)!)-1))
P(J from 54)= 17.82%

However, lets add that extra Joker

P(J from 55)= 1-((((55-3)!)-((55-3-5)!))/((55!)-((55-5)!)-1))
P(J from 54)= 25.29%

Quite a significant increase - 7.47%.  In other words, if I sit here with a 
deck of 54, and you with a deck of 55, you will pull a joker 1 more time 
than I for approximately ever 14 pulls.  With our Huxter, that's once a game 
session.

This is 'joker gap' gets even more significant the more cards you pull.  Up 
to 8.60% for 6 cards, 9.61% for 7 cards.  (To put a fine point on it, the 
increase in the gap is decreasing, so at a certain number of cards the gap 
will significantly increase, and eventually will decrease, but your huxter 
has to pull 18 or more cards.  The gap reaches a difference of 0 when you 
pull 52 cards, obviously.)

So, basically the logic here is, yes increasing the deck size does lower 
your probability.  And yes, increasing the number of wild cards in your deck 
does increase your probability of getting a wild card.  The question here is 
one of magnitude.  When your hand size is small, the increase in the deck 
size is not enough to drag down the bonus from increasing the number of 
jokers.

I will just add here that having a joker (or any wild card for that matter) 
greatly increases the probability that you will have an excellent hand.  I 
think I will get agreement here! ;-)

Jeff "Whew, that hurt, but in a good way."  Tolle
___________________________________________________

>From: "Leybourne, Brian" <Brian.Leybourne@airnz.co.nz>
>
>>Well - for one thing, the odds of making a poker hand drop
>>drastically,
>
>Can you justify this one? I have been thinking through the math, and >have 
>not convinced myself either way yet
>
>Brian "enlighten me, oh master" Leybourne.
>

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