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        riddles >> easy >> Another Casino Scam
        
(Message started by: Nick on Jul 6^th, 2003, 3:59pm)

Title: Another Casino Scam
Post by Nick on Jul 6^th, 2003, 3:59pm

Yes, I know, I have a gambling problem. I was playing Carabian Stud Poker. All players and a dealer recieve 5 cards at random. If the dealer does not have Ace + King or some other higher hand, your bet is automatically paid. What are the number of possible hands that have Ace + King (or higher) and what are the number of hands that do not have Ace + king (or higher)? Just listening to "table talk" I've heard that you have a 52% chance that the dealer will not qualify at all. Is this percentage accurate?

Title: Re: Another Casino Scam
Post by towr on Jul 7^th, 2003, 3:02am

It's doubtfull you normally have any advantage at a casino, so 52% chance in your favour is doubtfull.
As far as I know the only game you can win at is black jack, and that's by card-counting (which has been made increasingly difficult to do by using multiple decks, and changing to new decks long before they've all been delt)

Before I try answering your question I'd like to know what counts as "or higher" in Carabian Stud Poker. Is that anything in normal poker, 2,3,4 of a kind, straights, flush etc?
And also, are all cards in play (except jokers)?

Title: Re: Another Casino Scam
Post by Nick on Jul 7^th, 2003, 1:21pm

I've lost a good deal of money playing this game, most attributed to drinking while playing. But the hands that you can recieve are standard poker hands. Pair, 2 Pair, 3 of a Kind, Flush, Full House, 4 of a Kind, Straight Flush and Royal Flush. I'm sure I probably messed up the order of rank too. One thing I forgot to include before, one of the Dealers cards is face up. How many possible hands can the dealer have, and still not qualify? Assuming you see an Ace or King face up, or otherwise seeing another lower card.

Title: Re: Another Casino Scam
Post by towr on Jul 8^th, 2003, 2:41am

I get 56.28% that the dealer does have ace+king or higher.
(of course it's not impossible I made a mistake in my program
[e]Moreso there actually was a mistake..[/e])

given the open card he has is an Ace or a King there's 33.62 % chance he doesn't qualify against 45.56 otherwise.
(Unless he can choose which card lies open)

Title: Re: Another Casino Scam
Post by SWF on Jul 9^th, 2003, 5:10pm

Probability of dealer getting A+K or better can be found by adding various possibilities, while being careful not to count the same thing twice:

N=52*51*50*49*48
A=P(2 or more of a kind)= 1-P(all cards different value)= 1-52*48*44*40*36/N
B=P(all values different and there is a K and an A)=20*(4*4*44*40*36)/N
C=P(straight beginning with A,2,3,4,5,6,7,8, or 9)=9*120*(4*4*4*4*4)/N
D=P(flush)=52*12*11*10*9/N
E=P(flush which includes K and A)=20*(4*11*10*9)/N
F=P(straight flush which is not a royal flush)=4*120*9/N

G=P(dealer has A+K or better)=A+B+C+D-E-F

E and F are subtracted because E was double counted (in B and D) and F was double counted in C and D. Straights beginning with 10 are not included because those hands include a K and A which is already accounted for.

A=0.4929; B=0.0650; C=0.00354; D=0.00198; E=0.000254; F=0.00001385

This results in probability dealer has A+K or better of 56.32%, which is pretty close to towr's simulation.

Title: Re: Another Casino Scam
Post by towr on Jul 10^th, 2003, 12:59am

I didn't really use simulation (in the sense of playing the game a gazillion time and look at the average), I just had a program count all possibilities.

I wonder where the 0.04% difference comes from..