Figure out my odds mistake in a black jack lucky ladies game

[ohkanada]

Hi,

My friend won 5k playing by putting $5 on a "Lucky Ladies" spot. He told me the odds and I figured I would calculate it. When I do the calculation myself I am off by an order of 2. Can someone find my mistake please:

To win the 1000x payout, the following needs to happen:

1) Double deck black jack.
2) He needs to be dealt both Queen of hearts.
3) Dealer needs to be dealt a black jack.
4) Odds listed on the website is 114,953 to 1.

Odds of getting both Queen of hearts (104/2 * 103) = 5356

Odds of dealer getting black jack (102/8 (8 aces)) * (101/30 (30 tens, jacks, queens, kings left) = 42.925.

When I multiple the two answers I get 229906. What obvious thing am I doing wrong?

Ken

[elitegimp]

[ QUOTE ]

Odds of dealer getting black jack (102/8 (8 aces)) * (101/30 (30 tens, jacks, queens, kings left) = 42.925.


[/ QUOTE ]

When you calculate the odds of the dealer getting blackjack, you only accounted for the dealer being dealt an A and then a (T,J,Q, or K). You multiply by 2 because the dealer can be dealt a (T,J,Q, or K) first and then an A.

[LetYouDown]

Consider this one vote for doing nothing wrong. I don't see what you're missing here. I had my own approach to getting to the exact same numbers. I'm hoping I'm not missing either. Typically, casinos don't screw things like that up. This is going to drive me nuts.

[Lost Wages]

Probability of being dealt Q [img]/images/graemlins/heart.gif[/img]Q [img]/images/graemlins/heart.gif[/img] = 1/C(104,2) = 1/5356 = .000186706

Probability of dealer blackjack = 8*30/C(102,2) = 8*30/5151 = 0.0465929

P(Both) = 0.000186706 * 0.0465929 = 0.000008699197

Odds against = (1 - 0.000008699197):0.000008699197 = 114,952:1

Lost Wages

[LetYouDown]

Then I did it again from a blank slate and came up with Lost Wages' answer. I wonder what the hell I was doing wrong. Oh well. Seems right.

[LetYouDown]

I think I got it. Looks like your (our) calculation for blackjacks is off by a factor of two. Seems we were treating Ac Jc the as one instance and Jc Ac as another...when it's the same.

[ohkanada]

Thanks all. Figured it was something silly.

Ken