larwiz1
Joined: Sep 16, 2010
• Posts: 58
June 28th, 2013 at 4:50:49 PM permalink
I am twisting in the wind. What I want to know is how often do both dealer and myself have a Q high hand and how to go about calculating it.

I looked at the Ask the Wizard section and saw that dealer will have a Q high hand "The probability for queen high is: (combin(10,2)-1)*(43-4)/combin(52,3)=0.119457". Dealer having this removes 3 cards from the deck one of which is a "Q" thus reducing my chances of having one. So do I use the total number of hands for me as combin(49,2)=18424 total hands?

The part of the answer combin(10,2)-1 should still be the same?

When it comes to the suit combinations. There are still 4 suits for me, but not all ranks have the same number since dealer has removed a Q and 2 other lower cards. What do I do to calculate this?

Any assistance is appreciated.
MonkeyMonkey
Joined: May 1, 2012
• Posts: 770
June 29th, 2013 at 1:38:26 AM permalink
Quote: larwiz1

Dealer having this removes 3 cards from the deck one of which is a "Q" thus reducing my chances of having one.

I'm not a math whiz, but FWIW, you get your cards before the dealer, so the dealer having a Q high hand didn't effect your potential for having a Q in your hand.
tringlomane
Joined: Aug 25, 2012
• Posts: 6182
June 29th, 2013 at 4:44:38 AM permalink
Quote: MonkeyMonkey

I'm not a math whiz, but FWIW, you get your cards before the dealer, so the dealer having a Q high hand didn't effect your potential for having a Q in your hand.

The dealer having a Q high hand does affect whether or not you have one. If the dealer MUST have a Q in his hand, the probability of you having Q high will change. I've been up all night though, so I will not even dare touch the math at this point.
larwiz1
Joined: Sep 16, 2010
• Posts: 58
June 29th, 2013 at 5:02:53 AM permalink
True I get my hand first, thus I would have the Wizard's calculated %s for the various hands. Therefore his changes for Q, K, and A hands. I thought about taking the % of the time he will have a Q, with only 3 available, and the % of time I will have a Q with 4 available and multiplying this ratio against the .119457 and using that as the % of time for him to have a Q high hand, but that seems to simple to be correct.
CrystalMath
Joined: May 10, 2011
• Posts: 1812
June 29th, 2013 at 5:07:08 AM permalink
The number 43 in the formula should be 43, or 64.

You do use combin(49,3) for the total combinations in the second formula.
I heart Crystal Math.
larwiz1
Joined: Sep 16, 2010