3 card poker probability

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.

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.

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.

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.

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 guess that the formatting when you copy and paste is not retained for things like the 4 cubed. There is probably some way to retain the formatting. The other was just typing error. Just what happens with old brains. Thanks for pointing these out to me.