Probability of 1 card

[tomcain]

Hello

Let me start by saying I love your books. I have not gotten through them all yet. I only started playing about 6 wks ago. I have a degree in math but statistics was not my strongest subject. Also, my brain cells have aged a lot since then.

Here is the question. In Texas Holdem, I have an A and the flop has an A. What is the probability of another A hitting the board. If I am reading the postings properly, it seems to be the same probability as any other card. However, I cannot quite reconcile that, in my mind, since 2 of the 4 possible A are already gone. If the answer is in one of the books, plz reference that also.

TIA. Tom

[daryn]

you're saying you have an ace in your hand, and an ace comes on the flop..

well assuming your other hole card isn't an ace, then you have seen 5 cards so far, your 2 and the 3 flop cards. that means there are 52-5= 47 unseen cards left in the deck. there are 2 remaining aces, so the chances of an ace coming on 4th st. are 2/47 or approx. 4.26%.

[Analyst]

And the probability of getting at least one more A (again, assuming you have 1 in your hand) on either the turn or the river is:

1 - (45/47)*(44/46) = 8.42%

[daryn]

correct, upon rereading the question, it seems he wanted to know the probability of an ace hitting the board on the turn or river.. so you are correct /images/graemlins/grin.gif

[tomcain]

Thx much.

This makes perfect sense to me and corresponds to what I was thinking. I must have interperted some other postings I read incorrectly.

As a follow up: if a third A hit on 4st, then the probability of the 4th A hitting on the river is 1/46. Sound right?

[NoTalent]

yes that is correct. I don't know if you saw it in the other thread, but there is an excellent discussion of probability here (http://forumserver.twoplustwo.com/favlinker.php?Cat=&Entry=2523&F_Board=probability& Thread=314196&partnumber=&postmarker=)

GL!

-NoTalent

[tomcain]

Yes I did. Thank you