Probability of hitting on the flop

I think I'm getting the hang of odds and probability .. but might aswell through to the experts out there ...

You hold AK suited .. what odds of hitting *anything* on the flop ....anything being defined (in the instance of AKs) as ANY pair, a flush draw, a straight draw or better ..

Can anyone do the math??

Thx

[SittingBull]

If U have AKs,then there are 3 A's that are favorable for flopping exactly a pair of A's.
Since U have 2 cards in your hand,there are 50 cards that U do not see.
Of the 50 cards, 3 are favorable,so 47 are unfavorable.
The odds against hitting exactly a pair of A's is the ratio: unfavorable outcomes:favorable outcomes.
For floppong a flush draw. U have two suited cards. So U need two of the remaining 11 suited cards to flop a flush draw.
The total # of combinations of flopping 3 cards from 50 remaining unknowns is C(50,3).
Of these,there are C(11,2) favorabe outcomes. This is the total # of ways of hitting 2 of your suited cards grom a group of 11 of the same suit.
Hence, the probability of flopping a 4-flush is # of favorable outcomes/total # of outcomes.
Hence C(11,2)/C(50,3).

H /forums/images/icons/laugh.gif appy pokering,Thunda!

If you have AK the number of combos where you flop a pair (of A's or K's) or more is

6(44C2) +6c2(44) +6C3= 6(44C2)+ 15(44) +20

you can flop a flush 11C3 ways, and a flush draw (w/o a pair (of A's or K's) 10C2(27) ways.

You can flop a straight (but not a flush) 4^3-1 ways.

Finally for straight draws which aren't flush draws

a) in a paired board 6(4*6 -3) = 126 ways.

b) in a non paired board 27( 64- 1 -12)= 51*27 ways.

Now add all these up and divide by 50C3 to get your desired probablility! (and forget anything you read by the sitting bull
/forums/images/icons/smile.gif ).