Pre- flop odds

[ron8]

I understand how to calculate my odds to improve once the flop is out, but I am really confused about pre-flop odds.
I have a good collection of books but they don't seem to deal with this subject in any detail. I have read, on several occasions (including David Sklanskys books)that if you hold a pocket pair, you are 7.5 to 1 to hit your card to make a trip on the flop, similarly if you hold A.K. you are about 4.5 to 1 to hit either another A.or K.plus other examples.
With regards to hitting a trip when holding a pocket pair I was thinking (and please don't laugh) I have two cards that won't help me improve and of the 50 that are left I have two cards that will. At first I assumed that I was 25/1 to hit the trip. Obviously this is COMPLETELY wrong!
Any help to explain how the 7.5 to 1 is arrived at and any books that deal with such matters would be gratefully received.
Regards
ron8

[Officer Farva]

You've come to the right place, Ron.

There are many ways to solve this problem, but the most straightforwards way to understand it is this:

The P(hitting trips on flop)
= 1 - P(all three cards are not your trip)
=1 - (48/50)(47/49)(46/48)
= %11.7551

So you will hit your trips 1 in every 8.5 hands, meaning you're 7.5 to 1 not to hit...

[Eder]

during play if you need a quick calculation you can count each out as 2%(1/50)...say you need hit A or K preflop odds = 6 outs(if you're holding AK) x 5 cards x 2% = 60% to hit if see all cards...not accurate but definetly close enough and easy to figure

[ron8]

Elder
Thank you very much for your help, much appreciated.
ron8

[ron8]

Officer Farva
Thank you very much for your help, much appreciated.
ron8