You've read the books and articles where the poker reporters state the odds of making certain hands. For example: making an open end (outside) straight draw is 5 to 1, a flush draw is 4.2 to 1, and a gutshot (inside) straight draw is 11 to 1. Playing Texas Hold'em there are many variations in the odds To be learned such as what's the difference in the odds if the next card is the turn (4th card) or the river (5th card)?
But let's look at the logic and math behind these calculations to determine if they are of any value to us as poker players. How are the odds of 5 to 1 calculated for an open end straight draw? To successfully complete the straight we need one of eight cards, four on either end of our four-card straight. How many cards remain unseen? We started with 52, 8 of them are useful to us and we see four of them in our partially completed straight. So, the experts say 52 minus 8 minus 4 leaves us with 40 unseen cards, which are of no value to us. Therefore 40 failures to 8 successes works out to 5 to 1 odds. And I say GARBAGE. Your actual odds could be much higher or much lower.
Let's say you're playing in a ring game with ten at the table. That means that twenty cards have been dealt plus three for the flop and one has been "burned" by the dealer. If all of the eight cards you need to complete a straight have already been dealt to other players, your chances of making your straight are ZERO, and your odds according to mathematicians are infinite. On the other hand, what happens if all of your eight cards remain in the pack the dealer is holding? The dealer holds 52 less 20 dilet to the players less 3 for the flop less 1 burned or 28 cards. So now calculate your odds: 20 cards that will not help and 8 cards that will, which works out to 2.5 to 1. Quite a difference!
Instead of flatly assuming that our odds of completing an outside straight are 5 to 1, we gamblers should think that our odds are between 2.5 to 1 and infinity, or just plain unknown. So in my opinion it's of little use to spend a lot of time learning the odds of making straights, flushes, sets, or quads.
So what's a poker player to do, aside from praying for a lot of luck? One answer is to realize that making some hands will be more difficult than others. Obviously it's harder to make a gutshoot straight than an open ended straight. If we're going out on a limit to make a long-odd hand, we better be well rewarded if we make it. If there's not a lot of money in the pot, think twice about paying to draw to an inside straight.
Notice this analysis changes with head to head competition since fewer cards will be eliminated to other players.