While you do not need to be a professor like Howard Lederer, have a PhD in computer science like Chris "Jesus" Ferguson, or have an engineering degree like I do to understand odds and probability, having at least a simple understanding of poker odds is a must for any beginning player. Odds and probability are very simple concepts actually. Take for instance, a two-sided coin flip. Any time that you flip the coin, there are two possible outcomes, heads or tails, and each outcome has the same chance or odds of occurring. So, if you were to bet someone that the coin flip would be heads, you have a 50% (50/50, 1:1, 1-1, or even money) chance to win. That's a fair bet if your winnings will be at least equal to how much you have to bet (i.e. bet one dollar to win one dollar). Poker odds are no more than an extension of a coin flip. Some odds calculations in poker can be quite complicated, but the ones that you really need to know are quite simple and easy to remember. First off there are 52 unique cards in a standard deck of playing cards that are used for most common games of poker. Within a deck of cards, there are also some important subsets of cards like the 4 suits (hearts, spades, diamonds, and clubs), the 13 different card face values (ranging from 2-10, and Jack-Ace), and the 4 different cards of each value (there are four Kings, Aces, 3's, etc.). All of these basic numbers are the same no matter whether you are playing Texas Hold'em, Seven Card Stud, Omaha, Five Card Draw, or any variation of these games of poker. Let's look at some simple odds derived from this information. If I told you to pick a card, any card out of a full deck, here are the odds for different possible outcomes of that one card draw: Card will be a heart: 3-1 (25%, 1 out of 4, 13 out of 52) Card will be a spade: 3-1 Card will be a club: 3-1 Card will be a diamond: 3-1 Card will be a club or spade: 1-1 (50%, 1 out of 2, 26 out of 52) Card will be an Ace: 12-1 (8.33%, 1 out of 13, 4 out of 52) Card will be a 9: 12-1 Card will be any specific value: 12-1 Card will be a 9 or King: 5.5-1 (18.18%, 2 out of 13, 8 out of 52) Card will be Jack of clubs: 51-1 (1.96%, 1 out of 52) Card will be any specific card: 51-1 Hopefully, you can see the basics of how this works. Most importantly, if you were to bet on the outcome of a one card draw, you would want to be sure that the payoff would be fair in relation to the odds. If you were betting that the card would be a heart, you will only win your bet when the card is a heart, and that only happens one out of every four times on average. You will lose that bet three out of four tries, so 3 times you lose for every 1 time you win (3-1 odds) and you need to be getting 3 dollars back if you win for every 1 dollar you bet for it to be fair. In any casino game, be it craps, blackjack, video poker, roulette, or slot machines, the casino sets the payout odds that you play for (and the house odds are ALWAYS against you). In horse racing, the payout odds are set by the pari-mutual system and calculated based on which horse has been bet on the most by the public. If you have ever wagered on a horse race, you know that the key to winning in the long run is only betting when you think the odds are a good deal. After the gate opens and the announcer says, "And They're Off", you are just hoping for good luck knowing that you've made a reasonably fair bet based on the odds. Poker is much like pari-mutual horse racing, except that the odds in poker never change. There are always the exact same 52 cards in every deck (unless someone is cheating like you might see in an old Western movie). With those same cards in the deck, the same possibilities occur repeatedly with the same odds. The good thing about poker is that you get to choose whether to play or fold, and most of the time you should be making that decision based on the odds for the cards you have been dealt. Above, I described the basic odds for a one card draw from a normal 52 card deck. That information is important to know, but poker is not a one card game. In the next lesson, I will explain some very simple ways to understand the odds that any given poker hand has of winning, and I will teach you how to bet when the odds are in your favor which is the single most important thing to know about poker.

Source: Poker In The Hole