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Concept #1 ? Pot Odds
Long-term profits in holdem come from making bets with a positive expectation. You only have a positive expectation when your payoff is higher than your risk. Casinos make money from negative expectation games like roulette. The single number bet in roulette pays off at 35 to 1, but the odds of winning the bet are 37 to 1. The difference between the 37 and the 35 is the casino's profit margin.
You need a basic understanding of how to calculate pot odds while playing in order to determine when to play. You should only play a hand when you have a positive expectation, otherwise you should fold. Basically you compare the number of chips in the pot with your chances of winning the pot when you decide whether or not to play a hand.
Suppose there is $150 in a pot, and you're on the flop with 4 to a flush. An easy way to approximate the odds of hitting the flush is to take the number of cards that will make your hand and multiply that by the number of cards that are still going to be dealt, and multiply that by 2. There are 13 cards in a suit and you have 4 of them. So there are 9 cards left. 9 times 2 more cards times 2% equals 36%, or about 1 in 3. You will win an average of once every three times and lose the other two times. So the pot needs to offer you at least 2 to 1 for you to call a bet. If someone bets $50, you stand to win $200 on a $50 bet, which gives you appropriate pot odds to call.
This basic concept is essential to holdem success. Other concepts to start thinking about are the odds of your opponent folding if you raise. This will change the pot odds. A rule of thumb is that the fewer opponents, the more likely you'll be able to take down an uncontested pot. Another rule of thumb is that if you have a drawing hand, a big pot, and a small bet to call, then you should call. If the pot's small, and the bet's big, then you should fold.
Concept #2 ? Starting Hand Selection & Position
Position is critical when deciding what kind of hands to actually play before the flop. The rule of thumb is that you play much tighter (have higher starting hand requirements) in early position and play looser in late position. Your advantage in late position is that you can see what the other players do before you decide what to do.
This is a simplification, and a lot of people aren't going to like the way I do it, but I divide starting hands into just three groups. There are definitely sub-divisions and subteleties between these groupsbut starting out, you're basically looking at just three different groups: strong hands, drawing hands, and unplayable hands.
Strong hands are pairs of 10 or higher, plus AK suited. AA's and KK's almost always warrant raising preflop, unless you're in early position and you're hoping for someone to raise behind you. AK suited, QQ's, JJ's, and 10's are worth raising with if no one else has raise, they're sometimes worth raising with if someone else has raised, and they're almost always worth calling with.
Drawing hands are hands that need to improve on the flop to win. Pairs of 99's or lower and suited connectors are usually drawing hands, and so are big-little suited. (Big little suited is an ace and one smaller card of the same suit, and it's a playable hand sometimes because of its flush potential.) Suited connectors are adjacent in rank and of the same suit, so they have the potential to make a flush or a straight or possibly even a straight flush. And the smaller pairs go down in value as they get lower in rank. They're normally worth calling if no one's raised unless you're in early position, when you should usually fold them. Sometimes pairs of 77's, 88's, and 99's are good starting hands to play strongly with too, especially if your opponents are very tight and you could win the pot right there without a showdown.
Concept #3 ? What to do on the Flop
"Fit or fold" is the common wisdom on this subject. You should be in a good position to decide what to do on the flop. I've always played overpairs and top pairs a little too strongly, and that works well at a weak table with calling stations, but you have to be more cautious with better players. The "average" winning hand in Texas holdem at a showdown is two pairs or better.
If your starting cards were a drawing hand, you need to hit your hand in order to play it. If you had pocket 66's, you really need to hit 3 of a kind to continue playing the hand, otherwise you should fold. 4 to an open-ended straight is playable unless there's a potential flush draw on the board. 4 to a flush is usually a good hand to play. But if you're playing a small pair and there are overcards on the board, you're probably going to have to get away from the hand. Texas holdem is a game of high cards.
This is a very basic introduction to the things you should think about in Texas holdem strategy. There are tremendous subtleties and complexities beyond this introduction, and entire books are written on strategies for limit, pot limit, and no limit Texas holdem. You're encouraged to start reading them and think about them while you play.
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