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High Card, Low Kicker
One of the most common mistakes a new/inexperienced player will make is calling a hand with an A or K and another unsuited, 4 or more gapped card. The only hope for this hand is to pair the high card, but in a game with 4 or more players, there's a good chance that someone else also has that high card and have a better kicker. If you pair your low card, you may have a great kicker, but your small pair will most likely be middle or low pair and that's not going to help you out either. Stick to the basic starting hand strategy and only deviate for a reason (heads up play, etc.).
Understanding Pre-Flop and Post-Flop Hands
It is important to recognize the difference between a pre-flop and a post-flop hand. Pre-flop, a pair of Kings is a strong hand. Post-flop, an Ace on the board causes a pocket pair of Kings to be weak. Pre-flop, AK is a relatively strong hand. Post-flop, 3 to a straight or flush could make AK a folding hand. Likewise, 56s is a weak pre-flop hand, but if the flop comes 347 you have the nuts (beating any of those high pocket pairs). One of the mistakes made by new players is that they get too attached to big pocket pairs or AK thinking that they have the best hand. Although that may be true pre-flop (and should be raising to knockout the draws), after the flop they need to be cautious of the possible hands that they may now be against. Too many times people bring 2 pocket Aces to the River and get beaten by 2 pair or better.
Failure to Recognize the Other Player's Hand
It is well known that beginner poker players focus on their own hand and give little thought to what their opposition is holding. This is somewhat similar to playing Video Poker, where the player feels that he/she will need jacks or better and they will win. The problem with this is that jacks or better (or any hand) does not guarantee a win in live poker. In Hold'em, 5 of the 7 cards are shared so the other players at the table have at least 60% of that hand as well. Keep in mind if there are pairs on board, 3 suited cards, or 3 sequential cards where the right two cards can make a straight, your top pair or even two pair may be beaten at the showdown.
Less than Top Pair
Because Hold'em uses 5 community cards and starts with up to 10 players, it is common to see some powerful hands at the river. While there is no set standard of which hands win, especially if there is bluffing and strong players at the table, it is most commonly a mistake to expect a hand that is less than Top Pair to win at the river. If you are confident of your hand reading skills or are an experienced player, then you may be able to tell when a player is ready to go the river with less than Top Pair against you, but in most circumstances players will show you Top Pair or better and beat your second or bottom pair.
Misunderstanding of the Hand's Strength
This subject can sometimes be upsetting for both the winner and a loser. A player will be very confident that his 2 pair is such a powerful hand, even though there are 4 suited cards on the board. This player bets and raises with all the confidence in the world expecting to win. When it comes around to the showdown, the player will show his cards with excitement to only be struck down by a player who limped in with a lone Ace and caught the nut flush draw when 3 suited cards hit on the flop. There is nothing worse than thinking you’re the winner all the way through to find out at the end that you were beaten the whole time and should have known. Sometimes during home games, a player will show 2 pair, see the other player had 3 of a kind and still think they won. That is always tough, even for the winner since home games are usually with friends and family and to take that pot away from your favorite uncle when he was so excited about being the winner. Be sure to learn the rules and pay attention to how strong your hand really is for the situation.
Home Game vs. Casino Game
There are some big differences between playing poker in a home game and playing in a casino. The key differences are in the types of people that play the games. In a home game it's usually a group of friends and relatives who want to enjoy a night of poker. There is a wide array of poker skill at the table and people play more to have fun than out to win everybody's money (obviously this depends on your game, but a blood thirsty home game where everyone wants to bust out the other players, most likely won't be a game for long). At a casino, usually the limit you play will dictate the kind of game you encounter. In the lower limits, there will be more recreational, fun oriented players looking for a good time and maybe win some money. In the higher limits players will be harder to beat and will be more focused on winning money than having fun. Also, the limits at a casino are often higher than the average home game. It's common to have 25 cent betting increments in a home game, while in a casino the lowest limit may be $2. That's a big difference if you are used to playing with quarters. You can lose your bankroll much quicker if you don't pay attention. Another impact of the higher limit is that people will play slightly tighter, especially in the later rounds when their draws don't pan out. It might be worth a quarter to see what the other player has, but if you're talking about $2 or $4 it's a whole different story. Recognize the type of game you are playing in and adapt your style of play.
Additional Things to Keep in Mind