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(Hold 'em) Poker Skills in Order of Importance
Disclaimer: I'm a poker novice, not an expert.
The exact order of importance of skills varies by game type. For example, you cannot read your opponent when your opponent does not know what he has. The list above is geared towards mid-level games where some sanity prevails but the game is not at an expert level either.
By far the most important skill is table selection, so it ranks better than #1, it's #0. It doesn't matter how well you play if you are always picking the games with no fish where even an expert can't beat the rake. Most of your income will come from a few very bad players. If you play fairly well, you won't lose much to the better players, nor win much from the slightly inferior players; it's the fish that count.
Now that you've found your table with a live one or two, be patient. More than just having the discipline to play good hands and the stomach for surviving the variance, you should realize that most of our income in Hold 'em comes from AA and KK, with notable mention to the other pocket pairs and AK. Your object is to not lose too much while waiting for these premium hands, and particularly not to lose too much to these hands when other players get them. At $10-$20 and below, go ahead and make it 3 bets if you can before the flop with your AA or KK; you'll be surprised at how little respect you get with people calling you all the way to the river even though your betting is screaming "I HAVE POCKET ACES!!!" And respect preflop raises done by other players, dumping a lot of hands you would normally play such as AT and KJ or even AJ and KQ, as you don't want to make top pair versus an overpair. On the flop, don't bet into someone who has made it three bets unless you can beat the shit out of AA and KK and *want* to be raised back and then just call and go for a check-raise on the turn.
Now, think about the range of hands and their probabilities that your opponents could have. Initially, when the players receive their first two cards, every possible two card hand is equally probable (unless you start grouping them like 87 offsuit, pocket aces, etc., but you get the idea.) Every action a player takes gives you information that you can use to adjust these probabilities. It's a Bayesian inference problem. Unfortunately, actually applying Bayes' rule exactly is beyond any puny human brain's capability. So, you make a major approximation and essentially just keep around a set of possible hands, which you then prune down as action take place.
Suppose a player just calls preflop in early position and the flop comes Q 7 2 offsuit and he suddenly goes berserk by reraising, you have to think about what hands are likely. The hands that make sense to reraise like that are AQ, KQ, Q7, 72, Q2, 77, and 22. QQ would probably be slow-played here instead. Now join that set with the possible hands before the flop. We can just look at these hands and see which are reasonable to just call preflop in early position. AQ and KQ are often raised in early position, but at least sometimes they just call, so they are still consistent. Q7, 72, and Q2 are not reasonable calls from early position. 77 and 22 are reasonable calls, though tight players would probably dump the 22. So that leaves AQ, KQ, 77, and 22 as his possible hands, which has narrowed down the field quite a bit. Be aware also of how other players may interpret your betting.
As play goes along, give yourself a running commentary of the events, "she open-raises, he folds, he cold-calls...". You must make a lot of mental notes based on this, and you must do this even when you're not in a hand, because in addition to being useful during a hand, it's useful for later hands. You want to see the frequency with which a player sees the flop, the frequency with which a player defends his blinds from raises, and the hands a player open-raises with, raises with, reraises with, cold-calls with, and just calls with. This in conjunction with narrowing down the hands above will often give you a good idea of what's going on even when there is no showdown. Your goal is to stereotype each player, as well as to note particular idiosyncrasies of the individuals for use not only now but in future sessions.
Especially when heads-up, you should be constantly applying pressure to the other player to make him fold. You may reraise when you think you're either beaten badly or your opponent is bluffing. It's a bit like chess or wargames, with attacks, feints, counterattacks, and graceful retreats. This is part of the "feel" of poker that's hard to put into words, but hopefully you get the idea. Bluffing and semi-bluffing is important to keep yourself unpredictable, and with since you're keeping track of the ranges of plausible hands, it's quite likely you'll often know where your opponent stands. Cold bluffing is usually restricted to the river, where you might bet into one or two opponents (who might fold) if you have no chance of winning the pot if there is a showdown. Semi-bluffing is betting with a hand that is not likely best but has some big outs. Your opponent may fold immediately, and if not, you may hit your out and your opponent may seriously misread you. There is an important balance here; you must have sufficiently tight hand selection criteria such that when you do bet your opponent is positively terrified that you may have a big hand like an overpair. Semi-bluffing is very powerful, because you've been so careful in choosing your starting hands that even if you aren't there yet you are likely to get there.
Generally, you want the loose aggressive players to your right and the tight passive players to your left. This is so that you can see a raise coming before calling the first bet. However, if the game is tight enough that it is being folded around to the blinds often, then you want some very tight passive players in the two seats to your right, so that your blinds will not be stolen. This is a very important skill, and just because you've found a good table, doesn't mean that every seat at that table would be a winning seat on average for you.
Because the nature of fixed limit Hold 'em makes calling one bet often correct for very weak hands, it's difficult to protect your hand. A major weapon you have to protect your hand is check-raising. However, you must be conscious of where you think the bettor will be. Typically, if you had a made but vulnerable hand you would check in early position if you thought there would be a bet in late position; you then raise and the players in between face two bets plus a risk of a reraise by the late position player, making it difficult for them to call. If you have an invulnerable hand that you want to make everyone pay you through the nose for, then you would check in early position if you thought there would be an early position bet, and then you would raise after everyone trailed in calling behind. The down side of check-raising is that you risk giving a free card if no one bets.
Be aware of tells. If a player has his hands on his chips and is leaning forward, all ready to raise if you bet, usually this is an act intended to get you to just check, as the player in fact does not what to raise you or maybe even call a bet. Two other incredibly valuable tells are the "what the heck, I raise" tell (get *out*, he has a monster!) and the "let me check to see if I have one of that suit with three on the board" tell (so you know he doesn't have a flush already.) Remember that if they think they're being watched, players typically act the opposite of what they have.
Be aware of pot odds. You can count the number of "outs" you have to estimate if calling is a positive expected value play. You may be surprised that I rank this so low. Although it is a subjective opinion, particularly when heads up it's much more important outplay your opponent rather than outdraw him. In loose games, outdrawing becomes much more important, but then the pots are so big that you usually have odds for any half way reasonable draw anyway.