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I'm taking a long (perhaps permanent) break from online poker, but when I was playing a lot, one on one matches were my favorite. To me, they were essentially about trying to enter the mind of your opponent, by understanding how he approaches the game, how he acts in different situations, how he is likely to respond to your actions (e.g., does he have an inclination to call large raises with mediocre hands, or does he fold easily in the face of pressure?), and by paying attention to whatever information he may be giving you. Once you know how your opponent is approaching the game, then you adopt your own approach which is specifically designed to work against the weaknesses in your opponents plan. If he is playing hands primarily for value, then you can exploit that fact by simply betting and winning a lot of the time, since, statistically speaking, he will usually have nothing. When you're playing an overly aggressive player, your style should probably depend on the nuances of the players personality. This, I think, is because some aggressive players can be tamed, and others can't. Once I was playing against a player who simply had to control the action on every single hand, regardless of how much I raised him by. I had tried a few tactics to slow him down, such as calling out of the big blind when he raised from the button, then check-raising on the flop regardless of what I had, or by limping from the button and then reraising once he raised, but he would almost invariably reraise. In this type of situation, the best plan is probably just to wait for a hand, at which point your opponent will be glad to give you all his money (In the game against the overly aggressive opponent I faced, it was a hand where I had 2-4 offsuit in the big blind, and my opponent limped in. The flop came 2, 2, K with two clubs, so I check-raised him, and he quickly reraised me. I called, a blank fell on the turn, and I checked to him. He moved all-in, so I called and won the pot when he showed jack high.). If you're facing an aggressive opponent who can be slowed, I think that it is probably advisable that you do so, since you will otherwise be giving up too much equity when you're unable to find a hand, since it will be difficult and often very risky to win a pot without one. This can be done, I think, using tactics like the ones mentioned above.
Usually, a good player will have at least a moderately dynamic style, and therefore it's important that you're able to quickly pick up on patterns in his play and also be able to adjust your play just as he is beginning to figure you out. In many ways it becomes a sort of silent dialogue between two players. In these cases, your success will probably largely depend on how alert and deceptive you are.
I think those are the essentials of how to play heads-up poker. The fundamentals are very simple, but once your opponents become increasingly more intelligent and informed about the game, then the game can quickly be brought to a level of fairly sophisticated psychological strategy.
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