Is poker, be it free online poker or big stakes cash a math game, or a game based primarily on psychology?
Players are still debating on how to classify poker, although they will unanimously agree that poker contains both mathematical and psychological elements.
Some people advise knowing the pot odds in order to determine whether a call is proper or not. Some will instruct you to take the tells of other players. Some advise knowing the odds preflop. Some will tell you to bluff a tight player and trap a loose player.
I have tried to reconcile the mathematical and the psychological element in poker when playing. In some ways, they are intertwined. Knowing the pot odds is a mathematical way of playing. But if your opponent keeps betting weakly every Flop when you have a draw, then you can exploit this to your advantage. Call.
If you know that your opponent doesn't give mathematical attention to pot odds, then it is a part of his psychological character. Determine his character. Usually a mathematically-inclined player will get chips because all other players are making mathematically ill-advised moves. And the analysis behind this is a psychological analysis - the way how others play.
Usually, a math player is believed to play the cards; a psychological player plays the other players.
These distinctions are not so hard-fast, and many players can effectively do both. A math player in a board of 10-7-3-4-8 will bet or call a bet with A-7, if only he psychologically knows that (1) the board cards are small so that it would not help the other players , and (2) the opponent should raise if he has a hand better than top Pair. Both analyses are mathematical [note the 'small' in (1) and the 'better' in (2)] and psychological ['other players' in (1) and 'opponent should raise' in (2)].
Math and psychology, it turns out, go together. But there are situations where one of the two will prevail. When you are on a draw, you use pot odds to call. When you are short-stacked, you move all-in with a small Pair. When the table is so tight, you bluff without remembering at your hand. On a loose table, you wait for a trap.
In exceptional situations, they go together. Against a good player, you mix-up your play . This means playing in a way so random (math) that the other players get bothered over their inability to get a read from you (psychology). And when someone moves all-in against you when you have a marginal hand, you determine your stack size relative to him and use some pot odds (math) and figure out the chances he may be bluffing or trying to steal with a more marginal hand , and this requires a track history (psychology).