Is poker, be it free poker games 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 players believe that it is essential to know pot odds before deciding if you should call or not. Others will tell you that the tells other players give you are the key factor. 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 many ways math and psychology are deeply connected. 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.
Generally mathematically biased player win chips when the other players make bad math based moves. And such a situation in itself is a psychological analysis - playing styles are revealed and these can be taken advantage of.
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)].
Poker math and psychology, then it seems are joined at the hip. But there are situations where one of the two will prevail. When you are on a draw, you use pot odds to call. Or maybe you move all in with a small pair when short-stacked. Or on a very tight table, you bluff without remembering at your hand. Or you wait for a trap at a loose table.
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).
Doing poker math in game as well as the whole mind game thing takes a while to learn. For best result practice hard on free poker games sites at first and when, only when, you are confident, move up to low stakes cash games.
And what better place to practice your poker mind and math trickery than at free poker games site http://www.NoPayPOKER.com where you get to play poker online for free with 0 degree kelvin absolute zero risk of loss but can still win real money and get your bankroll paid for entry into cash sites when you're ready to step up to cash games.
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