In Texas Hold'em poker, when it is a player's turn, he tries to make a best hand out of his hole cards (private cards) and the communal cards.
Now my question is: On what factors does he decide to add more chips and play for the next round or fold?
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It's a hard question to answer, and depends on the player's style and whether the player likes to bluff, as well as the style and skill of the other players.
If I don't have decent hole cards (low cards or nothing matching) I fold. I might risk it if I'm one of the blinds, but if I'm raised I'll fold. If I have a decent starting hand I usually wait for the flop.
In my opinion you should bet based on the strength of your cards. Generally speaking, the games I've won have always been ones where I've consistently been conservative, and I find the same applies to my opponents. By conservative I mean don't bet unless you're sure the odds are in your favor.
For more on odds, read this article.
The general concept here is known as "pot odds". The basic goal is to figure out your probability of winning, and then compare the amount of money to "call" to the total amount of money you would win if you are successful. Neither of those are known values though, so you need to do your best to guess what they are. That requires both thinking about both the probability of upcoming cards that might improve your hand, as well as what hands you opponents might be able to create based on their private cards and upcoming cards.
All of this ignores the idea the concepts of bluffing as well as the fact that you often want to raise people if you feel you have better pot odds than them, to raise the amount of money you can potentially win and to decrease the chance that they stay in the pot and win on a lucky card on the river. So you can imagine that many books have been written on this subject, and thus it is impossible to give a complete answer on a site like this.
A player "folds" when someone bets and he decides he can't win.
He may have a bad hand, with "long odds" to improve, and there are one or more bets from players that seem to have a better hand.
The players at the table can't be bluffed out (particularly in limit), and are not known for playing hands worse than the player holds.