What does it means to take risks

I am constantly trying to understand what is really meant by the idea of taking risks. But to be honest, I just can't. In the 2K13 WCC, many are saying that carlsen should take more risks. But risks is defined as something that puts you in a dangerous, or unfavorable situation. I honestly believe that this word choice is incorrect. Rather it should be, Carlsen should use more insight into his positional understanding and calculation. Besides, MC is known for secondary openings like this. When you say take risks, you are really just saying play the game and see where it takes you. Risks in chess honestly have the eqivalence of sacrificing pieces, inaccuracies, mistakes, and blunders. In WCC play you surely don't want to do that. And with a several time champion like Vishy Anand, taking a risk is a risk in itself. The only thing I have to say is I hope they play their destiny. Anand will accomplish his by retaining his title, beating world No.1 in the process, and having more elo points. Carlsen's destiny would be to achieve the highest title ever in chess, prove he is truely No.1, win the title at an extraordinary age, and have a slight increase in his rating. I hope everyone will understand the point I am trying to drive home. But, I do agree that these games are kindof short. I hope the game reaches at least the Middle game point. But in respect to them both, I say let the players play.

Taking a risk is closely related to faith. Imagine walking into a fiery furnace and hoping to survive. Or crossing the Red Sea surrounded by walls of water. Hope this helps.

I like the idea you are driving at, knowlege.  Any game you could potentially lose with a bad move is a dangerous game.  To answer the question you posed in the thread title, I quote Fischer: "You have to give squares to get squares."  It is a matter of degrees how many squares you give and get.

You take a risk on the ability of your opponent figuring out what your up to.

A full house!

A risk in chess is making a certain move which leads to a position where if you play perfectly, you will win but if you make a mistake you will lose. Simple really.

The only perfect move in chess is checkmate.

It's the only move with gain and no options.  A perfect position.

Or a move that forces checkmate

A good analogy for taking risks in chess is playing the 3-4-3 in soccer (which, if I were a coach, is something I would never do). You are more concerned with attacking your opponent than with your own safety.

To explain risk taking : 
If you play the Petrof as black, you will probably not lose, but you will probably not win. You have no risk to lose, no chance to win.

If you play the sicilian dragon, you will probably not draw, but you can either win or lose. You are taking the risk of losing, but you increase your chances of winning.

However, playing the Petrof or the Dragon is equally good. 

And yet I've never played either of them in any of my games - well at least I know I've enevr played the Dragon. I don't know what the Petrov is, so I'm assuming I haven't played it, but of course I can't be sure.

Risk means increasing the chance of losing in order to also increase the chance of winning.

No risk means neither side has any realistic chance to win: a draw is extremely likely.

Whether incurring greater risk is the best idea or not depends on the position, the strengths and weaknesses of the players, the match results and the implications of a win or loss for the rest of the match.

I think both Carlsen and Anand have made good decisions so far, from the point of view of them maximizing their chances of success. Anand's best chances probably lie in continuing to force draws for a while and either enticing Carlsen to overextend in trying to win a drawn position, or take his chances in the rapids -- unless Carlsen commits a serious error before Anand has a chance to force a repetition, in which case Anand will of course go for the jugular. Carlsen will probably take on more risk as the match progress, and will try to prevent Anand from being able to force a draw via threefold repetition in order to reach playable middlegames or endgames in which he can still set problems for Anand to solve and strive to outplay him.

Imagine two people on a log on water, each trying to unbalance his opponent by turning the log with their feet, the danger is that if you push too hard you may fall off, thus its the same in chess, at this level players must unbalance their opponent by pushing hard and taking some risk, otherwise you end up with rather insipid chess as each simply tries to retain a balanced position.

A risk in chess is when a player makes a move which leads to a position which requires accurate play to win, innaccurate play will lead to a loss.

Most people can simply understand what people mean without being condescending.

"Hope Chess" is the equivalent of "Fish" at a poker table, both of which entail unsound risk taking, with little regard to known outcomes. 

Consider the diagram that watcha provided.  Normally 10 deuce off suit is a crappy hand, and the player with pocket Qs would likely make an aggressive position in the preflop.  I suspect the reason why you see 10 deuce off, and a 7-3 suited at the river is because the Qs limped in, maybe because he made the judgment that people were playing too tight.  Then when the Ks popped up in the flop, he didn't want to be fully committed, although you still have to bet with Qs to test the water if you're in front of the button.  10 Deuce off can be a sound risk if the cost of entry to see the flop is low, AND your relative chipstack is in a good position to see more hands.  The cost is in line with the probabilities.  It's likely the Qs played wrong.  If on the other hand, the Qs made a strong bet like he should have, then if you call with 10-2off, the risk to call becomes less worthwhile if these conditions are modeled over time, and likely even be a losing proposition. 

The point is your risks need to be calculated.

Hope chess is an obvious unsound risk by definition.  A more subtle risk is playing gambits, where you sacrifice a pawn for some sort of compensation.  It's a calculated risk.

Calculated risk entails limiting actions, otherwise what's the point.  "Just thinking about it" is just thinking about it.  Doesn't mean your responses are favorable, or even rooted in concrete analysis.

I'm not defining risk by itself.

The difference between calculated risk and uncalculated risk is the difference between gambling and investing.  One relies on luck, hope, faith, and all that soft stuff.  The other is a disciplined approach, relying on hard metrics and projected outcomes.  Both entail risk, but both accept risk in different ways.

People take uncalculated risks all the time, particularly when they don't even appreciate the magnitude of the risk.  Just saying "it's risky", is not the same as "based on information available, there's an 89% probability that you won't hit, and that it's probably not a good idea to call unless the cost of entry is proportional to the odds of hitting, such that if this decision were repeated indefinitely, you'd actually come out on top."  Saying to yourself "it's risky" is your "just thinking about it" approach.  You've not calculated anything.   

Just "thinking about it" can be an intuitive proposition, not necessarily concrete.  A call based on intuition is an uncalculated risk.  You might have that "gut feeling", but you really can't quantify it reliably. 

I used "Hope chess" as an example for a reason.  You can take an uncalculated risk by "hoping" your opponent doesn't see an obvious refutation to your deadly attacking move.  Can you honestly say for certain you've calculated the risk?  You can have concrete analysis tell you that such and such move is no good, but can you concretely analyze your opponent's perception?  If not, why do people take this type of risk that goes against what you concretely know to be a poor move?  What is "hope", if not uncalculated? 

Taking a risk in chess is playing a move (or line) that isn't clear, it may be good for you or it may not but you give it a shot trying to win. The 'risk' is linked to there being a 'safe' alternative that doesn't promise much but doesn't give the opponent any chances either.

That's not very clear either is it?