That depends on who your opponent is. Against inexperienced players, projecting confidence can sometimes make them miss the fact that you made a mistake. However, against strong experienced players they will almost always notice and take advantage of mistakes, confidence and psychology will not factor into it.
Notice, for example, how the top AI players are now pretty much unbeatable by humans. They don't make use of any psychological tricks but play purely rationally -- read up about min-max and decision/game theory for a general framework for how such AI is written.
Yes, obviously you need to be smart to play chess. But on the professional level they are all very smart and capable people. So it's not only about being smart but also understanding who you're facing and how you can crash his mind.
Actually I did and still am.
And I have a 9 years old kid studying & playing 4 times a week.
I also met a few professional chess players in my life and talked to them about chess.
That's interesting. In contrast, some people, for example, me, tend toward overconfidence in chess.
Specifically, I'm more likely to lose the first (speed-chess) game of the day, especially if I have not played for a few days, than to lose subsequent games because until I have the cold water of reality splashed in my face, I tend not to put in enough mental effort!
Feeling confident, in other words, makes me relax, which is great at a party, but exactly the wrong thing when I am playing chess (or doing math or debugging a program).
(Specifically, I use the fear of losing or anger at just having lost a game to create enough tension for me to play chess well. By "tension" I refer to activation of my sympathetic nervous system, i.e., what is informally referred to as "adrenalin".)
When I am carrying enough tension to play chess to my potential, I tend to get pessimistic -- with the result that I resign a game every now and then that I should have continued, but that effect is very small compared to the (opposite) effect of my underestimating the amount of mental effort required to win.
I'd be interesting in hearing more about how chess is for you (or your 9-yo kid).
Notice, for example, how the top AI players are now pretty much unbeatable by humans. They don't make use of any psychological tricks but play purely rationally -- read up about min-max and decision/game theory for a general framework for how such AI is written.