What is the true value of a piece?

I learned early on that a pawn was 1 point, knight 3, bishop 4, rook 5, and queen 9.  Sometimes the bishop isn't as strong as a knight and 2 rooks are stronger together (we could extend this by also adding the queen).

I played a game where my opponent's bishop was essentially trapped.  It evaluated the exchange (pawn for bishop) to be 2.09 or something like that.  I got curious and put in a "neutral position" which only removed the bishop and got the following.

2.15 depth 24
2.19 depth 27
2.18 depth 28

Without seeing the position, does this seem reasonable, to evaluate a capture of a bishop (hanging) about 2 points instead of 3 or 4?

I'm a newbie to chess, but seems to me that the value of the pieces is in fluxus, and depend on the development of the game.

Short answer is the position you used wasn't neutral. Engines evaluate more than just the pieces. They're also programmed to give value to things like king safety and space.

The more involved answer is the 1, 3, 4, 5, 9 system is just a rule of thumb. It's sort of like an average for all positions. The true value for every piece actually chances every move (if only a little bit).

An easy example is when you have center pawns locked on one color. The bishop on that color is less mobile by nature, and worth a little less. The bishop of the opposite color is more mobile by nature, and worth a little more.

Another example is, as pawns come off the board, bishops and rooks are a little better each time, and knights are a little worse.

There are also more intangible factors like if a piece is an important defender or attacker. As the game goes on, maybe you transition into an endgame and now what was once your most valuable piece isn't as important.

This link has a lot of detail, but may be interesting to you:

https://home.comcast.net/~danheisman/Articles/evaluation_of_material_imbalance.htm

Depends on the position.

well my set, with the 4.25" King and two extra Queens cost me 48 dollars