user25815: I'm a total beginner in Chess. I've known the basic rules for at least 20 years, but have never played it somewhat serious. Only toddler-level.
I recently started trying to learn how to play properly. I've been using LucasR to train myself. But I don't always how the scoring system works. Sometimes it says that a higher (positive) score is a blunder, while a lower (positive) score is a good move?
Take this row in the post game analysis for example:

(I accidentally cut off the headers, but the 2nd column is my move, the third is the "best move" according to the engine)
So, according to the engine I made a blunder in the 4th move. I'm not asking why it is a blunder or not. But I wonder why a score of +4.82 is a blunder while a score of +0.62 is "decent"? I thought that this score (the centipawns) are a measure of how well your strategic position in the game is? Shouldn't a higher value be better then?

user26335: Basic Interpretation:
As mentioned in this answer, the evaluation +0.5 (+50 centipawns) means a half-pawn advantage for White while a –2 evaluation (-200 centipawns) implies a 2 pawn advantage for Black.
Relationship to Win Probability:
There is also a natural link to the probability of the game's outcome. Instead of the centipawn-based evaluation that Stockfish uses, some neural network-based engines such as AlphaZero or LeelaZero estimate the probability of a win from the position. The figure below illustrates this.(1)
The exact nature of the mathematical relationship may vary slightly.
Given the probability of a win, feval, the centipawn evaluation has been given by cp = 290.680623072 * math.tan(3.096181612 * (feval - 0.5)) but was updated to be cp = 111.714640912 * tan(1.5620688421 * feval).(2–3)
Various Models:
In addition to inverting the functions above, there are additional models for converting a centipawn evaluation to the probability of a win.(1,5)
winning chances = 50 + 50 * (2 / (1 + exp(-0.004 * centipawns)) - 1)
The figure below illustrates the model: W = (1 + 10^(P/K))^(-1) where W is the probability of a win, P is the pawn advantage evaluation, and K is an unknown constant (set to 4).(1)

Thus, a higher evaluation implies a higher probability of White winning and a lower evaluation (negative) implies a higher probability of Black winning.
100 centipawns ≠ 1 pawn. As pointed out in the comments by @Allure, 100 centipawns is no longer truly indicating a 1 pawn advantage. Stockfish's recent documentation (see Normalize evaluation) explains that with the rise of the NNUE framework Stockfish now uses "'100 centipawns' for a position if the engine has a 50% probability to win" under specific conditions for the engine.
References
 1. https://www.chessprogramming.org/Pawn_Advantage,_Win_Percentage,_and_Elo 
2. http://chessforallages.blogspot.com/2019/08/winning-percentage-to-centipawns.html
3. https://github.com/LeelaChessZero/lc0/pull/841
4. https://zwischenzug.substack.com/p/centipawns-suck
5. https://lichess.org/forum/general-chess-discussion/what-does-that-evaluation-mean-
6.Normalize evaluation, Stockfish commit, 5 Nov 2022.

user32763: The score is from white's perspective. So 4.82 is much better for white than 0.62. Also notice that on the next move, white does not play Qa4, and loses the advantage, and the score becomes negative from white's perspective, i.e., the position is now better for black.
Also, note that in the above example the score is not 4.82 centipawns (100 centipawns = 1 pawn), but 4.82 pawns, which seems reasonable since if white played Qa4, you would lose the knight, so straight 3 points (approximately 3 pawns) loss.

25815: <p>I'm a total beginner in Chess. I've known the basic rules for at least 20 years, but have never played it somewhat serious. Only toddler-level.</p>
<p>I recently started trying to learn how to play properly. I've been using LucasR to train myself. But I don't always how the scoring system works. Sometimes it says that a higher (positive) score is a blunder, while a lower (positive) score is a good move?</p>
<p>Take this row in the post game analysis for example:
<a href="https://i.stack.imgur.com/Tox6b.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Tox6b.png" alt="post-game analysis" /></a></p>
<p>(I accidentally cut off the headers, but the 2nd column is my move, the third is the &quot;best move&quot; according to the engine)</p>
<p>So, according to the engine I made a blunder in the 4th move. I'm not asking why it is a blunder or not. But I wonder why a score of +4.82 is a blunder while a score of +0.62 is &quot;decent&quot;? I thought that this score (the centipawns) are a measure of how well your strategic position in the game is? Shouldn't a higher value be better then?</p>
 26335: <p><strong>Basic Interpretation:</strong><br />
As mentioned in <a href="https://chess.stackexchange.com/a/40239/26335">this answer</a>, the evaluation +0.5 (+50 centipawns) means a half-pawn advantage for White while a –2 evaluation (-200 centipawns) implies a 2 pawn advantage for Black.</p>
<p><strong>Relationship to Win Probability:</strong><br />
There is also a natural link to the probability of the game's outcome. Instead of the centipawn-based evaluation that Stockfish uses, some neural network-based engines such as AlphaZero or LeelaZero estimate the probability of a win from the position. The figure below illustrates this.<sup>(1)</sup></p>
<p>The exact nature of the mathematical relationship may vary slightly.
Given the probability of a win, <code>feval</code>, the centipawn evaluation has been given by <code>cp = 290.680623072 * math.tan(3.096181612 * (feval - 0.5))</code> but was updated to be <code>cp = 111.714640912 * tan(1.5620688421 * feval)</code>.<sup>(2–3)</sup></p>
<p><strong>Various Models:</strong>
In addition to inverting the functions above, there are additional models for converting a centipawn evaluation to the probability of a win.<sup>(1,5)</sup></p>
<p><code>winning chances = 50 + 50 * (2 / (1 + exp(-0.004 * centipawns)) - 1)</code></p>
<p>The figure below illustrates the model: <code>W = (1 + 10^(P/K))^(-1)</code> where W is the probability of a win, P is the pawn advantage evaluation, and K is an unknown constant (set to 4).<sup>(1)</sup></p>
<p><a href="https://i.stack.imgur.com/dXxhV.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/dXxhV.png" alt="Relationship between pawn evaluation and the win probability." /></a></p>
<p>Thus, a higher evaluation implies a higher probability of White winning and a lower evaluation (negative) implies a higher probability of Black winning.</p>
<p><strong>100 centipawns ≠ 1 pawn.</strong> As pointed out in the <a href="https://chess.stackexchange.com/questions/40238/how-does-centipawn-scoring-work-why-is-a-higher-positive-score-horrible-while/40240#comment65216_40240">comments</a> by @<a href="https://chess.stackexchange.com/users/15223/allure">Allure</a>, 100 centipawns is no longer truly indicating a 1 pawn advantage. Stockfish's recent documentation (see <a href="https://github.com/official-stockfish/Stockfish/commit/ad2aa8c06f438de8b8bb7b7c8726430e3f2a5685" rel="nofollow noreferrer">Normalize evaluation</a>) explains that with the rise of the NNUE framework Stockfish now uses &quot;'100 centipawns' for a position if the engine has a 50% probability to win&quot; under specific conditions for the engine.</p>
<p><sub>References</sub><br />
<sub> 1. <a href="https://www.chessprogramming.org/Pawn_Advantage,_Win_Percentage,_and_Elo" rel="nofollow noreferrer">https://www.chessprogramming.org/Pawn_Advantage,_Win_Percentage,_and_Elo</a> </sub><br />
<sub>2. <a href="http://chessforallages.blogspot.com/2019/08/winning-percentage-to-centipawns.html" rel="nofollow noreferrer">http://chessforallages.blogspot.com/2019/08/winning-percentage-to-centipawns.html</a></sub><br />
<sub>3. <a href="https://github.com/LeelaChessZero/lc0/pull/841" rel="nofollow noreferrer">https://github.com/LeelaChessZero/lc0/pull/841</a></sub><br />
<sub>4. <a href="https://zwischenzug.substack.com/p/centipawns-suck" rel="nofollow noreferrer">https://zwischenzug.substack.com/p/centipawns-suck</a></sub><br />
<sub>5. <a href="https://lichess.org/forum/general-chess-discussion/what-does-that-evaluation-mean-" rel="nofollow noreferrer">https://lichess.org/forum/general-chess-discussion/what-does-that-evaluation-mean-</a></sub><br />
<sub>6.<a href="https://github.com/official-stockfish/Stockfish/commit/ad2aa8c06f438de8b8bb7b7c8726430e3f2a5685" rel="nofollow noreferrer">Normalize evaluation</a>, Stockfish commit, 5 Nov 2022.</sub></p>
 32763: <p>The score is from white's perspective. So 4.82 is much better for white than 0.62. Also notice that on the next move, white does not play Qa4, and loses the advantage, and the score becomes negative from white's perspective, i.e., the position is now better for black.</p>
<p>Also, note that in the above example the score is not 4.82 centipawns (100 centipawns = 1 pawn), but 4.82 pawns, which seems reasonable since if white played Qa4, you would lose the knight, so straight 3 points (approximately 3 pawns) loss.</p>
