Best Move > Alternative?

Every time the engine shows a move as "best move" and suggests an "alternative", the alternative seems to always be very slightly worse, usually by 0.01 - 0.05. 

This indicates that when a move is 0.01 - 0.05 worse than the best move, it doesn't show the alternative best move, which would be better. There are a number of possibilities:

1. The move is shown as "excellent", and what would be considered the "alternative" is shown as "best move";

2. The move is shown as "best move", and the real best move is not shown at all; or

3. Some internal bug in the engine causes the real best move to appear as lower rated for whatever reason, and then displays it as an "alternative".

Which of these is the case, and why is the analysis made this way?

Could you try that again? Perhaps providing examples would help.

Your question does not make any sense. If the engine says the move you made was the best move then this means that the engine did not find any alternative move that it evaluated better than that. 

In this game I was playing white. I made the move Bxc6 in this position, which the engine displayed as the best move. The engine suggested an alternative move, d4, which gave a difference in score of -0.01.

The engine displays this move, d4, as an alternative best move. However, as mentioned before, it is scored slightly lower than the move I made.

I've noticed that every time the engine suggests an alternative best move, the suggested alternative always scores lower than the move that was actually made. So, for example, the engine would never say "Bxc6 is best (+0.02); d4 is an alternative (+0.03)", as this would mean the alternative scores higher than the best move that was made.

My question is as follows. If I had made the move d4, rather than Bxc6, what would the engine rate it? Would it say it's the best move and just hide the Bxc6 alternative as it would have actually been better? Would it say d4 was "excellent", and Bxc6 was best? And why is the engine made in such a way as to only show alternative best moves that are worse than the moves actually made?

By the way, I'm new to posting on the forum. So thank you for being patient with me.

What I think @2Pana is referring to is why the "best move" according to the engine isn't always "best" or how it can change evaluation lines. The answer is of course fairly complicated (when understanding how chess engines function), but I can simplify it - "it is a computer and computers do not think like we human players do."  

When the engine claims that one move is "best", but then you test an alternative and now the new move is considered "best" it is for a few reasons. Usually it is just that the computer did not look at your alternative that deeply, but when you put it on the board (basically asking the computer to give this line a deeper look), the computer then recognizes that your suggested alternative was stronger. This is fairly common for two main reasons:

1) Chess.com Quick Analysis under the default membership is not a strong version of Stockfish. It is good enough to catch my tactical blunders and a decent learning tool (rated probably 3000+ still) but it isn't the strongest chess engine out there.

2) Look up "Horizon effect" in chess computers. Chess has a massive number of variations, lines, moves, positions possible, repeated positions possible and so on. The amount of memory/computer space alone to even record all of these lines isn't practical (and that doesn't even count the programming to "calculate" so as a result most chess computers do not try to do an analysis of every possibility. Horizon effect is essentially when a computer doesn't correctly evaluate how strong or weak a variation is because it didn't calculate far enough to "see" the compensation (or refutation). This is the core reason behind why chess computers struggle with positional aspects of chess compared to their tactical ability: positional moves may not offer concrete advantages until way farther down the line than the computer can calculate: especially if it is doing an analysis of all variations along the way.

Various engines use various methods. Brute-force calculation would be attempting to "calculate" every single possible option in chess, but like I said, this is not the most successful technique right now. Most chess engines look into some "main branches" that appeal to the engine (via pre-set programming and programming evaluations into a position) and calculate them out deeply. If you suggest an alternative (by playing it out on the board), the computer then begins to calculate the options after that given move.

In short, I don't think there is any bug; it is just the case that most players (especially beginners in chess) do not fully understand how the computer evaluates a chess position. Computers are both far from perfect and immensely strong at the same time. This is why your phone can have a stronger chess engine than GM-human ability, but how a GM can create a puzzle that a computer can't solve, but the GM can (draw fortress motifs are common for this because due to the computer horizon effect, they can't recognize the position as drawn - no way to make progress).