One of the reasons computers are so much stronger than humans, especially in the endgame, is because they have incredibly large pre-calculated tablebases[1] of 3, 4, 5 and 6 piece positions. So, if a computer calculates ahead 15 moves, and reaches a 6 piece ending, it already knows the exact evaluation of this position. And in some of these cases, the number of moves from that position to the final position (forced draw or checkmate) can be 10-100 moves [2]. But it is already calculated, the computer doesn't have to go any further. So in effect, the computer calculating 15 or 20 moves ahead in a late stage position can actually be calculating 50 or 100 moves ahead.
This is why the second part of Carlsen's quote is so important:
"Sometimes 15 to 20 moves ahead. But the trick is evaluating the position at the end of those calculations."
A human sees a late game position and has to actually calculate it all the way to its conclusion or at least a key position where they are confident of the evaluation [3]. A computer doesn't have to, and believe me, some of those 6 piece endgame positions are really weird. You move a piece just one innocuous looking square and it can alter the outcome from a win to a draw. There in fact were many endgame positions throughout chess history which were considered solved, only for the evaluation to change after a brute force calculation.
I'm not particularly good at chess [4], but in slow games I will routinely calculate 10 moves ahead in some sharp positions. Now, I'm not comparing my calculating ability to a GM, which is obviously better in every way, but the fact that a GM calculates 15-20 moves ahead is not why they are good. It is that at every step of that calculation they are evaluating the position incredibly accurately and are deciding the right moves to calculate.
In fact, due to the horizon effect, the reason computers got a lot better than humans wasn't due to raw calculation speed, it was due to massive improvements in their evaluation ability (like endgame tablebases) allowing them to put that massive calculation advantage to good use.
2: All of which are already in the tablebase by definition, because you can't add to the number of pieces on the chess board
3: For example, if I can calculate a position to where I have a rook and a king and you only have a king, I don't have to think any further, I know this is a win for me.
This is why the second part of Carlsen's quote is so important:
"Sometimes 15 to 20 moves ahead. But the trick is evaluating the position at the end of those calculations."
A human sees a late game position and has to actually calculate it all the way to its conclusion or at least a key position where they are confident of the evaluation [3]. A computer doesn't have to, and believe me, some of those 6 piece endgame positions are really weird. You move a piece just one innocuous looking square and it can alter the outcome from a win to a draw. There in fact were many endgame positions throughout chess history which were considered solved, only for the evaluation to change after a brute force calculation.
I'm not particularly good at chess [4], but in slow games I will routinely calculate 10 moves ahead in some sharp positions. Now, I'm not comparing my calculating ability to a GM, which is obviously better in every way, but the fact that a GM calculates 15-20 moves ahead is not why they are good. It is that at every step of that calculation they are evaluating the position incredibly accurately and are deciding the right moves to calculate.
In fact, due to the horizon effect, the reason computers got a lot better than humans wasn't due to raw calculation speed, it was due to massive improvements in their evaluation ability (like endgame tablebases) allowing them to put that massive calculation advantage to good use.
1: https://en.wikipedia.org/wiki/Endgame_tablebase
2: All of which are already in the tablebase by definition, because you can't add to the number of pieces on the chess board
3: For example, if I can calculate a position to where I have a rook and a king and you only have a king, I don't have to think any further, I know this is a win for me.
4: ~1300 rating