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  3. Switched colors

If anyone else would like to play around with the positions and see for themselves I've provided some links and codes to paste...

To play a game with 1.d5 as black go to the analysis board here:

lichess.org/analysis/standard/rnbqkbnr/ppp1pppp/8/3p4/8/8/PPPPPPPP/RNBQKBNR_w_KQkq_-#0

To play a game with 1.e5 as black go to the analysis board here:

lichess.org/analysis/standard/rnbqkbnr/pppp1ppp/8/4p3/8/8/PPPPPPPP/RNBQKBNR_w_KQkq_-

@skovikes I just provided you links to get the same data I collected. If you can prove the data I found wrong that is awesome and I would not be offended in anyway. I just simply gathered data to share with the community as it seemed nobody else had done it yet. If you are willing to collect and submit further data, then please feel free to do so and I would be all for reading the results once you are done.

Its as simple as I was too lazy to go beyond more than a handful of moves before adding insight to other topics in the forum.

If I provided wrong data, then someone will eventually come along with the correct data and proof for it. Until then, I submitted what the computer told me about its analysis of the positions. Who am I to argue with stockfish?!

Your analysis comes at a lower depth, the first move for white was analysed at a depth of 50 where your moved at analysed at a depth of around 22ish

@skovikes @EXOprimal

See, said someone would come along and prove me wrong if I was wrong =) Exoprimal noticed what I didn't and that was the depth of the analysis. Good eye there!

Of course 1.e4 e5 is the same as 1.e3 e5 2.e4 reversed, but as far I know engines differ in their assessments for some non-obvious reasons.

But this is a technical coding issue biasing Black or White. Equal is equal and not more equal.

Yeah, that some engine or another evaluates them slightly differently at some arbitrary depth is NOT at all a demonstration that they are different.

They (the starting position where first player is white and the starting position where first player is black) are exactly the same.

That some engines to some arbitrary depth give slightly different evaluations would just be an indication of some asymmetry in the engine's handling of the position, nothing more.

That asymmetry could be from something odd in the code itself, or could just be from the conditions of the search (small timing differences can make modern engines' searches seem non-deterministic).

In the case of Stockfish, any differences you see will be from the searches you run being slightly different, as can be seen with an easy test.

Stockfish has an "eval" command that outputs the static evaluation of the current position. Most GUIs don't expose this, so it's easiest just to run it in a console. From there you can try a handful of positions as tests (I'm only going to show a couple to give some idea while keeping this post from getting overly long):

Traditional initial position:

position fen rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1
eval
Term | White | Black | Total
| MG EG | MG EG | MG EG
------------+-------------+-------------+------------
Material | ---- ---- | ---- ---- | 0.00 0.00
Imbalance | ---- ---- | ---- ---- | 0.00 0.00
Initiative | ---- ---- | ---- ---- | 0.00 0.00
Pawns | 0.35 -0.08 | 0.35 -0.08 | 0.00 0.00
Knights | 0.01 -0.17 | 0.01 -0.17 | 0.00 0.00
Bishops | -0.05 -0.41 | -0.05 -0.41 | 0.00 0.00
Rooks | -0.37 -0.02 | -0.37 -0.02 | 0.00 0.00
Queens | 0.00 0.00 | 0.00 0.00 | 0.00 0.00
Mobility | -0.94 -1.10 | -0.94 -1.10 | 0.00 0.00
King safety | 0.72 -0.08 | 0.72 -0.08 | 0.00 0.00
Threats | 0.00 0.00 | 0.00 0.00 | 0.00 0.00
Passed | 0.00 0.00 | 0.00 0.00 | 0.00 0.00
Space | 0.62 0.00 | 0.62 0.00 | 0.00 0.00
------------+-------------+-------------+------------
Total | ---- ---- | ---- ---- | 0.00 0.00

Total evaluation: 0.10 (white side)

You can actually already see that all the static evaluation terms are the same for both sides; the 0.10 is just the side-to-move bonus. Just for completeness, though, here's initial position with side-to-move flag switched to black:

position fen rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR b KQkq - 0 1
eval
Term | White | Black | Total
| MG EG | MG EG | MG EG
------------+-------------+-------------+------------
Material | ---- ---- | ---- ---- | 0.00 0.00
Imbalance | ---- ---- | ---- ---- | 0.00 0.00
Initiative | ---- ---- | ---- ---- | 0.00 0.00
Pawns | 0.35 -0.08 | 0.35 -0.08 | 0.00 0.00
Knights | 0.01 -0.17 | 0.01 -0.17 | 0.00 0.00
Bishops | -0.05 -0.41 | -0.05 -0.41 | 0.00 0.00
Rooks | -0.37 -0.02 | -0.37 -0.02 | 0.00 0.00
Queens | 0.00 0.00 | 0.00 0.00 | 0.00 0.00
Mobility | -0.94 -1.10 | -0.94 -1.10 | 0.00 0.00
King safety | 0.72 -0.08 | 0.72 -0.08 | 0.00 0.00
Threats | 0.00 0.00 | 0.00 0.00 | 0.00 0.00
Passed | 0.00 0.00 | 0.00 0.00 | 0.00 0.00
Space | 0.62 0.00 | 0.62 0.00 | 0.00 0.00
------------+-------------+-------------+------------
Total | ---- ---- | ---- ---- | 0.00 0.00

Total evaluation: -0.10 (white side)

As expected, still all equal and then the side-to-move bonus, now flipped.

Traditional starting position after 1.e4:

position fen rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1 moves e2e4
eval
Term | White | Black | Total
| MG EG | MG EG | MG EG
------------+-------------+-------------+------------
Material | ---- ---- | ---- ---- | 0.03 0.00
Imbalance | ---- ---- | ---- ---- | 0.00 0.00
Initiative | ---- ---- | ---- ---- | 0.00 0.03
Pawns | 0.30 -0.07 | 0.35 -0.08 | -0.04 0.01
Knights | 0.01 -0.17 | 0.01 -0.17 | 0.00 0.00
Bishops | -0.05 -0.41 | -0.05 -0.41 | 0.00 0.00
Rooks | -0.37 -0.02 | -0.37 -0.02 | 0.00 0.00
Queens | 0.00 0.00 | 0.00 0.00 | 0.00 0.00
Mobility | -0.28 -0.29 | -0.94 -1.10 | 0.66 0.81
King safety | 0.72 -0.08 | 0.62 -0.08 | 0.10 0.00
Threats | 0.00 0.00 | 0.03 0.03 | -0.03 -0.03
Passed | 0.00 0.00 | 0.00 0.00 | 0.00 0.00
Space | 0.77 0.00 | 0.46 0.00 | 0.31 0.00
------------+-------------+-------------+------------
Total | ---- ---- | ---- ---- | 1.02 0.82

Total evaluation: 0.93 (white side)

Traditional starting position with black to move, after 1.e5:

position fen rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR b KQkq - 0 1 moves e7e5
eval
Term | White | Black | Total
| MG EG | MG EG | MG EG
------------+-------------+-------------+------------
Material | ---- ---- | ---- ---- | -0.03 0.00
Imbalance | ---- ---- | ---- ---- | 0.00 0.00
Initiative | ---- ---- | ---- ---- | 0.00 -0.03
Pawns | 0.35 -0.08 | 0.30 -0.07 | 0.04 -0.01
Knights | 0.01 -0.17 | 0.01 -0.17 | 0.00 0.00
Bishops | -0.05 -0.41 | -0.05 -0.41 | 0.00 0.00
Rooks | -0.37 -0.02 | -0.37 -0.02 | 0.00 0.00
Queens | 0.00 0.00 | 0.00 0.00 | 0.00 0.00
Mobility | -0.94 -1.10 | -0.28 -0.29 | -0.66 -0.81
King safety | 0.62 -0.08 | 0.72 -0.08 | -0.10 0.00
Threats | 0.03 0.03 | 0.00 0.00 | 0.03 0.03
Passed | 0.00 0.00 | 0.00 0.00 | 0.00 0.00
Space | 0.46 0.00 | 0.77 0.00 | -0.31 0.00
------------+-------------+-------------+------------
Total | ---- ---- | ---- ---- | -1.02 -0.82

Total evaluation: -0.93 (white side)

And so on.

Just as a side note, it's not just the depth of the analysis that matters with respect to whether you get different evaluations or not.

With SF, for example, you can still get different evaluations if you swap the side-to-move flag for a symmetrical position and issue a "go depth N" command, so that it terminates the search at exactly the depth you want.

Small timing differences, what's left in hash if you didn't clear it before searches, and such things can still lead to some small differences.

The main thing here is to realize that the positions are just logically the same.

It's not unlike looking at statistics for moves in opening databases that don't index by the resulting position from a move, so that transpositions to an identical position can have different statistics.

For example, in the lichess database, After 1.e3 e6 2.e4, 2...e5 has a different score than 1...e5 does after 1.e4.

It hardly proves that the positions are different :)