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Switched colors

Hey, me and my friend where thinking about the advantages of the starting positions. We wonder if the color that starts game due to position matters. Stockfish says yes a bit but is it possible to check on 2 engins (like match between them)?

Any thoughts?

*Sry for any mistakes in my English ;)
I'm not sure exactly what the question is, but here are two points that answer a couple of the questions you might be asking:

1) The side that moves first has some advantage, yes.

2) If black moved first, black would have exactly the same advantage white currently enjoys. There would be no difference.
But accualy if black moves first it makes it diffrent game due to diffrent position (q,K,2x B)?
no, its just the same position with switched colors.
One way to measure the first-player advantage would be to run any engine until it solves chess. That might be more difficult than checkers, however.
Switch king and queen for black and white you get;
Fischer 960 - 534
RNBKQBNR rnbkqbnr
The answer is yes…
If you keep the position of the pieces the same and allow black to go first it would make a difference. But one could adapt.
If white goes first and moves 1. d4 they have a +.01
If black went first, and played the mirror move of 1. d5 they have a -.03 (or a +.03 for black).

If white goes first and play 1. d4 and black follows with 1. d4 d5 then the position is +.01
If black goes first and plays 1. d5 and white follows with 1.d5 d4 then the position is -.04 (+.04 for black)

The benefit is even larger to black playing the position white would normally play because of the placement of the queen and king!
Interesting to note….
If you play white first you have a +.01 advantage after 1.d4 or 1.e4
But if you play black first… you have a -.03 after 1.d5 and a -.02 for 1.e5
The numbers don’t lie… placement of the queen and king matters.

Now, if we switched the placement of the king and queen it would be as simple as saying now we have a differently painted chess set and that is all. The results would mathematically be the same once you are able to grasp that concept.

For those people that say nay and want the math to back it up…. Unfortunately, I would have to rewrite the engines code to modify the rules of chess for this setup to analyze the results of the position if we allow black to go first after switching the placement of the king and queen. The reason for this is because the engine is only analyzing a position rather than understanding this is move number 1. It sees the position as both sides having moved their kings and not being able to castle so immediately the advantages are skewed.
@Episcopul isn't black going first from the same starting position exactly the same as white, except with queen/king flipped? Since all other pieces other than queen/king are symmetrical about the middle (line between 4th/5th files), wouldn't this be the exact same as when white moves first, just flipped over the middle?
@Skovikes from the computers perspective... if you keep all the pieces of modern day chess in the same place and the only thing you change is who goes first... then yes black enjoys better advantages... at least at the start as this is as far as I evaluated. It has to deal with the queen being able to support that piece etc etc...

For you to better understand this... think of castling in the game... when you start with white, you can castle king-side to the right. When you start with black, your king-side is to your left. Its very small differences but those any small change to a position on the board can see drastic changes in an evaluation. You may not see the benefits of playing this pattern at the open immediately, but a few moves in and it can mean all the difference that your queen and king as swapped without having done it using one of your moves and changing tempo...
@Episcopul
I respectfully disagree with this, mathematically I can prove that they are the same (unless I have a hole in my proof).

Notice any move in a game with white going first can be transformed into a game with black going first by the following mechanism:

Change
a<->h
b<->g
c<->f
d<->e

1<->8
2<->7
3<->6
4<->5

and we can form a bijection between all games with white going first and all games with black going first.

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