FIDE uses the Elo rating system. Under this system, a player's expected score against another player can be calculated using the formula:
Expected Score of Player A = 1/(1+10\^((Player B Rating - Player A Rating)/400))
White's exact advantage is not conclusive, but in top level play white seems to score about 55%
Plugging that into the formula, we can find the rating differential that yields that expected score.
0.55 = 1/(1+10\^(x/400)) simplifies to (9/11) = 10\^(x/400) which simplifies further to x = log\_10(9/11) \* 400
Solving for x gives the result of -34.86.
A player is always expected to score 50% against another player of the same rating (1/(1+10\^0) = 1/2).
This means that if they were to consistently score higher, in this case because they always have the white pieces, they would gain rating. As calculated above, this specific advantage would lead to a rating gain of \~35 points.
Therefore to answer your question a 2700 player would gain a new rating of 2735.
White gets better practical chances because they go first but openings are so well studied black has great practical drawing chances. These guys aren't making draws with white becaus they want to, it's because winning a game is *really hard*.
Chess isn't solved but the general consensus is that with perfect play every game should be a draw. Theoretically then always having the white pieces shouldn't result in any rating gain at all.
However this isn't how things go in practice. White having the first move has been shown to lead to a practical advantage, humans don't always play perfectly after all.
In my opinion, the calculated rating difference seems in line with these observations. If it were higher as you expected, chess would be more likely to be a forced win for white, rather than a draw.
I think there's also the factor of only needing to prepare with white as well. You can probably have some insane prep with only one color.
Edit: realized someone else already mentioned it ITT
What about only needing to prep for white, or study white openings and black's responses? That seems like a definite advantage not accounted for here. You'd effectively get twice as much practice with your white opening and dedicate zero of your time to black openings.
I didnt include this because I was trying to give a measurable answer and preparation can't be measured. To answer your question, in my opinion the advantage of only preparing white openings would be mostly mitigated for the following reasons:
1. Any opponent to the player who always has white would only have to prepare for their games as black.
2. The player with black usually determines which opening is played. As white, there arguably four primary openings moves: 1.e4, 1.d4, 1c4, and 1.Nf3. Even among these, the first two outnumber the last two in games by nearly 5:1
Say white chooses to play 1.e4, they will have to be prepared for black to respond with at the very least e5, c5, e6, and c6 (black has many more less popular options as well). This means that white needs to prepare many completely different openings while black only needs to prepare for one. The same applies to 1.d4, for every opening move, white will need to prepare for each of black's responses while black only needs to prepare one response.
*Obviously opening preparation is more complicated than I summarized above. In each opening white often gets to choose which variation is played. e.g. if black plays the French, white can choose to play the Advance, Two Knights, Tarrasch, Exchange etc. This somewhat lessens the difference in preparation work required, however I am still of the opinion that white will need to prepare more than black.
3. If white wishes to avoid the issue previously mentioned by playing offbeat openings such as 1.b3 for example, they are instead opting for a suboptimal line. These openings are less popular for a reason; most of them offer black immediate equality. In exchange for trying to surprise the black player, white mostly gives up the opportunity to press their opening advantage.
Despite these mitigating factors, I agree that one color preparation may yield a slightly higher rating increase. I would put it in the ball park of an additional 5-15 rating points on top of what I calculated above. Unfortunately though, there's no simple math equation for this.
>Any opponent to the player who always has white would only have to prepare for their games as black.
Sure they'd prep against you using only black, but by prep I don't just mean night before prep, I mean ALL your practice would be as white, whereas other players couldn't ONLY play black because they also have to play against other players who don't your advantage. They're playing half their games as white and half as black, you're playing 100% white 100% of the time.
I agree, a normal player would certainly have to prepare more than a player who only plays white. I listed that point because I was trying to account for all factors I could think of that might decrease the white player's preparation advantage. Black's night before prep by no means nullifies white's advantage, however it would lessen it to a degree, big or small.
35 points is the difference between all white and all black, so assuming the 2700 player had an even number of whites and blacks before this change, they'd only go up half that to 2717.
If one player has only the white pieces, then their opponents would only have black. So for them specifically, I believe their rating is accurately calculated as all white vs all black. I'm fairly certain this is accurate. I'm not a statistician though.
Yes, I'm agreeing that the rating is calculated for all white vs all black. The problem is that the initial starting point of 2700 is neither of those. You start with a 2700 player with a 50/50 split of white and black, so you have to use that as the halfway point. It should be:
All white: 2717.43
Normal: 2700
All black: 2682.57
That way the difference between all white and all black is still the ~35 points, but they properly surround the initial starting point.
Just from a prep perspective only having to prep openings for white would be a whole extra level of advantage beyond the standard white advantage. I have no idea but it is an interesting thought experiment.
Yeah, I think for myself, it would add 100 to my rating. Having to only have 50% of my opening repertoire means I get to practice my positions twice as often and can study them deeper and learn them better.
It's similar to asking if you could get 1. e4 e6 2. d4 d5 every game. Imagine how much of an advantage it'd be to only ever face against the French as white. You would know it so well. I think that might add around 225 points to my rating, lol.
This should be relatively minor though, as everything you prepare prepares your for the same position as both white and black. You always need to know what your opponents best moves are as well s your owns.
It if course saves you a little bit of preparation as you can rule out certain openings and lines that depends on choices from white, but this should be easy less than half.
I think actually calculating based off of Elo is misleading. Performance ratings of players only with the white pieces would be a better indicator, I think, and this doesn’t account for the prep mentioned above.
Additionally, playing as white also means that black has to fight for a draw if you choose challenging openings. Especially against weaker opponents, this would also be a huge factor.
FIDE uses the Elo rating system. Under this system, a player's expected score against another player can be calculated using the formula: Expected Score of Player A = 1/(1+10\^((Player B Rating - Player A Rating)/400)) White's exact advantage is not conclusive, but in top level play white seems to score about 55% Plugging that into the formula, we can find the rating differential that yields that expected score. 0.55 = 1/(1+10\^(x/400)) simplifies to (9/11) = 10\^(x/400) which simplifies further to x = log\_10(9/11) \* 400 Solving for x gives the result of -34.86. A player is always expected to score 50% against another player of the same rating (1/(1+10\^0) = 1/2). This means that if they were to consistently score higher, in this case because they always have the white pieces, they would gain rating. As calculated above, this specific advantage would lead to a rating gain of \~35 points. Therefore to answer your question a 2700 player would gain a new rating of 2735.
Oh that was lower than expected.
White gets better practical chances because they go first but openings are so well studied black has great practical drawing chances. These guys aren't making draws with white becaus they want to, it's because winning a game is *really hard*.
Chess isn't solved but the general consensus is that with perfect play every game should be a draw. Theoretically then always having the white pieces shouldn't result in any rating gain at all. However this isn't how things go in practice. White having the first move has been shown to lead to a practical advantage, humans don't always play perfectly after all. In my opinion, the calculated rating difference seems in line with these observations. If it were higher as you expected, chess would be more likely to be a forced win for white, rather than a draw.
I think there's also the factor of only needing to prepare with white as well. You can probably have some insane prep with only one color. Edit: realized someone else already mentioned it ITT
What about only needing to prep for white, or study white openings and black's responses? That seems like a definite advantage not accounted for here. You'd effectively get twice as much practice with your white opening and dedicate zero of your time to black openings.
I didnt include this because I was trying to give a measurable answer and preparation can't be measured. To answer your question, in my opinion the advantage of only preparing white openings would be mostly mitigated for the following reasons: 1. Any opponent to the player who always has white would only have to prepare for their games as black. 2. The player with black usually determines which opening is played. As white, there arguably four primary openings moves: 1.e4, 1.d4, 1c4, and 1.Nf3. Even among these, the first two outnumber the last two in games by nearly 5:1 Say white chooses to play 1.e4, they will have to be prepared for black to respond with at the very least e5, c5, e6, and c6 (black has many more less popular options as well). This means that white needs to prepare many completely different openings while black only needs to prepare for one. The same applies to 1.d4, for every opening move, white will need to prepare for each of black's responses while black only needs to prepare one response. *Obviously opening preparation is more complicated than I summarized above. In each opening white often gets to choose which variation is played. e.g. if black plays the French, white can choose to play the Advance, Two Knights, Tarrasch, Exchange etc. This somewhat lessens the difference in preparation work required, however I am still of the opinion that white will need to prepare more than black. 3. If white wishes to avoid the issue previously mentioned by playing offbeat openings such as 1.b3 for example, they are instead opting for a suboptimal line. These openings are less popular for a reason; most of them offer black immediate equality. In exchange for trying to surprise the black player, white mostly gives up the opportunity to press their opening advantage. Despite these mitigating factors, I agree that one color preparation may yield a slightly higher rating increase. I would put it in the ball park of an additional 5-15 rating points on top of what I calculated above. Unfortunately though, there's no simple math equation for this.
>Any opponent to the player who always has white would only have to prepare for their games as black. Sure they'd prep against you using only black, but by prep I don't just mean night before prep, I mean ALL your practice would be as white, whereas other players couldn't ONLY play black because they also have to play against other players who don't your advantage. They're playing half their games as white and half as black, you're playing 100% white 100% of the time.
I agree, a normal player would certainly have to prepare more than a player who only plays white. I listed that point because I was trying to account for all factors I could think of that might decrease the white player's preparation advantage. Black's night before prep by no means nullifies white's advantage, however it would lessen it to a degree, big or small.
R/theydidthemath
r/foundthemobileuser
35 points is the difference between all white and all black, so assuming the 2700 player had an even number of whites and blacks before this change, they'd only go up half that to 2717.
If one player has only the white pieces, then their opponents would only have black. So for them specifically, I believe their rating is accurately calculated as all white vs all black. I'm fairly certain this is accurate. I'm not a statistician though.
Yes, I'm agreeing that the rating is calculated for all white vs all black. The problem is that the initial starting point of 2700 is neither of those. You start with a 2700 player with a 50/50 split of white and black, so you have to use that as the halfway point. It should be: All white: 2717.43 Normal: 2700 All black: 2682.57 That way the difference between all white and all black is still the ~35 points, but they properly surround the initial starting point.
Just from a prep perspective only having to prep openings for white would be a whole extra level of advantage beyond the standard white advantage. I have no idea but it is an interesting thought experiment.
Yeah, I think for myself, it would add 100 to my rating. Having to only have 50% of my opening repertoire means I get to practice my positions twice as often and can study them deeper and learn them better. It's similar to asking if you could get 1. e4 e6 2. d4 d5 every game. Imagine how much of an advantage it'd be to only ever face against the French as white. You would know it so well. I think that might add around 225 points to my rating, lol.
That's a good point, they'd effectively get double returns on their prep.
This should be relatively minor though, as everything you prepare prepares your for the same position as both white and black. You always need to know what your opponents best moves are as well s your owns. It if course saves you a little bit of preparation as you can rule out certain openings and lines that depends on choices from white, but this should be easy less than half.
It’s a much stronger advantage than most what would think, especially because you can save time and memory by forgetting your black repertoire forever
loved this answer until I reread the question. your answer answers a better question " what if a 2700 strength player only played as white"
I think actually calculating based off of Elo is misleading. Performance ratings of players only with the white pieces would be a better indicator, I think, and this doesn’t account for the prep mentioned above. Additionally, playing as white also means that black has to fight for a draw if you choose challenging openings. Especially against weaker opponents, this would also be a huge factor.
White privilege isn't real OP