How ratings relate to statistical chances of winning a game?

@Physicist1993 You are still wrong because of RDs

@jimj12 Clearly there has been a miscommunication as if you understood exactly what I meant then you wouldn't be disagreeing with it simply because you cannot reasonably disagree with a correct statement. With this in mind I'll explain what I meant in a different way at exactly 20:49 02/03/2017 GMT your classical rating was exactly 1920.74, if you were to play a game against yourself then this could be used as an analogue of 2 players with exactly the same rating(skill level) playing against each other. I hope you agree that if you were to play a game against yourself then the chances of the white side winning are exactly the same as the chances of the Black side winning. This is what I meant before when I was saying that 2 players with an equal rating should be evenly matched and have equal chances of winning the game (provided that this is their true ratings and these ratings accurately represent their strengths as chess players).

its very simple; take the points the lower player would gain if he wins and divide them by the points the higher player would gain if he wins, for example lower player wins +14 points, higher player wins +2 points. 14:2= 7 so the likelihood of the lower player winning is 7 times less 1/7 or 14.3%.

@Physicist1993 I assumed you knew what RD meant, my mistake. If you read the paper on Glicko-2 linked earlier, you will see that this system uses rating deviation (RD) in addition to a point estimate. This basically means that your rating is not a single number like 1920.74, but a 95% (or some other number) confidence interval e.g. 1920.74 +/- 77.32 i.e. the system is 95% sure my true rating lies between 1843.42 and 1998.06. So you can see why your statement was wrong - you don't know if two people are rated equally in the first place, so you definitely can't expect a 50-50 game split between them

P.S. your statement "then the chances of the white side winning are exactly the same as the chances of the Black side winning" is also wrong as white has an edge

@jimj12 I understand what you are saying with each players rating number being expressed as essentially being between upper and lower bounds, but what I was saying was lets assume that the 2 players did have the exact same rating and when I say this I don't mean 2 players with the same rating number and vastly different RD's, I mean 2 players of precisely equal playing strength at chess, the example I gave was if you were to play a game against yourself, this would be an example of a game between 2 players with exactly the same playing strength. Such a game would give an equal chance of winning for either side, (White/Black). On this topic in response to what you said, yes it is widely acknowledged in chess that the white side has an advantage, However!!! It is also widely acknowledged that this advantage is in no way a decisive advantage which would thereby make the actual game pointless because the white side would always win. In fact, many strong openings tend to lead to positions which allow the Black side to equalise (reduce whites initial advantage to effectively zero) after maybe 10 moves or less, with this important fact in mind I do not believe it is wrong to suggest that a game taking place between 2 players of equal strength would be a 50/50 as to who is going to win.

@Physicist1993 That's not what you said in your first post at all

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@jimj12 In what way? If 2 players have precisely the same skill level and they play on the same site with the same rating system then they will end up at the same rating and this means when they play there will be a 50/50 chance of either player wining and they will have the same rating exactly as I said in the original post. That's the whole point of a rating system it separates players based on skill level using numbers to represent their skill levels.

@Physicist1993 What you said first was, and I quote, "so if 2 players are rated 1500 each then I would expect it to be a 50/50 they should be evenly matched"

I pointed out that this was wrong and explained why

@jimj12 That's fair, but on the other hand if the 2 players are truly equal in strength and have the same rating then they are evenly matched and it is a 50/50.