How statistically likely is it to play a perfect game?

Was close to 2100 rapid, tilted all the way back to 1900 so I am not playing my best. But some of these games I feel like my opponent literally plays perfectly. I know variance is a thing, so you will have some good games and bad, I have also had games that were ~95% accurate according to game analysis. Is there a formula or distribution curve you can plot based on your elo to figure out how likely you are to play a perfect game? Am I not considering other other variables or factors that would prevent people from actually having perfect games? I do have a science background but I still have a lot to learn about statistics, I am interested how people here would approach this problem.


Having these thoughts because of my most recent loss, I don't want to jump the gun and say everyone is cheating (a la Kramnik) because that really changes how I play. I usually like playing sharp and complicated positions (I like attacking and gambits), but when I think my opponent is cheating I start playing defensive and try to survive by running out the clock. The latter is not how I like to play and I want to avoid that mindset and focus on what I am good at, since most of time my opponent isn't cheating (I am just being outplayed for a couple moves) and I am playing worse for no reason. If I can rationalize some of these losses it would give me some peace of mind and play how I want to play.


The loss in question:

And the chess.com analysis:

i got to 2092 which is basically one win away from 2100, then i went all the way to 1898 lol. At some point I started to think every one was cheating because I was very confident about my play being around 2050. Apparently chess.com said there was only one fair play violation in all those games. I think a lot more cheated, but also some of them played memorised lines, I say go get some rest and come back later

You are probably right man, thanks

From a theoretical point of view it is possible, but it is uncommon even for GMs, especially when the games are long, as a general rule, especially in high elos, any game with a move count lower than 25 is mainly based on purely theoretical basis, and therefore almost perfect, openings.

Damn, first 25 moves is considered theory? Maybe that is the case for computers but I doubt humans are capable of memorizing that deep unless you know what your opponent plays before hand. Even in GM games I am pretty sure they leave known territory much earlier than 25 moves in. I guess I have to learn theory now if I want to make progress in Rapid.

I have played a perfect game more then once. Since people I have played have fallen into known opening checkmate traps.

Remember chess is played by two players. So it is much easier to play a perfect game against Noobs.

You really shouldnt put that much weight on the chess.com post game analysis of the perfection of the moves played. Its extremely inaccurate and varies widely. Ive literally seen the percentage accuracy for a game change based on who reviews it.

its there for a general idea of what happened in the game, not a full depth analysis. if you really want to see whats going on get a very strong chess program or something to analyse every move and see how close it is to its number 1 choice in every position. 
Also the game that you showed for example, is only 22 moves long. In games under 25 moves its very easy to get 95%+ games because the first 10 moves is usually book, especially as you get higher and higher in ELO, so you're really only playing about 12 moves on your own and at 2000+ rating on chess.com, players are strong enough to play those 12 moves quite well. 

I don't doubt you're running into some cheaters, but its probably not as much as you think, its just the effect of versing opponents who are very strong, and when your games end in under 25 moves, the chance is high for the percentage to be something ridiculous like 99% or 100%.