Probability Theory, Marginal Openings, And The Interaction With Objective-Subjective Factors

Consider the Ponziani Opening:
1e4 e5 2Nf3 Nc6 3c3 , considered a marginal or an equal game...
I have never faced it over the board, and I only ever recall ever seeing a team mate playing it a decade ago.

Let's assume I play it as white. I consulted Lichess stats for this. If I intend playing this as white, it works out to 0.23 x 0.85 = 0.1955, say 0.2
I have a one in five chance of getting this on the board.
Let's say I am an 1e4 e5 player as black and prepared to answer Nf3 with Nc6. I work out 0.45x0.92x0.01 = 0.002
I have 1 in 500 chance of facing the Ponziani

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For every 500 games with white, I get to practice 100 Ponziani games
For every 500 games with black, I get to practice 1 Ponziani game
In an even game therefore, I argue the knower of territory is at a BIG advantage.

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But, is it that simple?
Most of us may play in leagues and have reputations to what opening we play. Of the five hundred games, it is likely that as games played, my opponents have "got wind" of me? They can prepare...

This is where I think "game theory" is a further level of consideration – and "game" - above that of the pieces and squares themselves. A player instinctively tries to adjust what he regards as "objective chess" - a la Fischer - to accommodate the "subjective factors"; and especially the element of surprise. Perhaps these are a sort of Yin and Yang of chess where most player have various mixes of these two different imperatives.

The would be "objective" player even if prepared for always has the possibility of finding the best move against his usual fayre, while the "subjective" - e.g. b6 player say - probably knows like a funded mainstream historian or environmental scientist with a picture of St Greta on the wall, he is on the wrong side of history...but still may gain short term victories: win a few more games and make enough mortgage payments to purchase his house - how long can the short-term last though?

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The “game theory” approach to chess is I believe something everyone has subconsciously been aware of. It is meta chess...

i was thinking of something like this but you materialised it PERFECTLY

this is a semi correct way to accurately measure "consistency"

there are transpositions to deal with though

semi correct coz you can get similar but not same positions with systems and stuff

this can also be used to measure how "covering" your repertoire is

like, if you say "i play scotch and exchange french as white" then this can show the percent of your games where you ACTUALLY play these openings

imo 90% is good here coz people do weird stuff online so that would skew the database (if its the players database)

but a masters database is unrealistic, so its two evils you have to choose from

good thought though!

Well there’s also the issue of some openings being “objectively” worse than others. I have never prepared against the Old Benoni a day in my life, and yet I’ve never lost to one before that I can remember. I’ve played 10 Old Benonis as White in recent memory, so assuming that my opponents all have approximately the same number of total games played as me, they play the Old Benoni ~175x more than I do, but I’m still going to slaughter them without knowing any of the theory or ideas beforehand because “objectively” I’m simply much better on move 1.

yes yes

we have to remember this is one of many subjective and objective metrics in choosing an opening

like, objective strength, win rate, draw rate, personal win rate; then for subjective there is easiness, style (do you like it), whether you have a book, familiarity...

but if there are two lines objectively and win-rately similar, both variations of the same opening (so like xx opening 5 yy variation and 5 zz variation) but one is rarer, then the rarer one might be better

and how much better it is can be quantified

also fun stats yay!

and... you can see how much you personally get to play it as well

@Ethan_Brollier

The Old Benoni is an opening I've encountered as white and not done so good, and also played as black and have done better than I should. My ELO is ~1930 and I recently beat a 21** (OTB long-play) as black with 1d4 c5. He did get a better position out of the opening, but I had been sampling Charlie Story's g6 "home brew" recently that allowed for the same g6 positions arising from 1...c5. I believe his territorial unfamiliarity aided me; not that I'm an expert on the Old Benoni, only that on this occasion my home prep trumped his handling of "classical chess".

Notwithstanding, I believe certain systems only allow a player to rise so high even if played to their full potential. I've mentioned this to a friend of mine who plays 1b3. He's around 2150, but it depends what one's ambitions are. I've said to him something like playing 1b3 is like practicing to be the best mountaineer to climb the sixth highest mountain in the world. To be fair, a very well worth ideal, but always falling a little short of the higher peaks…

And of course there are jobbing grandmasters who are happy to be able to climb the third or fourth highest peaks and play reasonably objective chess, but still not quite state of the art. Mark Hebden comes to mind. I believe Tony Miles was similar in opening repertoire consideration if not style...There is money to be made from climbing peaks other than Everest and where different equipment is needed.

@Ilampozhil25

Thanks for your thoughts as well...

Of course experience will vary from player to player, I most likely score much worse in openings that you score much better in and vice versa. 
I don’t agree about this point though. Gata Kamsky plays primarily the London System, an “objectively” worse opening than the Queen’s Gambit or Indian Game, and yet he is a GM with great results. Richard Rapport plays whatever he feels like playing, often simply inventing lines out of thin air, and yet he is a top 10 player. Many of the top 10 GMs play 1. b3 or 1. g3. There are other, more striking examples should you look long enough, and really I believe that essentially any opening which doesn’t have a refutation line can be used at any level below the immediate top to great effect and at the top level to some effect.

Was Kamsky good because of it or in spite of it though...

I don't feel I disagree with you even if you feel you disagree with me. Essentially, I'm saying practical human reasons for an opening against another known player are mediated by degrees by the extent an opening is by degrees viable...

"Levels below the immediate top" just reflects what I said about various peaks...

rapport doesnt play the same wacky line every game

he plays different wacky lines, which surprise the opponent for that game, and with his creative mind, that gives considerable winning chances