# Can one theoretically prove that these moves are marginally better?

I heard that for the first move, 1. e4, 1. d4, 1. c4 and 1. Nf3 are equally good and none of them is better than others, even marginally. However, after 1. e4, both 1... e5 and 1... c5 are marginally better than 1... e6 and 1... c6; but none of 1... e5 and 1... c5 is better than the other. I am wondering if there is a way to theoretically prove this, either using an engine, or using statistics, or using opening theories.

So my question is: Can the following statement be proven?

After 1. e4, both 1... e5 and 1... c5 are marginally better than 1... e6 and 1... c6; but none of 1... e5 and 1... c5 is better than the other.

• Yes, theoretically such a statement (if true) can be proven - once you solve chess completely. Then again, after a full prove of that kind, the situations cannot be marginally better: They are either won or lost or remis – Hagen von Eitzen May 7 at 20:30
• What does it mean for a move to be "marginally better"? Other than "this move leads to a win/draw/lose", I can't think of a way to determine if a move is objectively better than other. Note that statistics can be biased. For example, if a move is popular among beginners, it will probably underperform – David May 7 at 21:12
• Even when statistics are unbiased they can be misleading. If c5 is the go-to move for Black players who want to avoid a draw, then you will see fewer draws in those lines. That might mean that e5 is intrinsically more drawish than c5, but it could also be a reflection of the fact that many Black players take greater risks in the c5 lines. – John Coleman May 8 at 15:02