Has there been any analysis done on if white wins if it gets a free move in the starting position (let’s say `e4`)? Then, the game continues as normal.

From a human perspective it seems playing e4 and d4 as the first two moves would give white an advantage. But is it enough to be winning?

Edit: After thinking for over 1.4 trillion nodes, Sf dev thinks the following after white plays e4 and d4. Not conclusive, but worth further investigation with such a high evaluation.

67/92 **1,495,349,364k -1.34**

e7-e6 Bf1-d3 d7-d5 Nb1-c3 Bf8-b4 e4-e5 b7-b6 h2-h4 Qd8-d7 Qd1-g4 Bb4-f8 h4-h5 Bc8-a6 Bd3xa6 Nb8xa6 a2-a3 h7-h6 b2-b4 Ng8-e7 Nc3-d1 c7-c5 c2-c3 c5-c4 Ng1-e2 Na6-c7 a3-a4 O-O-O b4-b5 f7-f6 Bc1-f4 f6-f5 Qg4-f3 g7-g5 h5xg6/ep Ne7xg6 g2-g3 Bf8-e7 Nd1-e3 Be7-g5 Rh1-h5 Rd8-g8 Ke1-d2 Ng6xf4 Ne2xf4 Qd7-e8 Rh5-h1 a7-a6 b5xa6 Nc7xa6 Kd2-e2 Bg5xf4 Qf3xf4 Kc8-b7 Rh1-h4 Na6-c7 Qf4-f3 Qe8-c6 a4-a5