White is much better off in 3 check, if not outright winning, by move 0. 1.e3 is interesting, preparing developing moves while preventing any attacks/checks on f2 from the a7-g1 diagonal. Against 1.e3, I usually play 1...Nc6, developing a piece with the idea of preventing Bb5 from being a check after ...d7-d5. In addition to 1...Nc6 preparing ...d7-d5, it also helps prepare ...e7-e5, as 1...e5 immediately gives white 2.Bc4 threatening Bxf7+, where 2...d5? loses to 3.Bb5+, so in response black must defend f7 awkwardly with 2...Qe7/Qf6 or 2...Nh6.
White can also play 1.e4, which gives white more space and central control, and the e4 pawn can even be a significant attacking unit, threatening e4-e5 to chase away a Nf6. There are even ideas similar to: 1.e4 Nf6 2.e5 Nd5?? 3.e6! when black cannot escape a check, as white threatens 4.exf7+, and 3...dxe6 allows 4.Bb5+, and 3...fxe6 loses to 4.Qh5+ g6 5.Qxg6! hxg6 6.Bd3 1-0. Although 1.e4 doesn't keep f2 defended from the a7-g1 diagonal like 1.e3 does, white can work around this. For instance, 1.e4 e6 2.Nc3 Bc5? 3.d4 and white is safe.
Most respond to 1.e4 with French Defense or Sicilian Defense, although I like Alekhine's Defense (it can transpose into French Defense though): 1.e4 Nf6 2.e5 e6! (2...Nd5 loses to 3.e6! as seen in the last paragraph) 3.exf6 Bc5 4.Qf3 Nc6 5.fxg7 Rg8 gives black some wild attacking chances, in my opinion not unreasonable compared to black's inherent disadvantage at move 0.
I think the white has more chance to win in 3 check games because it starts the game.but it's interesting to me that what do you start it? I usually play e3