After 1.c4 c5 2.b4 cxb4 it seems White can continue in typical gambit fashion with a number of moves (3.a3, d4, ...) yet I have never seen a game with this gambit. Did anyone strong ever try this? Is there a clear refutation?
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1.c4 c5 2.b4 cxb4
According to the Database of 365Chess, the English Wing Gambit has not been tried by a grandmaster in a rated game.
Although there might not be a clear refutation, the gambit seems to be somewhat dubious. Compared with most gambits, white does not obtain a quick development. Compared with the Sicilian Wing Gambit, white acquires less control in the center. Compared with the Benko Gambit, black's central pawns are still flexible (which was already pointed out by Brian Towers).
After 1.c4 c5 2.b4, the most principled reply is to accept the gambit by 2....cxb4. Now, white has two logical continuations: 3.a3 (Benko style) and 3.d4 (trying to occupy the center). Regardless of white's third move, black can play 3....e6 and 4....d5, after which white doesn't have enough compensation.
Instead of accepting the gambit, black is also more than fine after 2....Nf6, as he will regain the pawn after 3.bxc5 e5.
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1.c4 c5 2.b4 cxb4 (2...Nf6 3.bxc5 e5) 3.d4 (3.a3 e6) e6 4.e4 d5
With your c pawn on c4 it seems pointless unless you shift the b4 pawn with a3. Otherwise black's pawn just stops you developing your b knight and you've given away a pawn for no compensation and made your position worse.
What makes this completely unlike the Benko Gambit is that Black's d pawn is still at home on d7 from where it can move to d6 to blunt the bishop on a3 if white gambits with a3. Or it can stay on d7 if black doesn't take the pawn on a3 or the a pawn is not offered on a3. If this were a reverse Benko then the d pawn would be on d4 vulnerable to attack, needing to be defended by e5 and/or Nf6.
As it is Black can just defend the b4 pawn with e6 or e5 because Qa4 would not be check.
