White: b6-g4

A complex situation. White cannot prevent Black from recycling pieces. If he prevents it on the a3-g1 line, he'll always create another possibility.
White knows that if Black plays 1...b1-f4;x (and, as things are for the moment, he must do so), he'll push the white GIPF on e4 onto f4. With that in mind, White plays 1.b6-g4 and pushes another of his GIPF-pieces into a good position (i.e. onto f5, diagram below).

The GIPF-piece on f5 doesn't look dangerous yet, but it will become a threat... with Black's help.
White created for Black a second way to recycle pieces (i.e. on the g1-g7 line). Black has the choice between 1...b1-f4;x or i5-d4;x. No matter which of the two moves he'll choose, he'll put his Gd5 in danger, because White will make the move Black didn't make! So, 1...i5-d4;x will be followed by 2.b1-f4, through which White forces Black to remove pieces either on the d1-d8 line or on the a3-g1 line. This manoeuvre costs White two pieces, but he has 2 GIPF-pieces attacking Gd5 now, and, even more important, he made that Black has no pieces left on the side of the board where he established his attack. (diagram below).

If i5-d4 and b1-f4 would have been played in reversed order, the result would have been exactly the same. It also makes no difference whether Black captures on the a3-g1 line or on the d1-d8 line. If he chooses xd2,d3,d4,d6, he would leave himself 2...a2-f6 to push his GIPF away from the dangerous d5-spot, but the white piece on f2 makes that escape impossible. So, the only thing Black can do to postpone losing his GIPF-piece (no matter which row he removed), is pushing the piece on h2 towards g2 or h3. But that postpones it just with one move: White occupies g3 with his third move and captures Black's GIPF with his fourth move. White wins with 4 moves, which is the shortest way!

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