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Suppose you are playing a grandmaster with the White pieces and you are on the verge of losing the game.

The overconfident grandmaster offers you a bet: You will make two consecutive moves with White pieces. If you manage to win the game, you win the bet; otherwise, you lose. enter image description here

Will you accept his bet, or accept the loss?

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    $\begingroup$ I suspect it doesn't make a difference to the answer, but just to check: Does the first of white's two moves have to be legal in the sense of not exposing the WK to check? (I would assume so, but in some sense "the reason" why exposing yourself to check is illegal is that it would allow your K to be captured next move, and that doesn't apply when the next move is yours!) $\endgroup$
    – Gareth McCaughan ♦
    Commented Mar 26, 2022 at 14:37
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    $\begingroup$ This is not a possible position. One side cant have 9 pawns. $\endgroup$
    – Varun W.
    Commented Mar 26, 2022 at 15:25
  • $\begingroup$ @VarunW. For the sake of the puzzle, let us assume it is. $\endgroup$
    – I'm Nobody
    Commented Mar 26, 2022 at 21:38
  • $\begingroup$ @GarethMcCaughan It is not allowed to include a move that involves checking your own king. It shouldn't change the answer even if it was allowed. $\endgroup$
    – I'm Nobody
    Commented Mar 26, 2022 at 21:40

2 Answers 2

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White should

accept the bet and play N-f8-d7

because

now the BQ can't escape from the cage on the Qside, and W will promote one of the Kside pawns. I think B's most promising try at this point is to try for a pawn-avalanche breakthrough with ...Bf5; gxf5 exf5 intending f4 when one of the BPs will get through and promote. But W has his own faster breakthrough at this point with e6. Can B instead ...Bh7 hoping to stop the pawns? No, because if ever ...fxg6 then f7. After W promotes, it should be easy to clean up all the BPs and promote another WP, at which point W can just mate the caged BK, or trade off the BQ and win boringly.

In comments Daniel Mathias

observes that if immediately after f8=Q or g8=Q or h8=Q, whichever happens first, B plays ...Qxb5+, then Kxb5 leaves B stalemated if there isn't still a BP or BB able to move. So let's be a bit more concrete about the lines. 1. N-f8-d7 Bf5; 2. gxf5 exf5 doesn't have this problem; there is always a mobile BP. 1. N-f8-d7 Bh5; 2. gxh5 does potentially have this problem but W has enough spare moves with the rear h-pawn to make sure the BK is on the back rank when the front h-pawn promotes, which will therefore happen with check. 1. N-f8-d7 Bh7; 2. h3 Bg6/g8 (note: if at some point B plays Bf5 instead of Bg6 or Bg8, everything proceeds as if 1. ...Bf5); 3. h4 Bh7; 4. h5. Now there's an actual difference between ...Bg6 and ...Bg8. If 4. ...Bg6; 5. hxg6 fxg6 (note that this move is forced unless B wants to give up the Q this move) and now there's a mobile BP so no stalemate when the W f-pawn promotes. If instead 4. ...Bg8; 5. g5 Bh7; 6. g6 and now after either 6. ...fxg6; 7. f7 or 6. ...Bxg6; 7. hxg6 fxg6; 8.f7 there is at least one mobile B piece on the Kside and hence no stalemate. On the other hand, after 6. ...Bg8; 7. gxf7 Bxf7; 8.h7 the W h-pawn is promoting and the BB is still mobile. These aren't literally all the possible lines but others involve B giving up more material for no gain.

And "I'm Nobody" suggested instead

promoting to a B or N instead of a Q or R, so that B's back rank isn't attacked and there's no stalemate. That avoids having to think about stalemate, but instead requires thinking about whether B can get the Q out of her cage with Kb8-c8 in time. I think W can win either way, but don't much trust my ability to figure this out by hand :-). Of course "I'm Nobody" is the person who posted the puzzle in the first place, which may mean they've checked that in fact underpromotion is the only way to make it work...

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    $\begingroup$ I'm deleting a comment from Daniel Mathias, now addressed in my answer, not because there was anything wrong with the comment but because it potentially gives spoilers for the answer :-). $\endgroup$
    – Gareth McCaughan ♦
    Commented Mar 26, 2022 at 15:28
  • $\begingroup$ Rot13(Haqrecebzbgvba gb n ovfubc be xavtug vf gur jnl gb tb. Ab cbffvovyvgl bs fgnyrzngrf ng nyy) $\endgroup$
    – I'm Nobody
    Commented Mar 26, 2022 at 21:41
  • $\begingroup$ @I'mNobody Ah, yes, that might be better -- though it looks to me as if rot13(cebzbgvat gb n D nyfb jbexf jvgu n ovg bs pner, nf va gur yvarf V tnir). But I haven't checked with a computer and so could very easily be wrong. $\endgroup$
    – Gareth McCaughan ♦
    Commented Mar 26, 2022 at 23:47
  • $\begingroup$ Both of them work. Rot13(Lbhe fbyhgvba vf cresrpg, V jnf whfg fnlvat gung haqrecebzbgvba vf n cbffvoyr guvat gb qb vs lbh'er whfg fyvtugyl hafher nobhg gur fgnyrzngr. Zbivat gur xavtug gb sbepr gur oynpx xvat hcjneqf jbexf rvgure jnl. Gur zbfg vzcbegnag guvat nobhg guvf chmmyr vf gb svaq gur A-s8-q7 naq gur jnl gb cebprrq nsgrejneqf) $\endgroup$
    – I'm Nobody
    Commented Mar 27, 2022 at 5:59
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White should:

Take the bet.

Logic:

Move 1 You attack the bishop. Your goal is to promote a piece: enter image description here Move 2 You want a passed pawn so you capture. Your opponent can't capture your knight because you will promote then: enter image description here

In this position your opponent has only 3 good moves. King a8 or b8 and pawn g6. If your opponent moves king move your h pawn to promote. If he takes your knight promote your f pawn. Remember his queen is useless because she is trapped until the king moves away. So you have to stop the king from freeing the queen using your knight.

One more scenario.

One more thing you can block the queen and king. enter image description here In this position the only reasonable move is the move the Bishop to f5. Then move pawn h3. Most people will mutually draw because of the lack of possible winning scenarios. Remember the Bishop is trapped in 5 squares.

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    $\begingroup$ White must win the game. If the game is drawn, White loses the bet. $\endgroup$
    – Daniel Mathias
    Commented Mar 26, 2022 at 18:17
  • $\begingroup$ I think that rot13(vs J gevrf guvf gura O pna trg gur D bhg bs gur pntr ba gur Dfvqr va gvzr gb or n ahvfnapr). $\endgroup$
    – Gareth McCaughan ♦
    Commented Mar 26, 2022 at 23:46

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