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Ke5 is not forced, QxR is better. d3+ after QxR shown in analysis is not the best move. d3+ leads to draw while Nd6+ Kd4 NxQ KxN leads to queen+2pawns vs queen+pawn endgame (theoretical win for white).
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I checked your analysis. It is only good for white whereas 'we' are playing as black. So there is no win for black as suggested by the TT. :)
Ouch. Its black to play actually.
Nd6+ Kd4 NxQ KxN Ke1 and white promotes a tempo faster.
That's why d3+ proposed in the analysis as the move that beats QxR is bad. And white promoting a queen tempo faster still gives more chances to black than playing against a queen + king while having nothing in the actual TT ending.
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