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Engines really push for a win in a dead-draw middlegame position, unlike humans who may agree on a draw. Why is that happening?

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If an engine continues to play on in a drawn position, the reason is because it simply hasn't been given the heuristic to offer a draw in a dead drawn position. There are a couple of reasons a programmer may not program in such a heuristic:

1) Suppose an engine calculates that the game is a forced draw at depth 30, but to a human (or much weaker engine) the position is very complicated and not at all drawn. It wouldn't make sense to offer a draw here.

2) Making a heuristic that assesses whether a position is "dead drawn" may be non-trivial. What constitutes "dead drawn" versus an equal position? Quantifying this could be tricky.

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It is not so much that engines "push for a win in a dead drawn position." Instead, they simply continue to play the most accurate moves--because they are engines and lack the volition to do anything else by virtue of their programming. Since it can be difficult for a human to continue to find the accurate drawing moves even in an equal position, especially when time trouble is a factor, the human simply feels as if the engine is pushing for a win.

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    Engines do sometimes offer a draw in a drawn position(usually endgames). Why don't they offer draw in dead-draw middlegame positions? – Software Player Sep 7 at 1:13
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    What is a "dead-draw" position? Is the starting position a "dead-draw" opening position? Why do human players start a game of chess and then agree to a draw before it's over? – bof Sep 7 at 5:35
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The simple answer is that most engines are not programmed to offer a draw, nor to accept draw offers when made. Those that do are the rare exceptions. Furthermore, for such an engine to make/accept a draw offer, it must judge the position to be equal, which might not correspond with the human intuition for what a drawn position is.

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