Constructing an evil maze against random exploration
No dead ends near the entrance, 21,477,560 21,485,005
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Yay, 21 million. The giant horizontal segments up to row 19 are also removed, so about 20% of the entire grid is just an open space.
Also, as the &quot;real maze&quot; starts at the leftmost column, moving the entrance to the top right gives a slight bump to the score. (Thanks to @Neil)


Previous version, 20,211,703
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Yes, 20 million. It's actually good to remove some dead ends and add some open spaces near the entrance, but it stops being good as it gets sufficiently far away from it.
This is a derivation from width-3 dead end maze by removing some h-walls (it's called h-walls in the code, but it is a vertical segment in the image):

The h-walls from row 1 to row 22 (inclusive) are entirely removed.
The h-walls from row 23 to row 40 (inclusive) are reduced by half, keeping the odd indices.