The [wikipedia for even-odd rule](https://en.wikipedia.org/wiki/Even%E2%80%93odd_rule#:%7E:text=On%20a%20simple%20curve%2C%20the%20even%E2%80%93odd%20rule%20reduces%20to%20a%20decision%20algorithm%20for%20the%20point%20in%20polygon%20problem) says

> 
> On a simple curve, the even–odd rule reduces to a decision algorithm for the point in polygon problem.
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On a complex polygon, there are clearly false negatives in the holes. For example, the hole in the middle of a pentagram is within the boundary of the polygon, but any ray to the hole intersects an even number of lines.

[![Shaded pentagram](https://i.stack.imgur.com/elpKL.png)](https://i.stack.imgur.com/elpKL.png)

However, I can't think of a way to put a point outside the boundary of a complex polygon that has an odd numbered ray. Are there any false positives like this?