<!-- English rule, 2017-11-26 -->
<rule id="WITS_AND_NOT_WIT" name="Wits and not wit">
<pattern>
<token>wit</token>
<token>'</token>
<token>s</token>
</pattern>
<message>Perhaps you meant to write: "wits'"?</message>
<example correction=''>He was at his <marker>wit's</marker> end</example>
<example>He was at his wits' end</example>
</rule>
This one is a widespread error and can be seen in many books and articles. The phrase should be: to be at one’s wits’ end as wits is defined as knowledge and this is what is being indicated here.
A. even a so called ‘Indie ploy’ is performed before one is at one’s wits’ end.
So it’s more likely to refer to one’s ability to think than to one’s knowledge.
B. according to Wiktionary both wit’s and wits’ are valid, but the former is the American notation and the latter is the British notation.
I was referring to the origin of the phrase, which can be traced back to the King James Bible and there the meaning of wits is knowledge. OED only mentions the plural in this context; however, Webster indeed says it is usually in the plural, which means wit is also correct in the US as you mentioned. This is the same as moot which drove me crazy when I heard it used in American movies and series, before I discovered that it has somehow taken on a different meaning in the US. Thanks for pointing this out!