Page 200 - Makino,Tsutusi.DictionaryOfIntermediateJGrammar

When degree interpretation is possible, both kekko and angai are both
acceptable, as already shown in [I]. In other words, kekk6 has to be
used with a predicate that is subject to degree interpretation, but the
degree interpretation is irrelevant to angai.
11. There is another adverb igai to 'unexpectedly,' 'to one's surprise'
which is very similar to kekk6. lgai to means that s.t. totally beyond
one's expectation occurs. Since both kekko and igai to express unex-
pectedness they are interchangeable when the predicate is subject to
degree interpretation.

Just like angai, igai to cannot be replaced by kekk6 when the predicate
is not subject to degree interpretation.
[4] a. It$+& /*%#%I hOSAIi%W~&i51h LkLQblh.
(The two might get married contrary to our expectation.)
b. bjb13Itlf-T .f --C=GiI:L.~Tb\%Qb~G?, +El Ci8B
bFDEIZL, {SVtI: /*%#$I %&fih L;kQb14?,
(That guy usually doesn't show up at a party, but today is
right before the summer break so he might come contrary
to our expectation.)
c. It9tt /*%#I, %&0fi;3'%~:~~.1~~.1&i51B L;kd@/.
h 0
(He may have arrived there earlier than us, contrary to our
expectation, you know.)

111. Another adverb wari(ai) to l ni or wariai 'a little more than one has
expected' expresses a slight gap between expectation and reality. In