"..The problem arises in positions like Dia. 3-7. Only neutral points are left, the number of neutral points is even, the black group at the bottom has lost its outside liberties, and the safety of this group is uncertain. Suppose it is Black's turn. Even if Black plays 'a' to remove the danger, he can still get one of the two neutral points. Under area rules, that is, he can make a free reinforcing move at 'a.' He does not need to verify whether it is actually necessary..." -- Section 3.5 "The disadvantage of Area Rules", On the Rules of Go, Ikeda Toshio
After (1) White assumes black is skilled enough to avert the invasion and occupies the last dame.
Territory+Prisoners Score W 30 - B 31 Area Score W 60 - B 61
Ikeda's Rule Black passes first W 60 - B 61
Button Go Black passes first +0.5 Black W 60 - B 61.5
Black unnecessarily reinforces its territory.
Territory+Prisoners Score W 30 - B 30
Area Score W 60 - B 61
Ikeda's Rule White passes first +1 white W 61 - B 61
Button Go White passes first +0.5 white W 60.5 - B 61
Obviously it loses, yet by keeping sente it prevents black from grabbing the last dame.
Territory+Prisoners Score W 35 - B 36
Area Score W 60 - B 61
Ikeda's Rule Black passes first W 60 - B 61
Button Go Black passes first +0.5 Black W 60 - B 61.5
White's IQ is getting worse, this time it not only invades but also loses sente by performing Baka no Itte. It is punished by losing both dame.
Territory+Prisoners Score W 30 - B 32
Area Score W 59 - B 62
Ikeda's Rule White passes first +1 white W 60 - B 62
Button Go White passes first +0.5 white W 59.5 - B 62