An important factor in a game of imperfect information is ______.

A．they didn't think the man was a thief
B．the man was old and very rich
C．they were not sure whether the man was the thief they wanted
D．they doubted that the man was responsible for a number of recent robberies

A．Though the man had some trouble, he got the necklace without paying cash.
B．Nobody noticed the man take the necklace with him.
C．The manager never thought an old man would be a thief.
D．The thief always stole things in famous jewelry shops.