\[
(A)\rightarrow(III)
\]
Eat one's words = admit that one was wrong.
\[
(B)\rightarrow(I)
\]
Fair and square = straightforward and honest.
\[
(C)\rightarrow(IV)
\]
Play with fire = do something dangerous.
\[
(D)\rightarrow(II)
\]
Poker-faced = expressionless.
Therefore,
\[
(A)-(III),\ (B)-(I),\ (C)-(IV),\ (D)-(II)
\]
\[
{\text{Option (D)}}
\]