Question on PRF security



Let F_x be a PRF with key x

Define the following game
Challenger selects a bit c, key k and a random oracle R
A selects n distinct messages m_i and makes queries of type (m_i, b_i)
where b_i is a bit.
If b_i = 0, the oracle returns F_k(m_i). If b_i=1, it returns G(m_i).

where, G(m) := F_k(m) if c =0 else G(m) := R(m)

At the end of the game A guess bit c

Is this different from a standard PRF game, where b_i is always forced
to be 1?

--Thanks

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