Joining the party late here, but I agree with Andrew. The wording for the Ps combat outcomes are:-
"[less than result]
Destroyed by Kn, Cv or Cm(S) or (O) in good going"
{This to me means if the mounted are in good going they quick-kill the Ps}
and
"[doubled result]
Flee if in close combat against mounted troops whilst in rough or difficult going."
{This to me means if the Ps are in difficult going}.
I realise that there's a very odd situation here, where the Ps are in RGo or DGo and the mounted in GGo, whereby if the Ps are just beaten they die, but if they are properly doubled they flee...!
Tim Child