Your explanation is not so clear... do you mean that you need to select some columns from table CFBP and from table CFBG and in case that CFBP.Pick =1 select the column CFBG.Away and in case CFBP.Pick=2 select the column CFBG.Home ? (I didn't include the WHERE to simplify).
If that is what you want then the function ELT should solve it... like
SELECT CFBP.<some column>,
ELT(CFBP.Pick, CFBG.Away, CFBG.Home) AS "something"
FROM CFBP LEFT JOIN CFBG ON CFBP.Game_ID = CFBG.ID
WHERE CFBP.User_ID = $user;
