DC9 CLRED TO HOLD SW OF LGA AT GREENE INTXN IN A L-HAND PATTERN TURNS R INSTEAD.

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I WAS FLYING AS CAPT; PIC; OF A SCHEDULED PART 121 REVENUE FLT FROM RIC TO LGA ON DEC XX 1996. THIS WAS THE LAST DAY OF A 4 DAY TRIP AND WAS OUR 19TH FLT IN 4 DAYS. WE DEPARTED RIC AT AA13 AND WERE ENRTE TO LGA WHEN WE WERE GIVEN A HOLD AT YARDLEY VOR AND STAYED IN HOLDING THERE FOR APPROX 20 MINS. AT THAT POS THE HOLDING PATTERN WAS R-HAND TURNS. WE WERE THEN ALLOWED TO PROCEED WITH THE ARR AND DSNDED TO 8000 FT AND HANDED TO NEW YORK APCH CTL. WE WERE BEING VECTORED FOR THE ILS RWY 4 AT LGA WHEN WE WERE TOLD THAT THE RWY HAD CLOSED DUE TO AN RVR OF 'NIL.' WE WERE TOLD TO HOLD ON THE LOC AT 11.1 DME SW OF LGA. WE WERE ALSO TOLD L TURNS WHICH I DIDN'T HEAR OR; BECAUSE OF FATIGUE; DID NOT CONSCIOUSLY ACKNOWLEDGE (ALTHOUGH THE FO WROTE IT DOWN). WE INTERCEPTED THE LOC HOLDING COURSE AND AT 11.1 DME I STARTED A R-HAND TURN. THE APCH PLATE DOES NOT DEPICT A HOLDING PATTERN AND I HAD JUST FINISHED 20 MINS OF HOLDING IN A R-HAND PATTERN. THE CTLR CAUGHT OUR ERROR HALF WAY THROUGH MY TURN AND GAVE ME AN IMMEDIATE TURN TO THE LEFT TO RE-ENTER THE HOLDING AIRSPACE. HE EVENTUALLY GAVE ME A TURN TO A HDG OF 170 DEGS. AGAIN BECAUSE OF FATIGUE I TURNED TO A HDG OF 190 DEGS (10 DEGS TO THE WRONG SIDE OF S). I FEEL THAT THIS PROB OCCURRED FOR 2 REASONS. FIRST; THE FO WAS BUSY COORDINATING A POSSIBLE DIVERSION (OUR FUEL WAS BTWN 8000-9000 LBS) AND SO HE WAS NOT MONITORING ME WHEN I MADE MY INITIAL TURN. SECOND; THE CUMULATIVE EFFECT OF FATIGUE HAD CAUGHT UP WITH ME AND I JUST DIDN'T HEAR THE INITIAL HOLDING CLRNC CORRECTLY; PLUS I JUST FINISHED A HOLDING PATTERN WITH R-HAND TURNS. UNFORTUNATELY MY EMPLOYER SCHEDULES US ON MANY HARD TRIPS WITH LONG 12-14 HR DUTY DAYS AND UP TO 8 LEGS A DAY! THIS IS TOO TIRING FOR THE AVERAGE PERSON. NO ONE CAN REMAIN SHARP WHEN FOLLOWING THESE HVY SCHEDULES. MANY OF MY FELLOW PLTS ARE COMPLAINING ABOUT THESE TRIPS BUT NOTHING IS BEING DONE TO CORRECT THE SIT. I WOULD HOPE THAT SOME ONE FROM NASA WOULD CONTACT ME DIRECTLY SO THAT THIS MATTER CAN BE ADDRESSED. IT IS ONLY A MATTER OF TIME BEFORE FATIGUE FACTORS CAUSE THIS CARRIER ANOTHER MAJOR ACCIDENT. FORTUNATELY; THIS MISTAKE WAS CAUGHT BY THE CTLR QUICKLY AND WE WERE NEVER IN SERIOUS DIFFICULTY. WHO KNOWS WHAT MAY HAPPEN NEXT TIME.