The third half hitch should be redundant. If there is any strain on the second half hitch, it is the "round turn" that is inadequate. A common error is to pass the rope just once around (i.e. a turn of just 180 degrees). The correct round turn of 540 degrees is usually pretty secure with just one half hitch, but if you have a very slippery post and rope combination you are better off with extra turns than with extra half hitches.
My favourite is a lazyman's hitch, made in a very long mooring line when you can't be bothered finding the free end.
Double loop round turn, then two half hitches done with the rope doubled.
Beware Round Turn and Half Hitches!. Many years ago I lost a perfectly good Avon Dinghy off Foreland Point in bumpy conditions. I was asked afterwards whether it was fastened with Round Turn and Half Hitches by an "old salt"," nylon rope too?", he asked. "Yes", I replied. That's why you lost her then he said. I did some tests afterwards and discovered that continual snatching will unloosen the round turn, which in turn loosens the half turns and hey presto the knot fails! An expensive lesson!
If you want to use a RTaTHH as a semi-long tyerm knot, it is wise to seize the working end to the standing part - a couple of rounds of electrical tape would do.
I think it was in Peter Heaton that I read the conversation between the writer and the cox'n of the tender which the writer had just secured with a round turn and three hitches. As the cox'n undid the extra hitch, he pointed out that one hitch secures the know, the second is the safety measure. Any others only make it slower to cast off. All this was in the patient tones of the RN professional (seaman) instructing an amateur (officer.)
So - are your Mountaineering days so far behind that you must ask such inanities?
You of all people should know that "The strength of the knot is not increased by the number of half hitches used"
I put this in italics as it is a direct quotation from my old Cub Mistress - Akela to those of us within the circle of trust - even though Baloo would have been nearer the mark physically. I have always believed that she got it from Baden-Powell himself.
There's a short story by John Masefield, entitled Ambitious Jimmy Hicks, about the too-good-to-be-true sailor who did everything right, and who insisted on a third half hitch when securing a tackle to the yardarm in a typhoon on a Black Ball Line clipper.
The ship was sinking, the tackle was for a boat to abandon ship with, and Jimmy's last half hitch took that vital second and (as the old salt narrator tells us) , "Ker woosh, there comes a great green sea... and down they all go."
"You be warned by Jimmy Hicks, my son, and don't you be neither ambitious nor red-headed." concludes the old salt.
As the owner of my mooring found out this year. The riser was fastened to the ground chain with RT+2HH with a seizing. It seems the seizing parted and the knot untied itself. My boat took off across the creek and T-boned another boat. Ouch.