Eventhough there is a grammatical difference between ´herhalde´ and ´her halde´, you can assume that when you see it written (in an informal place), they all wanted to say ´herhalde=probably´, because many people dont know whether to write them apart or together.

If I were you Id forget about the difference and all understand them as ´probably´, because that is how it is used 99.9% of the time

Your friends are close enough...

Ohhh , I didn´t see all this before,

 Ok thanks to everyone who made it clear. I see that yes there is in fact a difference as I had thought, but it is not used often and basically I should not even bother with it and just accept herhalde    Cheers Yilgun, deli- kizin and Alphaf I  appreciate it .

 Excellent summary

I am not an expert yet but student in uni studying Turkish language and really surprised to see an expert give such an information. 

There must be difference between them.

Yes, hâl (not hal) is originally Arabic. (btw I don´t understand why you needed to mention it´s a loanword) 

Her is Turkish? Do you think it is originally Turkish?

Yes, herhâlde means probably.

But her hâlde never means probably.

You can find it in her hâlükârda (her hâlde + kârda) 

What does her hâlükârda  mean? probably or exactly?

her halde and herhalde is different but because you can not differenciate in the spoken language, people use her halükarda for her halde to mean that.  But Deli kýzýn is right too, as some people don´t know if it is written together or separate.. so you have to look at the context to understand what is meant.

The management of ETT (Expert Turkish Tutors) wishes to offer a public apology over this unfortunate incident.

Will Turkish Teacher be reducing his tuition charges now??  

herhalde = her halde = heralde(this is the most common one in spoken Turkish

1) People do not care about the spelling of this word. her halde or herhalde both are acceptable.

This word usually means probably

Heralde randevuyu unuttu = he must have forgotten about the appointment(logical conclusion)

sometimes it means exactly:

Example: Ben partiye gelmek zorunda mýyým? (Do I have to come/go to the party?)

HERALDE geleceksin . (=OF COURSE you do)

about reducing the charge:

Lady in Red: Heralde þaka yaptýn

My advice: never take lessons from a Turkish teacher who thinks it is totally acceptable to write ´heralde´ when teaching. 

He will be paying for any chance of tutoring he may get.