I want to know how manny tasks a demon butler does before you need to pay him again (am trying to figure out if it's cheaper to use the butler and buying logs than buying planks from players)

A suggestion, other then your question, but--this is assuming you have the levels to do it--it would save you money.

 

• Go to Castle Wars
   
  Equipt a hatchet
   
  Withdrawl a willow log, the cash to do 27 oaks (6750) and enough logs to fill you to 40kg weight (weight varries by boots of lightness, capes, etc)
   
  Use the

Balloon System to Varrock
 
Chop oak logs there to your max inventory
 
Plank all logs
 
Chop a yew log
 
Use Balloon System to return to Castle Wars

 

With this method I managed about 500 planks an hour

I know that system, but it's less speedy (altought a bit cheaper)

 

and I was planning on buying the logs.