Small Engines (Lawn Mowers, etc.): craftsman mower carb problem 19.5hp b@s, vaporlock, hello jeff

Question
i have a craftsman rider with a bs 19.5hp #42E707 type 2631-E1  my problem is it won't run unless choke is closed. i've taken carb apart so many times i can do it blindfoled. carb has been cleaned,blown out, float checked for leaks@sticking,tryed w/air cleaner fully on etc.this carb has fixed needles,gets plenty of gas,new gas@air filters,run w/ gascap off(no vaporlock) i'm at my wits end .any suggestions

Answer
 Hello Jeff:

 What are the Carb Air/Fuel Screw Set at. Turn them all the way in. *Do Not Jam* Then Turn them out 2 Turns. If it Runs without the Choke, then the Settings were Starving the Jets for Fuel. Is the Engine Exhausting Properly. A Clogged Muffler or Exhaust Port will Cause this Problem Too. I would Suggest a Compression Test; but the Engine is Pulling Fuel with the Choke Closed so the Valves and Rings Shouldnt be a Problem. Check the Carb. Its not Pulling Fuel through the Main Jet for Some reason. Hope this Helps. Let me know what Happens.

 Good Luck

 Respectfully

 John