I have a Sears model number 536.88521200 snow blower that only runs with the choke
On it runs OK but not as strong.if I turn the choke off it shuts down

Is the fuel in the tank fresh or old gas? If so drain old gas out out new in. I run High test gas in all of my 2 cycle and helps keep problems from arising. Is there a shutoff for the gas and is that completely open? The fuel filter in line or in the fuel tank could also be the problem. Restricted fuel so putting choke on full cut less air to carb and balances the fuel air mixture so its rich enough for plug to fire. Pull plug and see how dirty that is or worn. So it gas.fuel filter, spark plug. Or choke adjustments. I don't know your model Is it a cycle or 4 cycle do you mix oil in gas (2 cycle)? That would help to know. If you can look for small screws on carb and see if there is one for fuel and one for air. These valve seats can get dirty,worn or vibrate in or out in time. If it's a Newer 2 cycles have just air or just a idle adjustment After you know there is good gas, plug(s) and pug wire and fuel filter It's the carb adjustments or fuel diaphragm pump in carb. To adjust carb leave on full chock so it ideals. Move an adjust meant screw and see which way it turns before it dies. Do that for both screws. Now the are closer to each other in balance. Now back out the screw on fuel side and try to take the choke off, If it sputters you need more fuel or less fuel. Adjust the two carb adjustments to get a good idle. Once you have that we need to see if the carb is to lean on air and fuel. Throttle up and see if it doesn't stall. If it does you need more fuel and a bit more air to get the carb to run richer so when you throttle up it has the more volume of both to use to run more gas/air through the carb On a side note also check your air filter so carb van breath. Hopefully your problem is just bad gas or plug, I put a lot in here to help cover it all. Happy Holidays Good Luck hope this helps and let us know