I have an older craftsman snow blower 10 hp. It starts ok with full choke, runs ok half choke, backfires with no choke-run position.

It's too lean; not enough fuel mixed with the air. Look for the main mixture screw--it should be a large screw with a spring under it on the carburetor. Run the engine until it's warm.

With the engine running, turn the screw outward (lefty-loosey) about 1/8 turn slowly and see if it improves. Slowly turn the screw back and forth until it runs best with the choke completely off. Then set it 1/8 turn richer (turn screw outward 1/8 turn) than the best position.

Reason for doing this: Conditions change, even the barometric pressure. Small engines run okay if they are a little rich but not if they are a little lean.

Run it at half choke until hot then should be okay