Rule sets / OBR / Illegal Feint Balk
Illegal Feint Balk
It varies by rule set but feints to first base are prohibited and a feint to third base might be as well.
If there is a runner, or runners, it is a balk when the pitcher, while touching his plate, feints a throw to first or third base and fails to complete the throw.
MLB Umpire Development Manual Authoritative interpretation
The pitcher, while in contact with the rubber, may not fake a throw to first or third base. The pitcher is still allowed to fake a throw to second base while in contact with the rubber provided that he makes a legal step towards second. The pitcher, of course, may properly disengage the rubber and then fake to any base. The pitcher is considered an infielder after he properly disengages the rubber.
Note that a pitcher, when faking a throw to second base, is not required to have arm motion in the fake, although a legal step is required.
Video examples
Right-handed pitcher Dellin Betances feints a throw to first base.
Right-handed pitcher Yordano Ventura feints a throw to first base.
Right-handed pitcher Pedro Villarreal feints a throw to first base.
Right-handed pitcher Ryan Madson feints a throw to third base.
Right-handed pitcher James Shields feints a throw to third base.
Right-handed pitcher Josh Fields feints a throw to third base.
Right-handed pitcher Dylan Covey feints a throw to third base.
Pitcher feints a throw to first base.