Let me move with the flow just one more time
I'm the one who made the video where I cut the wire. It's true that it will also work without cutting it, but if you want a real bipolar motor, you should. Someone commented on my vid suggesting there's no need to cut it because the voltage will be the same in theory on both cuts. I measured it out, and it's true when the motor is running freely. It's not true when you add some load to it (which you always do, right?). I didn't test the torque with the wire not cut, but since there was a voltage (which means loss of power) , it might be a bit less torque.
I should point out that the actual voltage in the test was not 9V , but a rechargeble 9V battery which only provides 8.2V. The motor never overheated, so you could easily add more voltage (10-12V) and get more torque.
Later tests with the same driver chip and 24V + other software (I programmed an Arduino sketch) gave +30% torque when I simulated a chopper driver (a bit like a constant current driver) , I don't have exact results from that test anymore.