My laptop has a slightly damage headphone jack preventing automatic detection of headphones. Other than that, the jack is fine. In Ubuntu, it is possible to force audio to play through the jack (Shows up as Headphones(Unplugged) on PulseAudio.). Using that I've not had a single problem. I was hoping there would be a similar way in Windows.
Depending on your system's configuration and drivers, it may not be clear which of the Playback Devices will send audio to the headphones. Some may actually be labeled as headphones, some may be labeled as line-out, or the headphone output may be non-obviously bundled with another device. For example, my system uses the same Playback Device to address both the headphones and the laptop speakers - it automatically switches when something's plugged into the headphone jack.
Also be aware that, if there are problems with the headphone jack on your computer, it is possible that these settings may not persist if the jack is disturbed or experiences a malfunction. If this is the case, your only solution is to get the jack fixed, or get some headphones that take input from USB.