Should a program window remember its position on the screen?

I am currently making a game that has the option for being run in windowed mode rather than fullscreen, and while developing, I have come across this issue which is fairly specific to my setup:

When I press run from my code window, the game opens on my other monitor, which is not what I want, so I implemented a feature that stores the current position, and starts it again here next time.

However this got me wondering, is this good practice from a UX point of view? Do users expect the window to open in the same position, even across multiple monitors?

Another issue I thought of is if the user changes their screen configuration and the game opens somewhere they can no longer get to, but I may be overthinking it at this point.