Topic: How to stream a gaming system display to another TV?

I know this is an odd scenario but I want to take the display of a ps3 or ps4 or what have you that I have in my bedroom and stream it to the TV in the family living room. I have my nieces over frequently and I'd like for them to be able to play games in the living room when I'm busy without having to disconnect and lug the whole dang setup downstairs and redo it when they leave. And also there's a buzz quiz game I've wanted to play with the family but haven't been able to because they have issues climbing stairs. As little lag and cost as possible would be preferred.

@TestingTheWaters if you don't mind drilling holes in the floor/ceiling and your bedroom is above your living room then a hardware solution would be this.

Use a 1 in - 2 out HDMI switch and a 10m HDMI switch and run the cable down from your bedroom to your living room. You may want to run some USB extensions for the controller's too as the connection may be spotty at that distance. All you do is press a button on the switch to change the output device.

Alternately, for a software solution (PS4 only), you can download the PS remote play app onto a laptop and plug that into the TV. The controller's connect directly to the laptop via bluetooth. There will probably be screen lag with this solution and degradation in display quality even if both your PS4 and laptop have wired network connections.

My final solution would be just to buy an additional power lead and HDMI cable for your TV downstairs. Leave them loose and just unplug the console from your bedroom (leaving its original wires there) and bring it to your living room and plug it in. It's probably the easiest, cheapest solution that works on both PS4 and PS3 and means you only take the console down instead of unplugging all the wires upstairs.

Would a HDMI transmitter and receiver get a good result? Never been clear on how those work.

I have a Ps5 and I tried "ps remote" app on my phone and on my laptop. All I needed is to connect a controller. It worked fine.
So I guess you can e.g. download this app on your laptop(if you have one) and connect it to your TV with a cable.