How to set the game to open on the second monitor (not on the main screen)

I have two monitors for two days, one 1280x1024 and the new 1366x768, and since the graphics card allows me to use both at the same time, the larger one is set as the main one and all games are launched on it, etc., which annoys me, because I would prefer to play on the latter (better visibility on the sides of the game). Is there any program or anything that would allow you to set what runs on the second monitor? I tried UltraMon and set my hotkeye to flip, but while playing it just doesn't work.

Oops, sorry I think I gave the wrong department

Two options ... or change the order for the monitors (opposite to the current one), and another option that comes to mind (and also the question here ...) what kind of graphics card do you have and have you not looked at the available software dedicated to the card? Both NVidia and ATI have software that allows advanced modification of settings.

I have an NVidiA Ge Force 9800 GT, played with the settings, checked everything but there is no there to set exceptions where what opens. And this change of order will be tiring later.

I have not checked with games, but it works with other programs in multi-monitor mode.

Set the game to not run in fullscreen window mode only.
Move the window to the second monitor (grab the mouse by the bar on the top and move it to the 2nd screen)
Set back to fullscreen in game - it should maximize on the screen you choose.

Don't forget to set the correct resolution in game :)

Alternatively, enable screen duplication - you will have the game on both screens at once. Quick duplication / extension change you do with windows + P shortcut