The gain of the screen is a measure of the light reflected back at the viewer. It isn't really to do with ambient light, but is sometimes used to compensate for ambient light once the prime objective of gain - the brightness of the picture - has been taken care of.
The gain of the screen you use depends on many factors - the projector's black level capability, the relectivity of the walls and ceiling, the required width of viewing cone (only really applicable for high gain screens), any ambient/stray light and so on... But the prime factors are the size of the screen and the brightness of the projector.
Here's a
useful article on screen gains.
You haven't mentioned screen size, but I would guess you'd go for a 96" diagonal 16:9 screen (83" wide). This will give you just over three feet each side to mount your front speakers and a seating distance of about 12 feet. The throw for a Z3 would then be about 10-12 feet.
Although a Z3 is rated at 800 lumens, probably after calibration and a few hundred hours bulb use you'd probably be looking at 600 - 700 lumens depending on how optimistic you are.
Now, a 96" diagonal screen is 84x47" = 3948 square inches, which (div by 144) is just over 27 square feet.
And foot-Lamberts = (projector lumens x screen gain) / screen area
So with a unity gain screen, (650 lumens * 1.0) / 27 square feet = 24 foot-Lamberts.
I think the American Society of Motion Picture and Television Engineers (SMPTE) recommend 16 ftL as a brightness in a blacked out movie theatre. Some enthusiasts adhere to this to create a true 'cinema experience' - others like their picture a bit brighter and punchier and aim at 20 ftL or even a bit more if they intend to watch sports as well as movies.
So with 24 ftL you should have a pretty bright picture. If you wish, you could choose to reduce the brightness by going for a 0.9 gain or 0.8 gain screen (which would give you 21.6 ftL or 19.2 ftL respectively) and still be around the 20ftL mark.
Going for a 0.9 or 0.8 gain screen would help improve blacks (because you're using LCD technology which isn't known for giving as good absolute black levels as DLP) and help darken any backwash from your light walls and ceiling.
A different approach would be to go with a bigger screen, which will dim the picture. For instance, a 108" diagonal would be 34.5 square feet and give you 18.8 ftL on a unity gain screen - probably as dim as you would want to go.
Now, I've made an assumption about your screen size and a guess

about the available projector brightness after a period of use. You can eliminate one of these variables by deciding your actual value of screen size depending on your seating distance, speaker placement and projector placement.
Hopefully I've shown you some of the factors involved in choosing screen gain:
- choose your screen size
- calculate how much brightness you've got to play with (depending on how bright a picture you'd like)
- decide if you want to lower the projector black level or compensate for ambient light or backwash in the room
Remember that backwash from the room can always be reduced by painting the room (and ceiling) in a darker colour - even going from white to a wheat colour can make a difference - so if you do decide you want more ANSI contrast this is something you can do later.
A practical thing you can do is when you have a projector demo, ask what size the screen is and what gain it is. Check if the projector is in an economy or high brightness mode. Then decide if you like the brightness. When you get back home you can plug the figures into the equation to work out the foot-Lamberts and then you'll have a reference of what 20 ftL, or 25ftL (or whatever it turned out to be) actually looks like.
Another useful tip is to play some of these 'what if' scenarios out on the projectorcentral.com calculator. Here's a link to the calculator for the Z3
calculator for the Z3
This should give you an idea of the basic principles you can take into account when making a choice.
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