1950s Brunswick Trophy Snooker cue.
I don't have any insight on value of these Brunswick Trophy snooker cues. Condition is key though.
One of the big condition factors in determining how much these older Brunswick cues are worth is the decal and how good a shape it's in. Yours is obviously damaged and that would mean collectors wouldn't likely be willing to pay full value.
Folks do collect these, so you might be able to get $200-$400 depending on condition, and how long you want to wait for the right buyer to come along.
But again, I could be way off on that. Some other folks here might have a better handle on the value of a Brunswick Trophy cue of this age and condition.
Wish you had posted photos of the whole cue so that we can properly assess it's condition. Condition is just about everything in pricing these older cues.
Unfortunately the Brunswick archives of that era are missing a lot of material, and as such, this is the only printed reference of the cue I could find. It's in an Volume 2, Number 2 (October 1950 edition) of "The Cue" magazine (published by Brunswick-Balke-Collender Co.'s Toronto, Ontario, Canada head office).
Brunswick Trophy Snooker Cue
Has a butt of selected ebony; the shaft is made of straight-grained white maple; a brass socket is set into the shaft to accommodate the brass screw that is set into the butt; the screw locking arrangement is sheileded with a ferrule of selected white fibre, attractively set between two bands of black fibre for greater strength and beauty. The length of the cue is 5'. It has a selected white fibre point and carries a high-grade French cue tip. Weighs 17 to 22 oz. Cue tip sizes are 11, 12 MM.
I've also been told (or read somewhere) that they were made in Toronto, Ontario as well, and possibly that some of them were made by the now-defunct Dufferin cue. Have not been able to verify this with 100% certainty though.
Here are two other examples of these Brunswick Trohpy snooker cues from my records: