If the seller wants to make a sale, then he or she
should tell you if said plant is self pollinating or not.
"The Green Gage is a very popular old fashioned English plum that grows well over a wide range of climates. It is a greenish-yellow, very sweet and juicy plum. The self-fertile Green Gage plum produces heavy crops that ripen in July. Due to very limited supply of Greengage Plum trees, you'll need to order from Willis Orchards now to get yours! (300-400 Chill Hours)"
"Gardening skill: Experienced
Picking season: Late Early September
Self-fertility: Not self-fertile
Pollination group: 3
List of other varieties that will pollinate Old Green Gage"
I would never plant just one fruit tree, the only way to use one trunk is to plant a tree that has four plum varieties grafted on it, these limbs will pollinate each other.
It is a fact of life that even the best self -fertility tree will do better with another tree of the same or at least blooming at the same time.
I was taught never buy a horse, car or tree from someone who does not know it history. It was the best advise, I have ever been given & with the internet one can learn many things at home.
Note: this is true for all fruiting plant.