Mix flour, salt, and cream of tartar in a large pot. Add water and oil.
Cook over medium heat until the mixture pulls away from the sides of the pan (about 5 minutes), stirring constantly.
Add vanilla extract (for smell, not taste). Mix thoroughly. Put play dough on a clean surface. When cool enough to handle, knead lightly.
Store in airtight container.
Add food coloring to the water to make colored play dough. Add sparkles during the handmixing time for sparkly play dough.