Not only does cream of tartar help provide elasticity to play dough, but it also acts as a preservative. For that reason, I don't recommend omitting the cream of tartar completely, as it will shorten your play dough's lifespan. If you don't have any cream of tartar, you can try replacing it with lemon juice or vinegar. (I prefer lemon juice because it has a milder scent.) For every 1 teaspoon of cream of tartar, add 1.5 teaspoons of lemon juice or vinegar along with the liquid ingredients.