1.
In the "phone stack" game, you had better not to pick up your phone, or else you'll have to pick up the check for lunch.
2.
Change had better not to shouldn't
In the "phone stack" game, you should not to pick up your phone, or else you'll have to pick up the check for lunch.
3.
Change had better not to ought not
In the "phone stack" game, you ought not to pick up your phone, or else you'll have to pick up the check for lunch.
4.
Change had better not to pick to had better not pick. (Omit "to".)
In the "phone stack" game, you had better not pick up your phone, or else you'll have to pick up the check for lunch.