AbstractIn a symmetric Silverman game each of the two players chooses a number from a set S⊂(0,∞). The player with the larger number wins 1, unless the larger is at least T times as large as the other, in which case he loses v. Such games are investigated for discrete S, for T>1 and v>0. Except for v too near zero, where there is a proliferation of cases, explicit solutions are obtained. These are of finite type and, except at certain boundary cases, unique