Will double strike trigger cipher twice?

Question

Say I am playing with a creature that has double strike (e.g. Two-Headed Cerberus), and I cipher Hidden Strings to it. This allows me to tap/untap up to 2 target permanents whenever the creature deals combat damage to a player.

If my creature then attacked a player and wasn't blocked, and he took the double strike damage, would I then be able to tap/untap 2 target permanents twice? In effect tap/untap 4 target permanents?

I am asking this because my friends and I play with a few different ciphers and have had arguments about this a few times.

Answer 1

Cipher triggers whenever the encoded creature deals combat damage to a player. An unblocked creature with double strike will deal combat damage to the player twice; once in the "first strike" combat damage step, and again in the regular combat damage step. As a result, if an encoded creature with double strike is not blocked, you will be able to cast the encoded card twice.