Usually protect only works one turn but would fail if you tried to use it the second turn.But in some occasional cases protect works two times in a row.What is the chance of that happening?
From Gens 2-5, the chance of Protect succeeding halves every turn, so the chance of a second Protect succeeding is 50%
From Gen 6 onwards, the chance of Protect succeeding thirds every turn, so the chance would be 33%.
Source (Bulbapedia)
Prevents any move that targets the user from taking effect for the turn it is used in. Does not prevent passive damage such as sandstorm or poison. This attack has a 1/X chance of being successful, where X starts at 1 and doubles each time this move is successfully used. X resets to 1 if this attack fails or if the user's last used move is not Detect, Endure, Protect, Quick Guard, or Wide Guard. If X is 256 or more, this move has a 1/(2^32) chance of being successful. Fails if the user moves last this turn. This move has a priority of +4.
~Smogon
Let's math:
Chance of 1st time: 100% Chance of 2nd time: 50%
4/4 x 2/4 = 2/4
