Speaking from tractor tyre experiance, 50% is an acceptable limit if you want to maintain an effective level of off road traction.
There is not point at which they become totally useless, its just the maximum thrust they can generate will become less and less.
From off road experiance, my BFG muds varry, the outer lugs on 2 of them are quite worn (approx 25 to 40% ish) and they still perform better than nearly new ATs though it does depend on the terrain. On hard ground worn tyres should still work OK as you don't need the lug depth that you would for muddy ground.
On wet roads tyres worn to less than 3mm can seriously reduce there preformance, its not just your off road performance you need to bear in mind.
