So let's say you have 3 people walking 100m, from one wall to another.
Each move each person independently draws 3 integers, each between -10 and 5 with equal probability. You, as the coordinator, get to choose whether or not all three people accept that move. If you accept, they each walk their respective number of steps forward or backwards.
What is the optimal strategy to get all three people to the opposite wall in the minimum number of draws?