This is probably wrong but I'll give it a go.
If you mix antidote and poison together you end up with water.
If you mix either with water nothing happens.
But if you mix one substance with the same substance nothing happens.
Therefore the effects must be like the list below.
Poison = -i (standing for infinity)
Antidote = +i (standing for infinity)
Water = 0
Taking one of my example cases (involving 2 poisons, 1 water and 2 antidotes):
-i-i = -i
-i+0 = -i
i-i = 0
0+i = i
I survived
But if you rearranged the order in which this occurred:
i+i = i
i+0 = i
i-i = -i
-i-i = -i
I would have died
Taking another circumstance (involving 3 poisons and 2 waters):
0-i = -i
-i-i = -i
-i-i = -i
0-i = -i
I died and there was nothing I could do about it.
The order sometimes matters, but not always.