actually, we are several times more productive than an ordinary ant and apparently only eat as much as a regular ant does, and if we gathered food 100% of the time we only break even.
How do ants exist?
We'd slightly more than break even:
AVG(1d20)=10.5
.5 progress per turn isn't much, but with a hundred ants that is 50 progress a sheltered-but-no-other-bonuses hive of 100 ants has.
50 progress that could be invested into infrastructure like the farm.
The basic farm gives 1 food per 5 turns
solo scavenging gives 1 Food per 10 progress
-> the basic farm is equivalent to 10 solo-scavenging progress per 5 turns
-> equivalent to 2 solo scavenging progress per turn
-> the effort for the farm pays of in 15 turns (assuming enough storage space for the farm and the produced food, so probably should also consider the cost to dig the storage)
That is ignoring that scavenging would be made up of the steps "find food" and "bring food home before source is lost" (loss of source -> something else eats it, rot takes it).
Solo scavenging means having to both find and haul it alone
In a group many ants work in paralel to find it and once something is found, many ants can then skip the "find food" step and jump to "bring food home", leading to much more efficient scavenging.