This type of problem, where you need to keep track of key/value pairs (county/map #), is best organized in a dictionary, where for each key (county) you increment the value (map #). See: 5. Data Structures — Python 2.7.15 documentation
Here's an example, not using the field calculator (sorry). In the field calculator, counter_dict should be global, and instead of appending to output_list, you'd return the value counter_dict[county]:
county_list =
['Marin',
'Napa',
'Napa',
'Marin',
'Marin',
'Napa',
'Marin',
'Marin',
'Napa',
'Napa',
'Napa',
'Napa',
'Marin',
'Napa',
'Marin',
'Napa',
'Marin',
'Marin',
'Napa',
'Marin']
counter_dict = {}
output_list = []
for county in county_list:
counter_dict[county] = counter_dict.get(county, 0) + 1
output_list.append([county, counter_dict[county]])
output_list =
[['Marin', 1],
['Napa', 1],
['Napa', 2],
['Marin', 2],
['Marin', 3],
['Napa', 3],
['Marin', 4],
['Marin', 5],
['Napa', 4],
['Napa', 5],
['Napa', 6],
['Napa', 7],
['Marin', 6],
['Napa', 8],
['Marin', 7],
['Napa', 9],
['Marin', 8],
['Marin', 9],
['Napa', 10],
['Marin', 10]]