"which is to vote for Lib-dem and Green and try to deny the SNP any more than the sizeable return they will get either way"
Clearly it remains to be seen how much voters in Edinburgh (the few that turn out) will vote according to 'national' politics - i.e. vote SNP because they 'like Alex' or don't vote LibDem because of Nick Clegg/Westminster coalition.
I think there will be many attempts at tactical voting.
Normally people will put a 1 against the candidate/party they want to win, but after that whether they put 2 etc. against any other candidates is personal choice.
A lot of people will put 1-3 or 1-4 against the people they would most like to see elected - most Edinburgh wards have 3 seats, some have 4.
Some people will favour their chosen party over all others in (the few) wards where their party has 2 candidates. Others will give their 2nd vote to another party.
IF the key intention is to stop a particular candidate/party getting a seat, obviously you wouldn't even give them a 4 - but it might be the case that you 'should' vote for the people most likely to get elected even if not in 'your' party!
Complicated...
Last night the SNP's Election Broadcast suggest that you put 1, 2 and 3 against their candidates so that they could have the slogan "SNP 123".
There can't be many (any?) seats with 3 candidates in one party.
Vote don't vote - your choice.
The reality in Edinburgh is that no party can have an overall majority - none has put up 30 candidates.
So coalition(s) formal and informal are inevitable. It's very unlikely that the combined number of SNP and LibDem seats will be enough for another 4 years of the current coalition. Even if the LibDem vote holds enough to get the number of seats to add to a (likely) larger number of SNP seats for a majority I can't see them working together again.
'Big' question is will Labour get more seats than SNP - it'll be close - who would they could partner with.
Labour and Greens have voted together (as opposition parties) quite often in the current council. It's likely that there will be more Green seats than the current 3, but there is no realist chance of L+G=30.
Labour has been talking about 'using talents from other parties' if they get the most seats and try to form a minority administration, but...
Interesting times!
Of course there is some evidence that Councillors don't have much control - money and dictats from Holyrood, with officials making key decisions (or ignoring Council - elected councillors - decisions).