Tacitcal voting is lessened significantly under AV. Whereas FPTP is a system that means 25%+ of the electorate (those who voted for 3rd placed candidates or lower, plus those already voting tactically) are encouraged to vote not for who they want, but for who they think will keep their main opponent out. FPTP is, at it's very first point, a negative voting system.
However while AV solves this by allowing people complete freedom to vote honestly from the get go, there may be constituencies where it is in people's interest to still vote tactically. The reason for this is that in such constituencies there is a hidden mostly preferred candidate, a true "least unpopular" that more people might be able to get behind than the more honest "most popular" that AV can result in if everyone votes honestly.
But this type of tactical voting doesn't work everywhere, and it doesn't work in all situations. The kind of organisation required means that some constituencies are extremely unlikely to be able to organise it, and that's if the results lie in such a way that the party looking to "benefit" is likely to even pick up the preferences it needs to win. More importantly it is a way of voting that always gives a result that returns an MP with a mandate of approval.
Take Aberdeenshire West and Kincardine...
LD - 17,362 - 38.42%
C - 13,678 - 30.26%
SNP - 7,086 - 15.68%
Lab - 6,159 - 13.63%
BNP - 513 - 1.14%
UKIP - 397 - 0.88%
Assuming this is an honest FPTP result (as opposed to tactical where LDs have got SNP and Lab support to help beat the Conservatives), how would this translate under AV? Lab tend to split to Lib Dems (and maybe SNP) or not re-voting, as would the SNP, as such the Tories don't have much chance of winning here, and the Lib Dems have an almost guaranteed victory next time around with AV.
At no point can the Tories game the system to promote themselves to a win...what they can do though is help another party to win.
Around half of their voters would need to vote SNP (or Labour, for the lulz), moving them to second place, which would allow the remaining half of conservative voters to place their second preferences for the SNP and promote them to a victory.
Obviously the co-ordinated effort required for this is huge, some 7k voters need to be convinced to not vote for the party they want to win, with the explicit knowledge it means that they cannot get a Tory win by doing so. Then the remaining voters, at least 80-90% of them, need to give second preferences to the same party to help beat the Lib Dems.
This begs the question...would the appetite be there for it to occur? Probably not. The fact remains that a party that would honestly get second place in AV cannot use tactical voting to gain a win, but they can change the party that does win...in doing so the party that wins changes from one (LDs) with a majority share to one with a different majority share (SNP, in this example). In both cases the party that wins has a mandate of sorts, the electorate as a whole hasn't lost out.
How about another constituency, one more finely balanced perhaps? Bristol North West...
C - 19,115 - 37.97%
LD - 15,841 - 31%
Lab - 13,059 - 25.94%
UKIP - 1,175 - 2.33%
Eng Dem - 635 - 1.26%
Green - 511 - 1.02%
Here we have a situation where the Tories would probably lose under AV to the Lib Dems, who would pick up Labour votes. Can the Tories game a win here?
In theory the Tories would need to convince about 3000 of their 1st preference supporters to vote Labour. In doing so they create a situation where it is Lib Dem second preferences that matter, not Labour. We know from studies that Lib Dems split fairly evenly between both Labour and Tories, so the Tories would likely pick up the win by doing this.
Unfair? Not exactly, in this constituency obviously lives the dichotomy of Lib Dems and Tories being supported individually by over half the electorate, while Labour are not. Both Lib Dem and Tory wins are good democratic results, though the type of MP received changes from honestly most popular to least unpopular.
But even this is able to be countered. Labour could see this coming and decide they don't want a Tory win, and could put more of their votes on the table to the Lib Dems, further pushing themselves back in to third and once again elevating the Lib Dems to the win. This situation, whereby tactical voting can be cancelled out, makes it extremely dangerous for parties to engage in it. If the Tories engage in tactical voting and so do Labour then not only do the Tories lose, but they appear to not be wanted in the constituency, hampering future funding and perhaps where the Lib Dem MP takes their policy direction from. If Labour engages in it but Tories don't then they can suffer the same situation of appearing weaker than they are.
This kind of counter-tactic doesn't work with FPTP, Labour can vote tactically for the Lib Dems to help them win, but the Tories can't counter it, their only way to win is to gain more votes from someone else. In this sense at least AV provides the opportunity to strategically "block" tactical voting.
There are also constituencies that would benefit from AV without any realistic possibility of tactical voting taking place. Take Stockton South where there are only about 300 votes in it.
C - 19,577 - 38.93%
Lab - 19,245 - 38.27%
LD - 7,600 - 15%
BNP - 1,553 - 3.09%
UKIP - 1,471 - 2.93%
Ind - 536 - 1.07%
Ch P - 302 - 0.6%
For tactical voting to take place, in order to prevent Labour moving in to first on transfers, the conservatives would have to abandon a full 12000 votes, around 60% of it's first preferences...and in doing so moving itself in to distant third position and being utterly unable to win. In these constituencies, if the mood really is for a Liberal-Left MP, then the Tories are simply not going to win (nor should they), while under FPTP vote splitting allows them to do so against the wider wishes of the constituency.
What it comes down to is this...
There are a lot of if's, a lot of buts, and ultimately no guarantees for your tactical voting to make the difference you intend under AV, if it makes a difference at all.