Three strikes as part of a suite of reduction measures is very effective, but not on its own. This has been shown in the 20+ states in the United States that have implemented similar laws. Three strikes is mainly about "incapacitation" of repeat serious violent offenders, through lengthy terms of imprisonment for repeat offences. It is also about providing justice to victims, who typically have their lives significantly harmed, impaired and sometimes completely destroyed by repeat violent offenders.
I would like to think this would help criminals learn a lesson and they would think twice about performing a second crime. Hopefully it would deter others from deciding to commit a crime if they know that they only have three chances before they get put away in prison. Although, this may make for higher population in the prison system, for those that choose not to learn from their mistakes.
Felonies should be much more strict for repeat offenders. A three-strikes rule would reduce crime in several aspects by keeping dangerous criminals off the street and prevent harm from coming to others. The caveat is that lesser crimes must be let go of. The justice system needs to focus on sexual predators, murderers and abusers and not on marijuana.
By the time someone has committed multiple crimes, the reasons for their behavior have very little to do with simply avoiding another punishment. It is true that the possibility of a life sentence or other serious penalty does deter some potential criminals, but I imagine that would happen to deter a first offense, not a third.
Tougher sentences such as 3 strikes won't reduce crime. For starters, it is optional, so many felons who don't plan to change their ways will opt out of it. Second, it will just make criminals go to great lengths to cover up their crimes so that they don't get a strike. Even in the event that it did reduce crime, I believe it would be so insignificant and do more economic damage than it would provide societal benefits