If you actually believe democrats and republicans are the same then yes, you “win”.

Why do you types insist on pretending that you're more obtuse than a caveman? Do you pretend not to understand arguments because you know you cannot make it in a straightforward discussion ?

Voting third party would be the correct choice.

If you put faith in the electoral system, yes. Glas we agree.

The existence of the phrase “strategic voting” proves a vote is not a blind show of support.

As did your statement that voted despite certain policies. As I've detailed, that doesn't matter. The existence of the catholic church isnt proof of god.

Adhering to the politicians’ lie that a vote means full support isn’t logically consistent with how people make choices in the voting booth.

So you admit politicians claim legitimacy from votes. Neat. What isn't logical is then continuing to support them, when that is what they do.
Again, the rest of your spiel is pointless. What matters is the practical reality of what a vote is and does, which you've admitted yourself is a sign that you support that politician. You can say whatever you want to make yourself feel good about voting for genociding police-state fascists, the police state fascists only care that you vote for them, not why.