Where is the best place to put the third move when you are black?on a 13x13 board
Well, if you are playing alone I would recommend tengen, because then you can have a symetrical picture two moves in succession.
However, if you are playing against an opponent I am afraid, it quite depends on what his moves were… And also what your first moves were…
But you are right, there are not really any fuseki study materials for 13x13 (at least that I know of). One advice I heard a while ago was to realize that what would be a “small” move on 19x19 could be optimal for this smaller board (i. e. not to be too greedy), but that’s all I’ve got 
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Thanks!!!
I’ve recently been experimenting with a bit of a makeshift “mini-Chinese” style opening on 13x13.
Start with the top right 4-4, then a 3-4 stone facing white’s stone, then a low approach to White’s bottom left corner. (See Review: https://online-go.com/demo/205513)
I like it since the third move serves as both an approach and a pincer if your opponent ever tries to come near your 3-4 stone. If you manage to enclose the 3-4 corner, it gives you great influence and sizable territory.
Another option is “The Orthodox”, especially against duel 4-4 openings. The corner enclosure gives you a significant territory advantage that’s hard for white to overcome - especially since black can always do 3-3 corner invasions.
I may easily be overlooking some flaws with these openings… but it seems to work at a kyu level. It’s gotten me to #32 and counting on the site 13x13 ladder so far.
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thanks!!!