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lets say i solve a postflop tree @ 3bb/100.
How does this exploitability spreads through the tree?
It's an interesting question which I didn't investigate much. Most of the exploitability is on the rivers (did experiments where I resolved rivers to very good accuracy leaving flop/turn intact and was often able to get very big improvement). To answer this question reliably though you would need to do a lot of research. It's likely quite dependent on the exact algorithm used as well.
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1) do we have the same 3bb exploit in every decision node,
No. One may hope relative exploitability (in % of the pot) is similar throughout the tree but there is no guarantee for that even.
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2) does it spreads accros all nodes so that in any particular node we have a fraction of the total 3bb?
The concept of "exploitability in node" need a clear definition. You may calculate sum of mistakes in a node but then sum of mistakes across the whole tree is bigger (and it's guaranteed to not be less than) exploitability. Maybe if you can tell me why you want the answer to those questions I would be able to give you some useful insight.
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3) if 2 is true then its a linear spread or as we progress through the tree, the fraction increases/decreases?
There are no guarantees what so over about how exploitability is spread across the tree.
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One difference between pro & basic is that the pro is "fully scriptable" what does this exactly mean? what commands are exclusive for the pro version? I'd guess that show_strategy, and things like this are available for the basic version as well?
Commands which make it possible to run scripts are disabled so for example "wait_for_solver" one;. You can still get all the functionality though as evident by the same viewer working with basic/pro/edge version (and the viewer uses the very same interface which is exposed to you and isn't a privileged program in any way).