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1. Does this mean that when an action is borderline EV-wise, Piosolver uses a mixed strategy?
First let me make a general point about EV. There isn't such a thing as "EV of an action" in vacuum. It only makes sense to talk about EV of an action against a given strategy of an opponent. Hands which are +EV against one strategy of the opponent might be -EV against different strategy of the opponent. Even if we play perfect equilibrium we may have -EV actions against non-equilibrium strategy of an opponent. We know however that if both sides play the equilibrium only the best (EV wise) actions are chosen by both sides and mixing only takes place when 2 actions have the same EV.
This is why solving for equilibrium is difficult. We may have perfect balance for our actions at some point (say mixing 50%-50% for actions which are both +10$/hand) but once the opponent adjusts it may not be a perfect balance anymore. What PioSOLVER displays is EV against current approximation of the opponent's strategy.
Now about mixing: we know the algorithm converges to the equilibrium and the balance for actions is closer to the equilibirum over time. It also means that differences in EVs for actions where there is mixing is smaller over time. It isn't exactly 0 because we don't reach perfect equilibrium but we are getting closer over time.
It also means that it's not that easy as taking EV of one action and taking EV of another action and determining the balance. The EV of actions changes over time as opponent's strategy gets close to equilibrium as well. We don't know what EV of an action in perfect equilibrium would be unless we actually get there.
With this in mind let me answer your specific questions:
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1. Does this mean that when an action is borderline EV-wise, Piosolver uses a mixed strategy?
No, it doesn't mean that. If Pio knows one action is better than the other it will always choose it. The problem is it's hard to determine because the EV of actions change during solving.
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For example a slighly +EV call will be sometimes a call and sometimes a fold?
No. It will be 100% call assuming it's always +EV call during solving.
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2. Can you explain how to calculate the threshold between "I do action A 100% of the time" and "I do action A x% of the time and action B the rest of the time"?
No. What the solving algorithm does is beyond human understanding. While it's very simple in principle it operates on millions of nodes and tries to find the balance. It's not something any human could hope to follow on anything but the simplest toy example. The algorithm tries to adjust in direction of a better action at every point but as that changes once the opponent does their adjusting it's not a simple process.
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if EV / action A > 1.1 * EV / action B, then do A always, but if not, then mix.
(it's an example for question #2 with Y = 10%)
something like that?
I hope it's clear from the above that it's not how that works. Mixing only takes place if actions have exactly the same EV in perfect equilibrium.