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If I give the solver the flop , turn and specific river. It solves very fast but are the flop actions solved according to the expected turn and river ? Or is it still independent until I get to the next card?
If you give it a flop, turn and river it only solves the river.
If you give it a flop an turn it solves the turn (which includes solution on all possible rivers).
If you give it a flop only then it solves the flop (which includes all possible turns and rivers).
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For example i7-8700K vs my i7-4700HQ:
Let's see:
1)i7-8700k has 6 cores @ 3.7Ghz which gives it 6 * 3.7 = 22.2 score
2)4700HQ has 4 cors @ 2.4Ghz which gives it 9.6 score
22.2 / 9.6 = 2.3125 whcih means 1) is going to be approximately x2.3125 faster. Approximately because those are CPUs from different generations although it's not worth that much as per core progress is very slow these days between generations.
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Anyway to only solve for the flop?
You can solve a flop tree by giving the solver 3 cards and clicking go. It will solve all turns and rivers as well because those are necessary to have a flop solution, otherwise you couldn't possibly know EVs of actions on the flop.
I invite you to watch a quick start video, it explains fundamental functionality of the solver. It's here:
https://www.youtube.com/watch?v=JqGQoQKbCB8
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Or for example i7-8700k vs i5-8600k.
12 vs 6 threads!!
Both CPUs have 6 physical cores. One supports 12 hardware threads and one only 6. This is called hyperthreading. Hyperthreading is worth around 15% speed-up in Pio case (this is not universal across all programs, it depends on the implementation). Hyperthreading is very useful if you want to run VMs (for example Windows on a Mac via Parallels so you can run Pio inside). It will also make computer run smoother if you need to run Pio and do other things at the same time and still retain decent performance.