I think there is confusion here. The frequencies do matter in aggregate but the individual EVs of hands aren't dependent on the frequencies they are bet or checked.

The fact that either option is chosen at all means that at some point the solver found that within the "blinds resolution" both options yield identical EV and then eventually settled on the frequencies for the aggregate line.

Also there is a lot of evidence prior to solvers that would suggest hands would have similar EV. Empirical data analysis of hands once people started tracking online and equity calculators were one could see that in certain situations a lot of different hands might have similar equity.

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Thanks for the reply Grinder.

Similarity is certainly likely to be commonplace, but equality seems a very high bar.

Why do frequencies matter if not to impact EV? If the line-frequencies don't shape the line-EVs within its own strategy then they must at least affect the EVs of other lines in other strategies (once the opponent has adapted). They won't affect the lines in other mixed strategies equally, thus we shift the EVs of the lines within a strategy.

The EV of any line has to be a function of the other lines within the range. A range is a function of line-frequencies. Therefore if we alter the line-frequencies we must alter the range and in turn the line-EVs.

Anyhow, there's only so much time that can be spent usefully on this point :-).

It's certainly possible I lack complete understanding of the abstractions in most of the solvers and at what point the EV of lines become equivalent.

I still don't think it's all that odd EV's are equivalent or why intuitively equivalency would be that surprising just by the idea of mixed strategies.

I agree it's probably an irrelevant thing to spend too much time on. Cheers!

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