CPL- DOF

OK , another stupid question - My CPL loses up to 2 stops , so does it increase the DOF on chart from 2.8 to F4 assuming you are wide open at 2.8 ?
I think f4 is f4 on chart however you get there .
I was wondering because I use a cpl most of the time and I lose up to 2 stops with it . Does that give me more DOF ?

Loss of two EV of light is not the same as using a smaller aperture! DOF is changed by smaller/larger aperture, but not by loss of light alone. The effect of a CPL is 'loss of light'

If the reading was 1/100 f/8 with no filter, but was 1/25 f/8 with the filter, there would be no change in DOF because of no aperture change. But if you used 1/100 f/4 with the filter, the DOF would change because the aperture changed.

Thank you , makes more sense now .