Are professors allowed to change their exam grading policy more than once within a semester?

Before I get into details, this subject is a senior level course which is a combination of two previously taken courses. The two previous courses (which where designed as weed out courses), taught by different instructors, allowed students, open book and to bring their own formula sheet on the exams. And it’s not like the open book and open notes significantly help the students, the amount of material covered in the semester for each class is, by the instructors admission, nearly impossible to grasp within a semester , which is why they allow open book/notes, to instead determine if we know how to apply what we learned. Still, many student fail these classes with open book/notes. the material is that much. I ended up scoring really well for these two courses.

Now, into the hell im dealing with: This semester, a fresh professor comes in, first year ever teaching at this school, on the last class before graduation. The class is a combination of both subjects, he starts the semester with saying closed book and no formula sheets on exams. Also, NO PARTIAL CREDIT, all or nothing. So with this info, I worked the exam in a way by only focusing on the questions I know I can get full credit on and spend no time on other questions which I thought I couldn’t 100% answer correctly. Made sense to me at the time, because why waist exam time on questions that you will end up getting 0 points on if you do not answer the 10-15min long problem completely correct, to the dot.

The class average got destroyed so hard he decided to give partial points on the test, but only after the fact we took it. The partial points he gave though, is like a slap in the face. Why you may ask? He gave at max 2 points per question that would have originally been 0 points (each question is about 30-40 points, so it’s like he said he gave partial credit but without the partial credit).

So now the professor sees that since so many students did horrible we are allowed to bring our own formula sheet with whatever we want on it. and that he will give us partial credit for this next test. Two days before the second exam he sends an email to all students redacting what he stated in class by giving us a set of guidelines to follow when making the formula sheet and that is must be reviewed and signed by him before the test. I get my grade that I knew I got an A on, but then it hit me.

My heart sunk, I answered the entire exam correctly except the very first question, I did not answer one part. BOOM 0 out of 30 points on that question (my grade for this was 70, should have been a 100). I sat with him in his office and tried to explain nicely that I feel the grading is unfair by going over my solution and showing him how I have the EXACT answers as his solution, it’s just that I did not fully complete my answer. HE SEES THIS AND GIVES ME 2/30 points. Now I have a 72 (needed a 90 to pass the class, otherwise I got to wait another year to take the class again). I express what’s the point of us waisting each others time for just two points, he got defensive and said “grading is at my discretion, and now, I will make the final exam no partial credit). I never experienced this before, is this right?

TL;DR Professor changed exam guidelines numerous times during the semester at the last minute And was very unclear in his grading criteria, resulting in students failing, not because they don’t understand the material, but because we not communicated to clearly.