Chlorine levels go down quickly is stabilizer inportant?

add 4lbs of stabilizer to get it around 40 (my pool roughly same size as yours)

The cya will bring down your ph a bit too, so don't bring that down yet.

edit: just noticed your using guess strips (test strips are just not very accurate)

you need a TF100 or Taylor K2006C test kit to get proper test results before you do anything.
 
Without any stabilizer in the pool water, the half-life of chlorine is about 35mins give or take. So, in a little over four hours of direct noon time sun, you will lose 94% of the chlorine in your pool. SO the answer to your question is - yes, stabilizer is very important.
 
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