I buy Clorox in the big jugs, 182 oz. at $8.41 for 3 jugs, that jug adds 2.7 FC to my pool for $0.73/FC
I buy trichlor pucks at the 2x40 lb bucket deal for $182, or $2.275/lb which adds 4.8 FC to my pool for $0.47/FC.
I buy cal-hypo in the big bucket, 100 lb, for $182, or $1.82/lb which adds 3.8 Fc or $0.49/FC.
If I use pucks only, and after the CYA goes from 30 to 60 I dump half my water, that will occur after 10 lbs of trichlor since 1 lb of trichlor adds 2.9 CYA to the pool. Since my pool uses about 2.5 FC a day on average I think, I will need 59 oz of trichlor a week to keep it stable. That will raise CYA by 11 each week so I will need to dump half my pool every third week. (Actually, given that we are on water restrictions most summers now that would be totally irresponsible but let's assume that I can do that although the cost for excess water use is about to skyrocket so let's assume water cost is at $35 instead of $25/10K gallons) So, half of 23k gallons is $29 for the pool water every 3 weeks, that's $10 a week. So I will expect to use $10 for water, plus $8.39 for pucks. Since my water has high TA and I am refilling so often, I will probably not need pH increaser or acid, not sure on that really. But my CH will go lower so I need to all Calcium Increaser, a lot, since my water is super low in CH. Assume with each dump of water I need to add 130 ppm CH. 45 lb Calcium increaser at $62 is $1.38/lb, I need 27 lbs so that is $37 with each water dump every 3 weeks so every week is $12.40. Um, where are we... $10/week for water, $8.39 for trichlor, $12.40 for calcium = $30.79/week.
if I use Clorox only ( I know, Walmart is cheaper but Sams is closer), if I use Clorox, I use 17.5 FC/wk as above, at $0.73/FC as above, is $12.77/wk for chlorine. I do have to add MA since my water has high TA, it varies with rainfall but I will assume 1 gallon a week. At 2 gal for $14.something, that is $7.50 a week. Total now is $20.27/week. That is it. No dumping water with all the angst over wasting precious water resources, no calcium needed. (really that seems high since I usually use 2 jugs a week maybe 3, but let's continue with these assumptions since I do not want to recalculate all this)
If I use cal-hypo it adds 2.7 to CH per lb, so if I can tolerate a swing of 100 ppm CH from 250 to 350, then I have to dump water and rebalance. I use 17.5 FC/wk so I need 4.6 lbs/wk at $1.82/lb of $8.37/wk. CH climbs by 12.4ppm/wk. I dump 28% of the pool after 8 weeks to get back to 250ppm. Cost for 6.4K gallons is $16 or $2/wk. TA will climb so I need a lot of acid, several times a week to rebalance, I dunno how much that is and I am getting tired of the calculations so let's just assign a PITA cost to that of 2 gallons a week at $15. So, we are at $8.37 for cal-hypo, plus $2/wk for water replacement, plus $15 for acid. Total $25.37/wk.
So, as far as I can tell, once you include the incidentals like acid and water and calcium, you get
bleach = $20.27/wk
Cal-hypo = $25.37/wk
trichlor pucks = $30.79/wk
And then you need to add in the PITA costs of dumping water and rebalancing. And the psychic trauma of sending water down the drain when in water restrictions.
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I have to admit, I really was not sure what the answer would be here. My real time cost analysis tells me that I don't spend much on the pool, even including Polaris parts. Pool store costs have been $500 over the past year, for chemicals like trichlor pucks and cal-hypo and liquid chlorine an testing reagents and Polaris parts. Chlorine bleach and acid are hidden and harder to find in my records as it is Walmart or Home Depot or Sam's spending. I have assumed that I spend about $5/wk on bleach, and about $3/wk on acid. I have never bought clarifiers or algaecides or scum enzymes or ion generators or flocculants. My pool is clean and clear and I am so happy that it is.
So, IMO, the answer is that YES, TFP methods do save money, they also save water and time. I do spend a few minutes testing water every other day. I also spend a few minutes cleaning skimmers every other day. I do a full test maybe every week or so. I also clean the pump baskets every week or so. I hardly ever brush, but that is Ok since my pool is clean and clear and sparkly.