The problem with the chlorination issue is that the amount of chlorine it takes to clear the pool is dependent on the stabilizer level of your water. You could very well be putting in chlorine but not enough to do any good, in which case you're wasting money and time.

Drop-based test kits are very much preferred over strips--drop-based testing is much more reliable and, even though more expensive at the beginning, will more than pay for themselves in chem savings. Taylor makes a K-2006 that can be purchased online at the Taylor site or at http://www.spspools-spas.com, or there is a similar test kit sold at http://www.tftestkits.net.

As Waterbear pointed out, the algaecides and clarifiers are not needed in properly maintained pools and can actually cause problems. Algaecides can often be useful when dealing with metal problems or prior to closing the pool, but in general are much better at preventing algae from growing than they are at killing a bloom.

Janet