A single 121 oz jug of 8% Walmart bleach will add about 8 ppm of chlorine to your pool.
If you've been using 'pucks' (trichlor) for years, your stabilizer levels are likely VERY high, possibly MUCH higher than 100 ppm. Read the info about the chlorine-stabilizer relationship: http://pool9.net/cl-cya/
You can manage a high CYA pool successfully, but you will need the K2006 kit to do so (honestly, you need it, anyhow): http://pool9.net/test/
You should maintain very high chlorine for at least a couple of days after there's no detectible trace of algae.
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