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Let's go over the published basics of the Opal system (I've simplified them so that they aren't as obfuscating as the official publications):
Trip - A trip is travel between a tap on and tap off.
Transfer - A transfer is made when there has been less than 60 minutes between the last tap off and the next tap on.
Journey - a journey is a collection of trips and transfers which ends when 60 minutes has elapsed from the last tap off. You can't end a journey manually - you must wait one hour from the last tap off in order to begin a new one.
Once you spend $15 in fares per day, the rest of the day's travel is free
After 8 journeys in a week, the rest of the week's travel is free
For journeys involving transfers from bus to bus, the fare is combined so that you do not pay a separate fare for each tap on and tap off.
One unpublished quirk with the Opal system is that the card itself stores the previous 8 journeys. This is to give information to the Opal readers to give them a general idea of what fare to apply, and so that inspectors can see what you've been up to.
Because of this, the Opal developers decided to limit a journey to four trips. This isn't officially acknowledged on the Opal website, but it is definitely there in the system.
Another thing to note is that after you reach the daily cap, which is $15, journeys are no longer counted for that day.
Now, onto the <$20 weekly. Most people would consider it an arduous task to undertake, so be warned. You will need to do this at the beginning of the week to enjoy maximum savings because the Opal week goes from Monday to Sunday, and weekly travel rewards are not carried past Sundays. The main difference of this technique over the other widely discussed fare minimisation technique is that instead of waiting an hour between tapping off and tapping on to add a journey, you catch three buses instead, which can often take less than 20 minutes in high frequency bus corridors.
For your information, the absolute minimum you can do this with is $16.80. That's 8x $2.10 (Opal <3km fare). In order to actually do this, I think the best way is to find a major bus corridor like Elizabeth Street in the CBD (prime roaming ground for Opal enabled buses at the moment) with buses coming very frequently and travel between, say, Circular Quay and Martin Place back and forth.
You can also do whatever route you want to take, but make sure that the combined straight line distance of your four trips (i.e. straight line distance from stop 1 to 2 plus straight line distance from stop 2 to 3 plus etc.) adds up to less than 3km or else you'll pay a higher fare. Circular Quay to Martin Place 4 times is 2.7km, so keep that in mind.
You'll need to tap on, ride at least one stop, and tap off. 29 times. Yes, 29. That's how many hops you need to do in order to invoke this loophole. As to whether it's worth wasting your Monday morning to potentially save $30 a week, I don't know, but you might find this information useful if you're interested in doing this spread over one or two days.
Anyway, after the 7th journey (25 taps) when you've spent about $14.70, you can stop the hopping. Journeys aren't counted after you hit $15, so you can enjoy unlimited travel for the rest of that day for 30 cents. The next day, keep hopping and you will hit the weekly travel reward once you finish your 8th journey.
I was insane enough to try this myself today and I got up to the 7th journey. I did most of my hopping at Circular Quay and around Bondi Junction (down the road from Waverley Depot, where most, if not all, the buses are Opal enabled) with a separate ticket to travel between Circular Quay and Bondi Junction - I would have hit the daily cap had I used the Opal card to go from the CBD to Bondi.
Tomorrow I'll be trying the 8th journey and I'm fairly confident that this will actually work. Here's my Opal card statement if you want proof of this 4 trip limit on a journey. Note that there's a tap on reversal and default fare there - those are either equipment failures or delayed updates and if anything's going to stuff this up, it's those, so watch out and keep a count of how many trips you're doing.
It has been around for year and you think you're the first to figure it out :)
Yes it works. It's not unpublished, it's mentioned on the official site:
Benefits of travelling with an Opal card
For example, you may work in the City and travel there and back by train each day. If you decided to take a couple of extra journeys within the City on any of the first three days of the week, you could reach you Weekly Travel Reward earlier and after that, travel the rest of the week for free excluding the airport station access fee
Enjoy it while it lasts, once more people use opal, they will change the structure.
Edit: ok the point is you don't have to wait an hour. You're better off spreading journeys through a day. An extra trip during lunch and you hit the reward by Wednesday, which is easy in the city. Use a train unless you really care about twenty cents, far more frequent. St James to Museum.