How to save 33% on your coffee

Every morning, on the way to work, I buy a large coffee for $3. The coffee shop runs a loyalty card scheme to retain my custom in exchange for free drinks. It works like this:

1. Buy 9 coffees ($27) - get one free
2. Buy another 8 coffees $24) - get one free
3. Buy another 7 coffees ($21) - get one free
4. Buy another 6 coffees ($18) - get one free
5. Repeat again from step 1.

By spending $90 ($27 + $24 + $21 + $18) on coffee I get four drinks free, worth $12. Without the scheme, the total 34 drinks would cost me $102, so with my free coffees I make an overall saving of 12%. Pretty good, but still a lot to spend of coffee, especially when I can make a cup of tea at work for nothing.

How can I maximise my value for money?

Medium coffees are $2.40 and aren't much smaller, they contain the same amount of coffee but slightly less milk. What if I only buy medium coffees, but take a large one as my free drink? Then how much do I save?

Cost: 30 x $2.40 = $72
Free: 4 x $3 = $12
Total value: $84
Saving: 14%

Not bad, every little helps. The next step is coffee for friends. There are two other people in my office who need a morning caffeine hit, so I offer to pick up their drinks on my way in, but keep using my loyalty card. So now I get more free drinks without spending as much:

X = My coffee, 0 = Friends' coffee

XOOXOOXOO - 1 free
XOOXOOXO - 1 free
OXOOXOO - 1 free
XOOXOO - 1 free

Combining this with the previous strategy, for every ten medium coffees I buy, I now get four large for free.

Cost: 10 x $2.40 = $24
Free: 4 x $3 = $12
Total value = $36
Saving = 33%

I save a load of money on my coffee, the barista gets my regular trade, and my friends get their coffee delivered. Everyone's a winner. (But I still hope none of them finds out.)