I already wrote it somewhere, but oh well...
(devs please correct me if I'm wrong anywhere)
In PROGRESSIVE MODE:
If:
-you set gi samples to X
-you set direct light samples multiplier to Y
-you have N passes and for each pass you get 1 AA sample
Then:
For each pixel of your image you get:
-X gi samples for GI
-Y*X samples for direct light
-N AA samples
In BUCKET mode:
If:
-you set GI samples to X
-you set direct light samples multiplier to Y
-you set bucket initial samples to 8
-you set passes to 4
-you set adaptive threshold to 0,01
Then:
Your bucket makes X gi samples for GI or Y samples for direct light * 8 (because of initial samples = 8, these 8 initial samples are virtually the same as passes in progressive mode, they will give you 8 AA samples).
After the whole image is covered with buckets, the next pass is started in which you will get your [initial samples]*2 which will give you 16 samples. So some pixels will get these additional samples and some won't - adaptive threshold decides about this.
Buckets will do this 4 times as you set passes to 4.
-in first pass you will have 8 AA samples
-in 2nd - 16AA samples for pixels above adaptive threshold
-in3rd - 32AA samples for pixels above adapt thresh
-in4th - 64AA samples for pixels above adapt thresh
Hope it's more or less clear. Sorry for potential mistakes, I'm in a hurry. :D