Trouble with nested IF formula

I'm trying to decipher someone else's spreadsheet and have come across the following worksheet formula:

=IF(D20=0,IF(rand<prob1,average+(0.5-RAND())*var,0),IF(rand<prob2,average+(1-RAND())*var,0))

It's the first part I am having a problem with. I always thought that the syntax for nested IF functions was along the lines of:

IF conditon is True THEN do this, ELSEIF the next condition is True THEN do this, ELSEIF the next condition is True THEN do this..............ELSE do this.

But this doesn't seem to be the way the above formula works. It has the first part: IF condition is True.....but then it goes straight into the next IF statement.

I.e. IF(D20=0, IF(rand.....

But I would have thought it should say: IF(D20=0, *do this*, IF(rand...

Can anyone explain what the formula is actually doing?

Thanks
-Rob