2.23454433
1.782252
3.3
1.362
1.6373342
0.8347223
1.2352
0.5243324
2.23
1.8729445434
2.356223
1.673
2.67
2.986363423
1.82786
And you know that a user has deposited 7.8 bitcoins.
Obviously you don't know the fee, it can be 0.03235 or 0.01342345, or 0.0284 or 0.152332 or whatever, it's random.
You don't either know how much of the rest of the amount the user withdraws.
Now please, do tell me which transactions go to this user using the last list and explain how that is less difficult than using the first list.
Or does anybody else see it?
If the amount is 7.8, even if we assume your fee could be absolutely anywhere between -0.5% and 2.5% (you DID say 2% before and didn't mention random fee until post #35)... for one, we can be virtually certain that the 3.3 was one of the outputs. Why? The 3.3 is needed for all possible combinations of three that add up to between 7.60 and 7.88.
The 2.67 is also extremely likely, as it's a necessary part of nearly all of the possible combinations that fall in that range. So, two for three... not bad for gumshoe statistical analysis.
As for withdrawing a partial balance... Sure, I suppose. Assuming they forgot about mybitcoin and assume that leaving bitcoins sitting on anonymous services is a good idea. You have heard of MyBitcoin right? And what good is an anonymizing service that only works if you use it a certain unusual way? If all of the security rests on the user remembering to take out a smaller amount than he put in, MtGox is already good for that today.
And I am sure you know by now that Bitcoins only divide to eight decimal places, and your examples with more than 8 places were just you getting carried away with extra digits.