Rare item creation

[adeyke]

i believe you can get:
Ethereal War Pike
Cruel +300% ED
Master's +150% ED +250 AR
Shocking +1-480 Lightning Damage
Of Quickness +40% IAS
Of Restoration 1 durability/20 seconds
Of Slaughter +20 Max Damage

yeah, I think mine will beat yours up any day.
Still I don't think they are the same.  The whole reason behind my question is to selectively choose what types of affixes are going to go on my items.  For example:
Let's say that the jewel affixes Tin, Nickel, Rusty, Pearl, Freedom, Avarice, and Realgar.  Next, I cube a jewel selectively with the 6 skull method for a new rare to give it an output Ilvl of 13, putting the maximum affix level at 13.  If this jewel can ONLY get 4 of these 7 affixes, which ones would it choose?  I know already that Tin and Nickel are both AR affixes in the same group and Rusty and Realgar are both in the +ed group.  Realgar and Pearl are too high Alvls to spawn on my jewel, so I'm left with 5 possible affixes.  Let's say that there is no limit to the number of prefixes you can have on a jewel, just that it doesnt go over 4.  Tin and Nickel are both in the same group yielding a possible choice of freedom, avarice, or rusty each at 1/4 chance.  If Tin and Nickel are not counted as the same group, then the probability decreases to 1/5.

It doesn't matter much to me how much the affixes are weighted.
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In your hypothetical case, there'd still be Tin, Nickel, Rusty, Freedom, and Avarice:
Tin: group 110, rarity 4
Nickel: group 110, rarity 4
Rusty: group 105, rarity 4
Freedom: group 30, rarity 3
Avarice: group 21, rarity 4
Total rarity: 19

Let's temporarily ignore the distinction between between prefixes and suffixes.

Now, by the first method:

it would first pick the group:
group 110: rarity 8
group 105: rarity 4
group 30: rarity 3
group 21: rarity 4
Total rarity: 19

So the first affix, there's a 8/19 chance of group 110, a 4/19 chance of group 105, etc.

Suppose it picked group 110. In that group, there are two affixes:
Tin: rarity 4
Nickel: rarity 4
Total rarity: 8

So, given that it's group 110, there's a 4/8 = 1/2 chance of Tin and a 1/2 chance of Nickel. If we multiply the chance of getting group 110 by the chance of getting Tin given that we have group 110, we get 8/19 * 1/2 = 4/19 total chance that the first affix is Tin.

For the second one, the group 110 wouldn't be considered, so the remaining groups would be:
group 105: rarity 4
group 30: rarity 3
group 21: rarity 4
Total rarity: 11

So then group 30 (Freedom affix) has a 3/11 chance of spawning as the second affix, and so on.

With the second method

If it first chose the affix regardless of group, it'd look at this list:
Tin: rarity 4
Nickel: rarity 4
Rusty: rarity 4
Freedom: rarity 3
Avarice: rarity 4
Total rarity: 19

As before, there's a 4/19 chance of getting the Tin prefix as first affix. Suppose that one was, indeed, picked. Then it'd look at the same list again. However, if, as you said, picking an affix in a group that was already on the item resulted in trying again, it's equivalent to simply not having those affixes in the list:

Rusty: rarity 4
Freedom: rarity 3
Avarice: rarity 4
Total rarity: 11

So the probability of getting Freedom as the second affix would be 3/11. Same as before.

The two methods are equivalent.

This brings up another point, though. In your example, there were only four affix groups total. That means that, if a jewel has 4 affixes, it'll definitely have every one of them included. So, if we ignore the order of the affixes, there'd really just be two possible jewels:
Tin, Rusty, Freedom, Avarice
Nickel, Rusty, Freedom, Avarice

These two jewels would be equiprobable, since Tin and Nickel have the same weight.

If this still doesn't make sense, let me reiterate: Only those affixes that can spawn on an item are considered when an affix is picked. An affix can only spawn on the item if the alvl of the item is sufficiently high, the item type matches, and no affix of that group already exists on the item.