Most efficient way to roll +3 gems?

To any mathematically gifted individuals out there I have a question:

What is the most efficient way to roll +2 (fire/cold/lightning) with +1 to all gems on an item?
The options are alteration spam + regal vs chaos spam vs buying one that already has +3 and then 6 linking it yourself.

I have a 6l staff that I would like to try and do this to but in terms of currency ratios I do have to wonder which course of action requires the least currency investment (naturally all of them require a great deal)

I know that the +gems rolls are among the rarer affixes but assuming an even distribution... educated guess?

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What is the most efficient way to roll +2 (fire/cold/lightning) with +1 to all gems on an item?
The options are alteration spam + regal vs chaos spam vs buying one that already has +3 and then 6 linking it yourself.

why dont you use an indexer to see if one exists.

if no, alt regal will probably be the better choice.

alt (prefix only), then regal if you have massive currency and chaos if you have even more than that.

definitely alts... they cost almost nothing

after IDing 2000 scepters i can say this combination is RARE as hell