Sacrifice up to half a stack of Cards Question

Hi, I wanted to ask a question about the mechanic:

"Sacrifice up to half a stack of Cards to receive between 0 and twice that amount of the same Card".

Is this harvest craft weighted (e.g. roulette) or fair (odds of increasing = odds of decreasing)?

Someone wrote a really good paper on this, If I find it I will add it here.

Might be a bit hardcore if your not into math
https://www.scribd.com/document/521232509/Div-Card-Harvest

The basic conclusion they came up with, if your goal is to just get a full stack, spending on average the least amount of currency, the method of gambling does not mater, but you should gamble in a way that will result in returning that exact number of cards, and not more. Other methods may be useful for other reasons, depending on what you are trying to achieve.

Someone else's work I found while looking for the above article, I haven't read through it so i'm not sure if it is any good, but they've certainly put in a lot of effort. Might contain something useful for you, particularly if you find visuals helpful.

https://www.reddit.com/r/pathofexile/comments/135e8s4/so_you_want_to_harvest_gamba_div_cards/

I think to answer your question, it is a "fair" distribution of outcomes, that is uniform, but you're paying for the function with your harvest mats, so you are going negative unless you have a way of benefitting, like getting outcomes you could not achieve without the gamble. i.e. stacks in ssf, or apothecary when the cards might be unavailable early in the league, or more expensive on average, or you cant afford a full stack and want to get lucky.