I'm not sure if this is going to be possible in Tableau. The only "Random" function Tableau has is an undocumented function called RANDOM().
The calculation creates a random value between 0 and 1, each time the Visualization/Data is refreshed. While you might be able to hack something together with 3 Random functions and maybe a Table Calc filters on Rank, it don't necessarily think it will be performant, or fit your exact needs.
Can you provide more details on your situation? Or perhaps share an example workbook?
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In addition to RANDOM(), you can generate your own random numbers in Tableau (see Random Number Generation). Other possibilities include using R or some kind of live pass through SQL.
Do you want a new random distribution each time you refresh the view? Or is a single randomization that is run once okay?
I actually managed to achieve this by passing a RAND() back to our original MySQL source and then using that as a seed to randomly select a index() number within a dimension range ( so each user had a high and low value - say 1 and 17. So i ended up with a selection from each group user.
Thanks for the link provided, it lead me down the right track.
This was perfect: https://community.tableau.com/docs/DOC-1474