Lets say I have 5 cards, a b c d and e. I group those as 2, 2 and 1, my first group contains a and b, second group contains c and d, and the last group contains only e. Then I mix those, by putting the last group on top and putting the first group to bottom, so my deck is now sorted as e c d a b, then I continue this procedure till I have a deck that is all random.
How many steps I should continue this procedure?
What is the general formula if I have 52 cards and group those as 12 12 14 14?
2026-03-25 20:41:23.1774471283
Shuffling Cards by Grouping
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For the case of the $5$-card shuffle you described, we get \begin{align*} 0\;\text{shuffles}\implies\;a, b, c, d, e\\[4pt] 1\;\text{shuffles}\implies\;e, c, d, a, b\\[4pt] 2\;\text{shuffles}\implies\;b, d, a, e, c\\[4pt] 3\;\text{shuffles}\implies\;c, a, e, b, d\\[4pt] 4\;\text{shuffles}\implies\;d, e, b, c, a\\[4pt] 5\;\text{shuffles}\implies\;a, b, c, d, e\\[4pt] \end{align*} so there are only $5$ distinct results, after which, the sequence repeats.
As to which of those $5$ possible results is the most random, it depends on your definition of "most random", but whatever it is, simply test each of those $5$ results, and take the one that best fits your "most random" criterion.