I think by Theorem 4.2 in https://math.dartmouth.edu/~pw/math100w13/haddadan.pdf https://math.dartmouth.edu/~pw/math100w13/haddadan.pdf the number of such shuff

I think by Theorem 4.2 in https://math.dartmouth.edu/~pw/math100w13/haddadan.pdf https://math.dartmouth.edu/~pw/math100w13/haddadan.pdf the number of such shuffles required to have a positive probability on all permutations is 6.