Use the scramble generator I posted above.
Seriously, just do it. It's not that hard to use (just press a button!), and you're
definitely getting proper scrambles if you check the "use random-state scrambles" option. The only downside is that you need to manually paste the scrambles into csTimer and that it takes a horrendous amount of time to generate the first batch of scrambles. (I have a rough idea of what to change to make it faster, so I guess I'll work on it this weekend.)
The next best thing is to use the hybrid scrambles. (Same program; just leave "use random-state scrambles" unchecked.) Again, you still have to manually paste the scrambles into csTimer, but they're still
guaranteed to be uniform random-state in one aspect (locations of the white and grey corner pieces) and almost-uniform in another (corner orientation).
The third option is to use standard megaminx scrambles. If 70 moves is too long for your liking, maybe cut it to 60 moves. Purely by gut feel, I think 40 moves (which we're using in the forum weekly comp) is too little, but at least there's precedent for that too.
The 12-gen scrambles are extremely bad. They're hard to read, slow to execute, and
need to be long to effectively scramble the puzzle. It's the worst of all worlds. But to address your original question: how long should they be?
We first have to note that csTimer's implementation is cursed and only returns 1/5 clockwise turns for each face. According to
this post by Herbert Kociemba, the number of canonical scramble sequences of length n, with the length being measured in terms of clockwise fifth turns, grows roughly like 12 × 9.249^(n−1). (It's probably off by a small constant factor, but this does not materially affect the conclusion.) There are around 2.4e25 states on a kilominx and only around 2e25 scrambles of length at most 25, so to even reach every possible state, you need at least 26 moves. If your scramble sequences are 25 moves or less, there'll be a bunch of perfectly legal scrambles you just won't get.
So, answer is 26 moves, and we're done, right? Wrong! The above computation allows for consecutive moves to be of the same face, but this is
not what csTimer does. Instead, csTimer does the whole commutativity check thingy and (i) never allows consecutive moves to be of the same face and (ii) doesn't even allow subsequences like L R L or U D U even when there's an intervening different move. This substantially reduces the number of possible scrambles, although now I don't have a convenient formula someone else already worked out to reference, so we can't continue with the scramble count analysis. What we
can do, however, is to look at where the pieces end up after so-and-so many moves, sampling a large number of old-style scrambles. (For that matter, this is a better way of analysing scrambles than just counting scramble sequences. More on this later.)
With 100000 scrambles, 21 moves, this is the distribution of what corner piece is in position #0 (the U-BL-BR corner), and what its orientation is.
[3704, 2073, 1380, 2608, 4005, 2748, 2005, 2609, 866, 1382, 463, 835, 1357, 1392, 2552, 277, 448, 881, 914, 437, 4603, 4003, 2120, 1318, 2853, 2015, 2875, 1295, 1355, 865, 468, 1413, 875, 2104, 2616, 307, 528, 794, 827, 486, 2394, 2876, 2887, 2478, 2046, 4150, 1376, 2568, 867, 803, 643, 866, 803, 2862, 1261, 305, 643, 1411, 1425, 680]
You don't need to load up any fancy statistical analysis software to see that this is very much
not uniform. With proper scrambles, you'd expect 100000/60 = 1667 hits per bin, and you definitely don't expect to see only 300 hits in any of the bins. If you bother to actually do a Pearson's chi-squared test, this thing has a p-value of basically zero.
What about 30 moves?
[3165, 2821, 1972, 1640, 2436, 2186, 2247, 1638, 1422, 1224, 941, 1437, 1260, 1943, 2198, 754, 887, 1169, 1186, 887, 2230, 2466, 2263, 2151, 2084, 2858, 1721, 2109, 1302, 1152, 935, 1240, 1170, 2393, 1634, 736, 993, 1524, 1494, 951, 2874, 2049, 1739, 2180, 2802, 2399, 1994, 2168, 1112, 1492, 869, 1152, 1431, 1724, 2185, 683, 931, 1257, 1256, 884]
Still "obviously" non-uniform from a casual glance, although it's less extreme. Again, p-value is still basically zero.
60 moves?
[1880, 1845, 1760, 1663, 1784, 1847, 1782, 1680, 1603, 1593, 1452, 1543, 1622, 1736, 1755, 1386, 1468, 1657, 1617, 1492, 1870, 1760, 1878, 1762, 1836, 1918, 1732, 1795, 1589, 1614, 1554, 1603, 1486, 1767, 1715, 1435, 1514, 1642, 1632, 1483, 1833, 1820, 1699, 1786, 1870, 1709, 1708, 1798, 1643, 1558, 1489, 1650, 1584, 1686, 1826, 1483, 1534, 1611, 1505, 1458]
p-value is now 5e−146 or within a few orders of magnitude of that. The distribution is starting to look uniform, but the discrepancies are still large enough that the chi-squared test is a complete failure. You have to go up to around 90-100 moves for the distribution to really start approaching uniform. Here's the distribution with 100 moves, just for posterity:
[1710, 1643, 1692, 1747, 1701, 1679, 1686, 1686, 1711, 1634, 1671, 1644, 1633, 1715, 1665, 1658, 1675, 1756, 1657, 1674, 1703, 1584, 1635, 1624, 1664, 1649, 1666, 1641, 1666, 1621, 1685, 1574, 1580, 1766, 1688, 1711, 1622, 1714, 1638, 1652, 1677, 1739, 1713, 1688, 1720, 1701, 1673, 1711, 1671, 1635, 1606, 1664, 1613, 1649, 1740, 1645, 1579, 1638, 1663, 1555]
And the p-value: 0.086. This means that
with 100000 samples, there is no statistically significant difference (at a 5% threshold) between ideal scrambles and csTimer "old style" 100-move scrambles. There still is a difference; it just needs more samples to consistently hit the 5% threshold.
Maybe you'd say that 100000 samples is kind of overkill, and I'd be inclined to agree, but the thing is that I'm
not analysing the full scramble, but only one corner piece; non-uniformity in the distributions among
multiple corner pieces might mean an increased chance of pre-made blocks compared to ideal scrambles, which means the scrambles are biased towards being easier. If the marginal distributions already deviate significantly from uniform, the joint distribution can't be any closer.
If you're sharp, you may have noticed that applying the scramble count analysis to the Pochmann R++/D++ scrambles actually also shows that 70 moves is vastly inadequate. There are only 2^70 = 1.2e21 such scrambles, which is much smaller than the number of kilominx states. Despite this, we currently believe that the Pochmann RDU scrambles are "generic": they don't have easily-recognised special features that allow you to solve them faster than the other scrambles, on average.
ADDENDUM:
If you're
really sharp, you might have noticed that I pulled a fast one on you. We don't actually need the distribution itself to be uniform; we just want the distribution
modulo rotations to be uniform (whatever this means—it's actually nonobvious how we should define "modulo rotations" here and I don't have a good answer). This is because the kilominx has no fixed centres, but unlike 2×2×2 (which also has no fixed centres), you can't just fix a corner piece and rewrite face turns that move that corner piece into face turns that don't—they'd be rewritten into
wide turns instead. Wide turns move 15 pieces, as opposed to face turns moving only 5, so they're truly very different in the case of a kilominx.
Nevertheless, there's no good reason to expect that modding out rotations will mysteriously and magically smooth out the nonuniformity.
ADDENDUM 2: Statistical significance versus practical significance
This is a topic that
should be taught in every introductory statistics class, but (to my knowledge) often isn't. (At least,
I wasn't taught this in high school. Then again, I also refused to take the AP Stats prep class then because I thought I was smarter than the teacher
(and, you know, I was). … I digress.)
In "real life", you almost never have exactly identical values. The outcome of an experimental drug versus the placebo is never going to be exactly identical; crank up the sample size enough and you
will find that the drug has
some effect. How large is the effect? The larger your sample size, the more sensitive your experiment will be to tiny differences. There is some point where the difference is so tiny that you just don't care—it may be
statistically significant with your ginormous N=1000000000 sample size, but not
practically significant in reality.
It's kind of the same thing when we're analysing scrambling methods. Markov chain random state is the ideal scrambling method (imagine doing a billion random moves, then replacing it with a shorter move sequence that has the same effect), but often isn't a practical option. So we compromise by using random moves instead, which brings us again to the question of how many random moves to use. With the exception of almost-trivial puzzles like a 2×2×1, applying random moves will never
exactly reach the stationary distribution. It converges there, and it even does so exponentially quickly, but it'll never be exact. So the real question here is: how much of a deviation from the stationary distribution can we accept?
If we can't do proper random-state scrambles, the state space is necessarily also too large to directly compare the distribution of random-move scrambles to the stationary distribution. Instead, we'll have to compare either some subset of the state space (this is usually not a good idea), or some quotient of the state space (this is usually what people do). What I mean by "quotient" here is grouping up similar-looking states together in the state space, for some sense of "similar-looking". That's actually one more parameter you get to choose when analysing the scrambles.
Some notions of "similar-looking" are more useful than others. For example, many years ago, Stefan Pochmann analysed the edge orientation of random-move scrambles for the 3×3×3. That's quite useful, since it was very relevant to the most common blindsolving method then (3OP). An example of a useless notion of "similar-looking" is to take the SHA-1 hash of the puzzle state and classify by the first 8 bits of that; the states being grouped together have basically no relation to each other.
So, once you've chosen your notion of "similar-looking", and also a threshold for the amount of acceptable deviation, you can either exactly compute the exact distribution for random-move scrambles (this is not always possible, but sometimes it is, e.g. the aforementioned EO analysis) or compute it empirically by doing thousands/millions/billions of scrambles with a computer program. You can then do an appropriate statistical test to determine whether this empirical distribution is within your threshold. (Note that this can require much larger sample sizes than just a basic statistical significance test like I did above! You're trying to find the shortest scramble length that lies within the threshold (because shorter scrambles are better, all else equal), which also means that you'll be very close to the threshold, which in turn means you need a lot of samples to determine whether it's
really under the threshold or if it's a statistical fluke.)