the trouble with human “random” is we try to be too random.

Examine a variety of “quick picks”. there will be quite a few with a sequential pair or several ending in the same digit (13/33, 21/41, etc.). Odds are one decade will be missing. Even likely that 3 of the 6 are in the same decade. (Our lottery is the 6 of 49.)

If a human is asked to pick random, we likely will not pick a sequential pair, or miss a decade, or over-represent others. we try too hard.

Then peruse the winning numbers - I suspect you will find the same. Decades missing or over-represented, sequential pairs, same last digits, etc.

The odds of getting 3 numbers the same out of 10 sets is not too bad, provided you don’t specify the number. After all, that’s 60 numbers, you will hav a lot of duplicates.

For the powerball - one select number -

each number can be one of 35. What one pick has, should have no bearing on the next. Random.

35^10 choices for 10 random powerballs.

There are 35 numbers. For “1” to repeat 3 times, there are 35^7 combinations (set 3 numbers to “1” and choose 7 randomly). Ditto for 2, for 3, to 35.

so there are 35^8 combinations where at least 3 numbers repeat.

Odds of that happening - 35^10/35^8=35^2 or about 1 in 1000.

But that was the first 3 positions selected - it could be any 3 - so divide by how many ways you can arrange 3 items in 10 -which is 10*9*8=720. But the 3 are identical, so now divide by 3! or 6 ways to arrange those 3.

(35*35)/(720/6) gives about 1 in 10.2 odds.

Buy singles, keep your old tickets and test this against any random combination of tickets.

If you win the jackpot before you prove the odds, stop caring…