I've noticed that Ruby's RNG is not that great. I've got a couple of small IRC bot scripts, one is a dice roller, the other is one that takes random items from a Google spreadsheet (using simple Random#rand in the first case, and Array#sample in the second).
The dice seems biased to certain numbers, and the spreadsheet has the same items come up more than mundane statistics would otherwise suggest. (A 1/50 roll landing on the same item 2-3 times in a row, multiple times per day?)
It's gotten to the point where my users don't want to use my bot for RPGs. I'll have to see if using SecureRandom#random_number produces any different results
As far as I know, Lua does not include Mersenne Twister. math.random() is just C rand().