Howdy, Blackjack Peeps!

Longtime player here, but been awhile since I posted anything. Wife just turned 30 so had a grand surprise party for her and been busy with life in general.

Anyway, my question is regarding general blackjack casino gambling, not Tournament play. I read before that in order to not go broke at a 4-hour session 95% of time, it is recommended that one's bankroll is 40x their average bet, and to not go broke 90% of time, 30x is recommended. My question is, where is documented, mathematical evidence of this? Because lately I've been averaging $75 but only have $1K bankroll while the wifey averages ~$35-40 and her bankroll is $500 and we won in both recent trips we had, $500 most recently, and about $2K at Beau Rivage and L'. I would think having 20x average bet would be good at least 75% based on the above %'s, but curious to know the exact % just bec I dont want to bring over $2K ($2250 to be exact!) playing $75 average!

Thanks in advance.