If you search Google for "21+3 blackjack online" there seem to be online sites that offer that game.
The casino your friend went to is doing a good job because they *want* games to appear beatable. Casinos love customers like your friend who doesn't understand how casinos make money.
Also ran across this page:
http://wizardofodds.com/blackjack/appendix8.html#21+3 where he analyzes pay tables and concludes the house edge is either 3.24% or 2.78% in b&m casinos depending on the payouts used. Or anywhere from 3.18% to 7.76% online depending on the number of decks used.