Since you rule out games of skill, we can't look at blackjack, which would otherwise be the correct answer, assuming the best of rules.
Since you rule out bets that require a secondary bet, we must rule out the odds bet in craps.
That said, I claim the answer to be the buy bet on the 2 or 12 in Crapless Craps, where the casino charges the 5% commission on wins only. It is my understanding the MGM/Mirage casinos as well as Resorts World charge the commission on wins only. That said, the win is 5.95 to 1 and the probability of winning is 1/7. That calculates to a house edge of 0.714%. I'm not aware of anything better that meets your requirements.