Echo Park
Five card stud. However, before dealing a second card to each player, that player decides if they wish to receive that card face-up or face-down. If the player chooses to receive the card face-up, then the dealer flips a card face-up to that player as normal. If the player chooses to receive the card face-down, then that player signals so by flipping his hole card face-up. The dealer makes the same option once reaching himself. Now, each player has one card in the hole and one face-up. Highest card face-up opens the first betting round.
The dealer begins dealing a third card to each player. If the player wants the third card face-up, the dealer deals it to him face-up. If the player wants the third card face-down, then he signals so by flipping up his hole card. Another betting round ensues.
The same is done with the fourth and fifth cards to each player so that at all times up until the end of the game, each player has one card in the hole and the rest face-up.