Rules of Let it Ride

The Basics:Let-It-Ride-229x229 Rules of Let it RideEach player puts up three bets of identical size and is dealt three cards; two more cards are dealt face-down in front of the dealer. After examining his three cards, the player may elect to have one bet returned or to “let it ride.” One of the down cards is then turned over, and then the player may again elect to have one bet returned — this election is independent of the prior election. Up to this point players are not allowed to disclose their three-card hands to each other. Now the second down card is turned over; the player’s three cards and the two common cards in front of the dealer comprise a five-card poker hand.

The player is paid on each of his one, two or three remaining bets according to the following schedule:
Player’s Hand- Payout
Pair of 10s or better- 1:1
Two Pair- 2:1
Three of a Kind-3:1
Straight- 5:1
Flush- 8:1
Full House- 11:1
Four of a Kind- 50:1
Straight Flush- 200:1
Royal Flush- 1000:1

Being able to have up to two of the three bets returned by the dealer is logically equivalent to starting with one bet and being allowed to put out up to two more. I surmise that the game is structured as it is because it would otherwise be too easy for players to covertly press bets — the bet circles on the layout are quite close together.
The optimal strategy for this game is as follows. On the first three cards, take back a bet unless one holds:
A pair of 10s or better, or three of a kind.
Three cards to a straight flush, provided:
contiguous and 543 or higher, or
one “hole” and at least one card is 10 or higher, or
two “holes” and at least two cards are 10 or higher.
On the fourth card, take back a bet unless one has:
a pair of 10s or better, two pair,
or three or four of a kind; or
a four-flush; or
an open-ended straight including a 10 or higher.