Let It Ride Rules

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From the rec.gambling Frequently-Asked-Questions (by Steve Brecher):

Each 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:

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; or
--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.

The following bets are optional,
i.e., expected return = 1.000...
--an open-ended straight not including a 10 or higher; or
--all cards 10 or higher (an inside A-to-10 straight).


Playing this strategy provides an expected return of 0.971352 per unit bet. The average bet per hand is 1.223707 units (where one to three units are bet per hand and no optional bets are made), and the average unit cost per hand is 0.035057.

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