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Face Up Three Card Poker
Introduction
Face Up Three Card Poker is a variation of traditional Three Card Poker, played in some of the poker casinos of Los Angeles County. I've also seen it at the Casino Caribbean in Yakima, Washington. The rules are the same as standard Three Card Poker, except as follows.
- One dealer card is dealt face up.
- If the dealer doesn't qualify, then the player must still beat the dealer to win the ante.
- There are no ante bonuses.
- There is a fee to play, usually 1% of the amount bet, rounded UP to the nearest dollar.
Here are the rules in their entirety.
Rules
- A single 52-card deck is used.
- Hards are scored accoring to poker rules, except the rank of hands is as follows.
Straight flush
Three of a kind
Straight
Flush
Pair
Ace high or less - Player makes an ante wager.
- The player and dealer each receive three cards. One of the dealer's cards is dealt face up, and two face down. The player's cards are dealt face down, which the player may examine.
- The player may either fold or raise.
- If the player folds, then he forfeits his cards and ante wager.
- If the player raises, then he must make a raise wager equal to his ante wager.
- The dealer will turn over his cards.
- The dealer needs at least a queen high to qualify.
- If the dealer does not qualify, and the player's hand beats the dealer's hand, then the player's ante will pay 1 to 1, and the raise will push.
- If the dealer does not qualify, and the dealer's hand beats or ties the player's hand, then the player's ante and raise will push.
- If the dealer does qualify, and the player's hand beats the dealer's hand, the the player's ante and raise will pay 1 to 1.
- If the dealer does qualify, and the dealer's hand beats the player's hand, then the player's ante and raise will lose.
- If the dealer does qualify, and the player's hand ties the dealer's hand, then the player's ante and raise will push.
At the Casino Caribbean they also had the Pair Plus and Progressive side bets. You can read about the math of these on my Three Card Poker page.
Strategy
The following table shows the optimal strategy according to the player's hand (down) by the dealer's up card (across). Obviously, if the player has a straight or flush, then he should always raise.
California Three Card Poker Strategy
| Player | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | T | J | Q | K | A |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A,9,2 and higher: Always raise | |||||||||||||
| A,8,7 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,8,6 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,8,5 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,8,4 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,8,3 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,8,2 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,7,6 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,7,5 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,7,4 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,7,3 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,7,2 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,6,5 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,6,4 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,6,3 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,6,2 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,5,4 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,5,3 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,5,2 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,4,3 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,4,2 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| A,3,2 | R | R | R | R | R | R | R | R | R | R | R | R | R |
| K,Q,J | R | R | R | R | R | R | R | R | R | R | R | R | R |
| K,Q,T | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,Q,9 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,Q,8 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,Q,7 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,Q,6 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,Q,5 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,Q,4 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,Q,3 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,Q,2 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,J,T | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,J,9 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,J,8 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,J,7 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,J,6 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,J,5 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,J,4 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,J,3 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,J,2 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,T,9 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,T,8 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,T,7 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,T,6 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,T,5 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,T,4 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,T,3 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,T,2 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,9,8 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,9,7 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,9,6 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,9,5 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,9,4 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,9,3 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,9,2 | R | R | R | R | R | R | R | R | R | R | R | R | F |
| K,8,7 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,8,6 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,8,5 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,8,4 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,8,3 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,8,2 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,7,6 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,7,5 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,7,4 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,7,3 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,7,2 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,6,5 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,6,4 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,6,3 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,6,2 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,5,4 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,5,3 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,5,2 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,4,3 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,4,2 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| K,3,2 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,J,T | R | R | R | R | R | R | R | R | R | R | R | R | R |
| Q,J,9 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,J,8 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,J,7 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,J,6 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,J,5 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,J,4 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,J,3 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,J,2 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,T,9 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,T,8 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,T,7 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,T,6 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,T,5 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,T,4 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,T,3 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,T,2 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,9,8 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,9,7 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,9,6 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,9,5 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,9,4 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,9,3 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,9,2 | R | R | R | R | R | R | R | R | R | R | R | F | F |
| Q,8,7 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,8,6 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,8,5 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,8,4 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,8,3 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,8,2 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,7,6 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,7,5 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,7,4 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,7,3 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,7,2 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,6,5 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,6,4 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,6,3 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,6,2 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,5,4 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,5,3 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,5,2 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,4,3 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,4,2 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| Q,3,2 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,T,9 | R | R | R | R | R | R | R | R | R | R | R | R | R |
| J,T,8 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,T,7 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,T,6 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,T,5 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,T,4 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,T,3 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,T,2 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,9,8 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,9,7 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,9,6 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,9,5 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,9,4 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,9,3 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,9,2 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,8,7 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,8,6 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,8,5 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,8,4 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,8,3 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,8,2 | R | R | R | R | R | R | R | R | R | R | F | F | F |
| J,7,6 | R | R | R | R | R | R | R | R | R | 2 | F | F | F |
| J,7,5 | R | R | R | R | R | R | R | R | R | F | F | F | F |
| J,7,4 | R | R | R | R | R | R | R | R | R | F | F | F | F |
| J,7,3 | R | R | R | R | R | R | R | R | R | F | F | F | F |
| J,7,2 | R | R | R | R | R | R | R | R | R | F | F | F | F |
| J,6,5 | R | R | R | R | R | R | R | R | R | F | F | F | F |
| J,6,4 | R | R | R | R | R | R | R | R | R | F | F | F | F |
| J,6,3 | R | R | R | R | R | R | R | R | R | F | F | F | F |
| J,6,2 | R | R | R | R | R | R | R | R | R | F | F | F | F |
| J,5,4 | R | R | R | R | R | R | 1 | R | R | F | F | F | F |
| J,5,3 | R | R | R | R | R | R | 1 | R | R | F | F | F | F |
| J,5,2 | R | R | R | R | R | R | 1 | R | R | F | F | F | F |
| J,4,3 | R | R | R | R | R | 1 | 1 | R | R | F | F | F | F |
| J,4,2 | R | R | R | R | R | 1 | 1 | R | R | F | F | F | F |
| J,3,2 | R | R | R | R | 1 | 1 | 1 | R | R | F | F | F | F |
| T,9,8 | R | R | R | R | R | R | R | R | R | R | R | R | R |
| T,9,7 | R | R | 2 | 1 | 1 | R | R | R | R | F | F | F | F |
| T,9,6 | R | R | 1 | 1 | R | 1 | R | R | R | F | F | F | F |
| T,9,5 | R | R | 1 | R | 1 | 1 | R | R | R | F | F | F | F |
| T,9,4 | R | R | R | 1 | 2 | 2 | R | R | R | F | F | F | F |
| T,9,3 | R | R | 1 | 2 | 2 | 2 | R | R | R | F | F | F | F |
| T,9,2 | R | R | 2 | 2 | 2 | 2 | R | R | R | F | F | F | F |
| T,8,7 | R | R | 2 | 2 | 1 | R | R | 2 | R | F | F | F | F |
| T,8,6 | R | R | 2 | 1 | R | 1 | R | F | R | F | F | F | F |
| T,8,5 | R | R | 1 | R | 1 | 1 | R | F | R | F | F | F | F |
| T,8,4 | R | R | R | 2 | 2 | 2 | R | F | R | F | F | F | F |
| T,8,3 | R | R | 2 | 2 | 2 | 2 | R | F | 1 | F | F | F | F |
| T,8,2 | R | R | 2 | F | 2 | 2 | R | F | 2 | F | F | F | F |
| T,7,6 | R | 1 | F | 1 | R | R | F | F | F | F | F | F | F |
| T,7,5 | R | R | 2 | R | 1 | R | F | F | F | F | F | F | F |
| T,7,4 | R | R | R | 2 | 2 | R | F | F | F | F | F | F | F |
| T,7,3 | R | R | F | F | F | 1 | F | F | F | F | F | F | F |
| T,7,2 | R | 1 | F | F | F | 2 | F | F | F | F | F | F | F |
| T,6,5 | R | 1 | 2 | R | R | F | F | F | F | F | F | F | F |
| T,6,4 | R | R | R | 2 | R | F | F | F | F | F | F | F | F |
| T,6,3 | R | R | F | F | 1 | F | F | F | F | F | F | F | F |
| T,6,2 | R | 1 | F | F | 2 | F | F | F | F | F | F | F | F |
| T,5,4 | R | R | R | R | F | F | F | F | F | F | F | F | F |
| T,5,3 | R | R | F | R | F | F | F | F | F | F | F | F | F |
| T,5,2 | R | 1 | F | 2 | F | F | F | F | F | F | F | F | F |
| T,4,3 | R | R | R | F | F | F | F | F | F | F | F | F | F |
| T,4,2 | R | 1 | 1 | F | F | F | F | F | F | F | F | F | F |
| T,3,2 | R | R | F | F | F | F | F | F | F | F | F | F | F |
| 9,8,7 | R | R | R | R | R | R | R | R | R | R | R | R | R |
| 9,8,6 | 2 | F | F | F | F | F | 1 | R | F | F | F | F | F |
| 9,8,5 | 2 | F | F | F | F | F | 2 | 1 | F | F | F | F | F |
| 9,8,4 | 1 | F | F | F | F | F | F | 2 | F | F | F | F | F |
| 9,8,3 | 1 | 1 | F | F | F | F | F | F | F | F | F | F | F |
| 9,8,2 | R | F | F | F | F | F | F | F | F | F | F | F | F |
| 9,7,6 | F | F | F | F | F | 1 | F | F | F | F | F | F | F |
| 9,7,5 | F | F | F | F | F | F | F | F | F | F | F | F | F |
| 9,7,4 | 2 | F | F | F | F | F | F | F | F | F | F | F | F |
| 9,7,3 | 2 | 1 | F | F | F | F | F | F | F | F | F | F | F |
| 9,7,2 | R | F | F | F | F | F | F | F | F | F | F | F | F |
| 9,6,5 | F | F | F | F | F | F | F | F | F | F | F | F | F |
| 9,6,4 | F | F | F | F | F | F | F | F | F | F | F | F | F |
| 9,6,3 | F | 2 | F | F | F | F | F | F | F | F | F | F | F |
| 9,6,2 | R | F | F | F | F | F | F | F | F | F | F | F | F |
| 9,5,4 | F | F | F | F | F | F | F | F | F | F | F | F | F |
| 9,5,3 | F | 2 | F | F | F | F | F | F | F | F | F | F | F |
| 9,5,2 | R | F | F | F | F | F | F | F | F | F | F | F | F |
| 9,4,3 | F | 2 | F | F | F | F | F | F | F | F | F | F | F |
| 9,4,2 | R | F | F | F | F | F | F | F | F | F | F | F | F |
| 9,3,2 | 1 | F | F | F | F | F | F | F | F | F | F | F | F |
| 8,7,5 and lower: Always fold | |||||||||||||
Key to table:
- R = Raise
- F = Fold
- 1 = Raise if at least one player card match dealer's suit, otherwise fold.
- 2 = Raise if two player cards match dealer's suit, otherwise fold.
Analysis
The following table shows my analysis of California Three Card Poker. The lower right cell shows a house edge of 4.30%.
California Three Card Poker Analysis
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Dealer qualifies, player wins | 2 | 290,810,508 | 0.238074 | 0.476149 |
| Dealer doesn't qulaify, player wins | 1 | 300,919,236 | 0.246350 | 0.246350 |
| Dealer doesn't qualify, player wins or pushes | 0 | 7,303,548 | 0.005979 | 0.000000 |
| Dealer qualifies, player and dealer push | 0 | 745,032 | 0.000610 | 0.000000 |
| Player folds | -1 | 308,444,832 | 0.252511 | -0.252511 |
| Dealer qualifies and dealer wins | -2 | 313,288,044 | 0.256476 | -0.512952 |
| Total | 1,221,511,200 | 1.000000 | -0.042964 |
On average, the player will raise 49.5% of the time. To be specific, the average final wager, counting the Ante and Play is 1.495160 units. This makes the ratio of the expected loss to the total amount bet, what I call the element of risk, 2.87%.