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Three Card Prime
Three Card Prime is very similar to Three Card Poker. In both games, the object is to have a higher ranking three-card poker hand the dealer. The only decision is to fold or raise after getting your hand.
- Player makes an Ante bet. At this time he may optionally bet on the Pair Bonus and Prime side bets.
- The dealer gives each player three cards and himself three cards. The player may examine his own cards. The dealer's cards are dealt face down.
- If the player made the Ante bet, then he has must either fold or raise.
- If the player folds, then he forfeits his Ante wager.
- If the player raises, then he must make an additional Play bet, equal exactly to his Ante bet.
- The dealer will turn over his cards.
- The dealer needs a queen high or better to qualify.
- If the dealer does not qualify, then Ante will push and the Play bet will pay according to the pay table below.
- If the dealer qualifies, then the player's hand will be compared to the dealer's hand, the higher hand wins. The order of poker hands is indicated below.
- If the player has the higher poker hand, then the Ante will pay even money and the Play according to the pay table below.
- If the dealer has the higher poker hand, then the Ante will lose. If the player has flush or less, the Play will also lose. In the unlikely event the player loses with a straight or higher, the Play bet will pay according to the pay table below.
- If the player and dealer tie, then the Ante will push and the Play will pay according to the pay table below.
- The Pair Bonus pays based mostly on the player's hand only. If the player has a paying hand of a pair or higher a dummy card will be revealed that will increase the win, if it is a deuce, according to the pay table below.
- The Prime bet pays at least 3 to 1 if the player's three cards are the same color. If all six cards between the player and dealer hands are the same color, then it pays 4 to 1.
The following table shows the hand order in Three Card Prime.
Hand Order and Probabilities in Three Card Prime
|Three of kind||52||0.002353|
The following table shows the pay table for the Play bet. All wins on a "to one" basis.
Play Bet Pay Table
Wins or Ties
|Three of a kind||5||10|
|Flush or less||1||Loss|
The following table shows the pay table for the Pair Bonus bet. All wins on a "to one" basis.
Pair Bonus Pay Table
|Three of a kind||30||40|
The Prime bet is nice and simple, as shown in the following pay table. The top award requires all player cards and dealer cards to be the same color. All pays are on a "to one" basis.
Prime Pay Table
|All six cards same color||4|
|Player cards all same color||3|
Comparison to Three Card Poker
Mathematically, the base game in Three Card Prime works out to the same thing as Three Card Poker, except the player wins more if he has a straight or higher and loses to the dealer. Semantically, there are some changes too. If the dealer doesn't qualify, now it is the Ante that pushes instead of the Play. No longer is there an Ante Bonus, but the Play bet pays a premium for hands of a straight or higher. It works out to the same thing except the Play bet pays a premium for a losing hand of a straight or higher, known as "Bad Beat Bonus."
In addition, the Pair Bonus is like the Pairplus but pays a premium of a fourth dummy card is a deuce. Finally, they add another side bet called the Prime, which wins if the player's three cards are the same color.
If you're not familiar with Three Card Poker rules, read the rules section for the complete rules.
Ante and Play Analysis
The next table shows the probability and return for all possible outcomes for the base game.
Base Game Return Table
|Player loses with flush or less||-2||91,126,832||0.223805||-0.447610|
|Player loses with straight||1||270,504||0.000664||0.000664|
|Player loses with three of a kind||4||3,312||0.000008||0.000033|
|Player loses with straight flush||5||968||0.000002||0.000012|
|Player ties with flush or less||1||249,216||0.000612||0.000612|
|Player ties with straight||2||18,288||0.000045||0.000090|
|Player ties with three of a kind||5||-||0.000000||0.000000|
|Player ties with straight flush||6||132||0.000000||0.000002|
|Player ties with mini royal||10||12||0.000000||0.000000|
|Player has flush or less, dealer doesn't qualify||1||80,937,492||0.198780||0.198780|
|Player has straight, dealer doesn't qualify||2||4,001,004||0.009826||0.019653|
|Player has three of a kind, dealer doesn't qualify||5||288,960||0.000710||0.003548|
|Player has straight flush, dealer doesn't qualify||6||239,316||0.000588||0.003527|
|Player has mini royal, dealer doesn't qualify||10||26,880||0.000066||0.000660|
|Player wins with flush or less||2||87,096,380||0.213906||0.427813|
|Player wins with straight||3||8,975,484||0.022044||0.066131|
|Player wins with three of a kind||6||665,776||0.001635||0.009811|
|Player wins with straight flush||7||570,240||0.001400||0.009803|
|Player wins with mini royal||11||46,804||0.000115||0.001264|
The table above shows the house edge, defined as the ratio of the expected loss to the Ante bet, is 3.10%. The player will raise 67% of the time, for an average wager of 1.67. That makes the Element of Risk, defined as the expected loss to the total amount bet, 3.10%/1.67 = 1.85%.
Pair Bonus Analysis
The following table shows the probability and return for the Pair Bonus bet. The lower right cell shows a house edge of 4.52%
Pair Bonus Return Table
|Mini royal with deuce||75||16||0.000015||0.001108|
|Mini royal without deuce||50||180||0.000166||0.008311|
|Straight flush with deuce||50||168||0.000155||0.007757|
|Straight flush without deuce||40||1,988||0.001836||0.073432|
|Three of a kind with deuce||40||204||0.000188||0.007535|
|Three of a kind without deuce||30||2,344||0.002165||0.064937|
|Straight with deuce||8||2,760||0.002549||0.020390|
|Straight without deuce||6||32,520||0.030030||0.180183|
|Flush with deuce||4||4,128||0.003812||0.015248|
|Flush without deuce||3||49,576||0.045781||0.137342|
|Pair with deuce||2||14,112||0.013032||0.026063|
|Pair without deuce||1||169,344||0.156380||0.156380|
The following table shows the probability and return for the Pair Bonus bet. The lower right cell shows a house edge of 3.62%
Prime Return Table
- at the Galaxy Gaming web site.
- in my forum at Wizard of Vegas.