Instant Poker Money

[casinoguy]

TRI-CARD POKER - Game Play
The player can place either the Pair Plus bet or the Ante bet, or both. After placing his bets, both the player and the dealer receive three cards. If the player bets on Pair Plus, he is rewarded according to the Pair Plus Payout Table if his hand contains a pair or better. If the player bets on Ante, he must now decide either to fold, if he does not think he can beat the dealer’s hand, or to raise and challenge the dealer. If the player chooses to fold, he loses the Ante bet AND the Pair Plus bet (if he placed one) and the game is over. If the player chooses to raise, he bets an additional amount equal to the ante bet, the dealer reveals his cards, a winner is determined, win paid if applicable, and the game is over.

To determine the game winner after the player has raised, the dealer’s hand must first “qualify”. In Tri-Card Poker, the dealer’s hand qualifies if it ranks as High Card with a Queen or ranks as a Pair or better. If the dealer’s hand does not qualify, the player wins 1 to 1 on the ante bet and “pushes” the raise bet (i.e. the player gets the raise bet back without winning or losing).

If the dealer’s hand does qualify, the best ranking hand wins. If the dealer’s hand ranks higher, the player loses both the ante bet and the raise bet. If the player’s hand ranks higher, the player wins 1 to 1 on both the ante and raise bets, and wins the raise bet calculated according to the Pay Tables, below. If both the dealer’s hand and the player’s hand have the same rank, the highest ranking card determines the winner (for example, a Pair of Kings beats a Pair of 10s). Finally, if the dealer’s hand ties the player’s hand both the ante bet and the raise bet are pushed back to the player.

If the player places an ante bet, raises the bet, and his hand contains a straight, three of a kind, or a straight flush, he is paid a bonus according to the Ante Bonus Payout Table (regardless of whether or not the dealer qualifies).

[markandreson]

Calculating Frequency of 3-Card Poker Hands

The following describes a method for calculating the frequency of 3-card poker hands. The calculations make extensive use of the combination without repetition formula (combine formula in Excel) nCr = n! / (r! x (n - r)!)

Any Hand - Total number of 3-card poker hands drawn from a 52 card standard deck.

52C3 = 22100

Straight Flush - There are 12 differently ranked straight flushes from A-2-3 up to Q-K-A in each of the 4 different suits.

12C1 x 4C1 = 48

Three of a Kind - There are 13 differently ranked three of a kinds using 3 of the 4 suits.

13C1 x 4C3 = 52

Straight - The are 12 differently ranked straights from A-2-3 up to Q-K-A. Each of the cards can be 1 of the 4 suits with the straight flushes being excluded.

12C1 x (4C1)3 - 48 = 720

Flush - A flush contains 3 of the 13 ranks, each card belonging to 1 of the 4 suits. The straight flushes are excluded.

13C3 x 4C1 - 48 = 1096

One Pair - There are 13 differently ranked pairs using 2 of 4 suits, the third card being 1 of the 12 remaining ranks using 1 of the 4 suits.

13C1 x 4C2 x 12C1 x 4C1 = 3744

Nothing - Any hand not being one of the above type of hands.

52C3 - 48 - 52 - 720 - 1096 - 3744 = 16440 ccda
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