Baccarat RedGreen

PLAYING RULES WITH BONUS

Baccarat RedGreen (first version) and Baccarat Mini RedGreen (second version)

Ranking

Three of a kind. (Automatically wins) see Note 1.
Pairs in descending order from A K Q J 10 9 8 7 6 5 4 3 2 see Note 2.
Individual ranking in descending order from A K Q J 10 9 8 7 6 5 4 3 2.

Note

three of a kind 222 outranks three of a kind AAA only but loses to all other three of a kind from K through 3; and three of a kind AAA outranks all other three of a kind from K through 3 but loses to three of a kind 222
pairs in descending order from A-A pairs to 2-2 pairs (however a 2-2 pair outranks an A-A pair only but loses to all other pairs, an A-A pair outranks all other pairs but loses to a 2-2 pair)

Comparison

Community hands:

Win / win, Win / tie or Tie / win – Wins
Lose / lose, Lose / tie or Tie / lose – Loses
Win / lose, Lose / win or Tie / tie – Pushes

A 5% commission is charged on the winning hand.

Baccarat Red & Green (first version) and Baccarat Mini Red & Green (second version) Dealing procedures.

The Dealer shuffles the cards and Player or the floor supervisor cuts the decks, the Players place their wagers then the Dealer deals three cards to each hand (the Red and the Green hands) The Dealer exposes the two community hands and arranges it according to house rules as described above.

The difference between the Baccarat Red & Green (first version) and the Baccarat Mini Red & Green (second version) are:

1. Baccarat Red & Green (first version), this version plays with three dealers (same as the standard Baccarat), the Dealers are dressed in tuxedoes or not depending on the House policy, one Dealer is on one side of the layout, and deals the cards, hands the cards to the Players, sets both the community hands (the Red and the Green hands) in house way, calls the winning hand or a tied hand. The other two dealers who are on the opposite side of the layout, they are the protectors and are the ones to pay the winning wagers, collects the losing wagers and tracks the commission. The one to the right handles all the Players on the right and the one to the left handles all the Players on the left. It can be played with one and up to six Players on each side, making a total of twelve Players. The Player (as the highest bettor) may peek at his/her hand after the Dealer hands the one face down cards to him/her, he/she will return the cards to the Dealer after he/she peeking the cards.
2. Baccarat Mini Red & Green (second version), this version is played with one dealer. The Dealer is dressed in a tuxedo or not depending on the House’s policy, the Dealer’s job is similar to Mini Baccarat’s. The player may neither peek nor touch any cards during game plays. Game plays with one and up to seven Players. To deal this version, the highest bettor has the right to ask the Dealer to set either the Red community hand or the Green community hand first then the other hand is exposed slowly (note: the key is for the Dealer to expose the cards slowly so as to build up excitement and anticipation for the Players) and then sets it in house way.

House takes 5% commission on all winning hands.

House Way

As mentioned above, the dealer must arrange the Green and Red hands according to the house way:

1. 1. 3 of a kind:
    - If the hand is 3 of a kind, turn it face up.
  2. One pair:
    - Always play a pair in the 2 Card hand, with the following exceptions:
      1. Split a pair of Aces if the 1 Card hand is not a King.
      2. Split a pair of Kings if the 1 Card is not a Jack or better.
  3. Nonpair:
    - Always play the second highest card in the front hand, and the other two cards in the back hand. (the 1 Card hand can not be higher than the 2 Card hand)

Bonus Side Bet

In addition to the mandatory bet played against Red and Green hand, the player has the option to make a bonus side bet. Both the Red and Green hands are used to determine the outcome of the side bet. The player will be paid if the best 5 of the combined 6 cards match any of the following winning combinations:

Cheat Sheets

Analysis

ANALYSIS

Rules of Play

Red & Green, Version 1, is a new casino table game that uses seven decks of cards. It can be played by up to 12 players.

The game begins with each player betting that either a “Red” hand or a “Green” hand will win. The dealer will deal three cards to the Red hand and three cards to the Green hand. The dealer will arrange each hand into a 1-card front hand and a 2-card back hand according to the house way. The front hand must not be stronger than the back hand.

The Red hand and Green hand will be compared according to the rankings below:

1) 3 of a Kind (Ace highest, Deuce lowest*)

2) 1 pair (Ace highest, Deuce lowest**)

3) High card (Ace highest, Deuce lowest)

* Three 2s will outrank three Aces.

**A pair of 2s will outrank a pair of Aces.

A 3 of a kind is the highest hand. If one hand is 3 of a kind and the other is not, the other hand loses. Otherwise, the higher 3 of a kind wins except in the case of 3 Aces vs. 3 Deuces.

When the Red hand is compared with the Green hand, or vice versa, the 1-card hands are compared first. The higher rank wins; if both are the same rank it’s a tie. Then the 2-card hands are compared. A pair beats no pair. A pair of 2s beat a pair of Aces. If neither hand is a pair, then whichever hand has a higher card wins. For example, 9-5 beats 9-4. In the event of a tie, it’s a tie. The outcome of comparing the Red hand with the Green hand is adjudicated by the following rules:

House Way

As mentioned above, the dealer must arrange the Green and Red hands according to the house way:

1. 1. 3 of a kind:
    - If the hand is 3 of a kind, turn it face up.
  2. One pair:
    - Always play a pair in the 2 Card hand, with the following exceptions:
      1. Split a pair of Aces if the 1 Card hand is not a King.
      2. Split a pair of Kings if the 1 Card is not a Jack or better.
  3. Nonpair:
    - Always play the second highest card in the front hand, and the other two cards in the back hand.

Mathematical Analysis

There are C364,3 x C361,3 = 7,971,964 x 7,775,940 = 61,989,513,746,160 ways to deal three cards to one hand from 7 decks of cards and then 3 cards to the other hand from the remaining deck of 361 cards. However, there are only 455 distinct 3-card hands since suits are irrelevant.

If there were no ties, then no mathematical analysis would be necessary to determine the house advantage since the Red hand and the Green hand would beat each other exactly 50% of the time to yield a house advantage of 50% x 5% = 2.5%.

Therefore, a computer program was written to determine the tie frequency in order to determine the exact house advantage. The software cycled through all hand combinations possible. For each distinct 3-card Red hand, the software would deal all 3-card Green hands from the remaining deck, compare the hands, and note down the results. It turned out that either hand will

1. - win 35.2472%,
  - lose 35.2472%, and
  - tie 29.5057% of the time.

Since a 5% commission is charged on the winning hand, the house advantage is 35.2472% x 5% = 1.7624%.

Bonus Side Bet

In addition to the mandatory bet played against the dealer, the player has the option to make a bonus side bet. Both the dealer’s hand and the player’s own hand are used to determine the outcome of the side bet. The player will be paid if the best 5 of the combined 6 cards match any of the following winning combinations: