PLAYING RULES

This game requires at least two Players and one House Dealer with the Players betting against the Player Dealer.  Each Player wagers on whether the Player’s hand will have a higher sum than the Player Dealer’s hand (without exceeding ten). This game plays similar to the game 21 (No Bust Black Jack).  It is played with six to eight conventional decks of forty playing cards consisting essentially of Ace through Ten for each of the four suits (Note:  all Face cards J,Q and K are removed).

Dealing Procedures

Each Player places a base wager at a Player wagering area on the table layout. After the cards are randomized, such as through shuffling and cutting, the House Dealer deals a single card face up to each wagering Player and a single card face down to Player Dealer. The Player Dealer always receives the last card and has to place it in front of him/her (or in front of House Dealer according to House policy).  The first card will start from the Player Dealer’s (or House Dealer’s) left to right (clockwise order) to each Player and the Player Dealer. Each Player in turn, forms a final hand by opting to receive additional cards or stand on the single card initially dealt. The values of the cards in the Player’s final hand are summed. In summing the cards, the Ace is designated as having a value of zero or one.  An Ace is valued (Zero) only in an initial two-card hand composed of an Ace and a 10,  in which case the hand’s total is 10 instead of 11 (busting hand) but with other cards an Ace has the face value of one. The Players’ objective in forming their final hand is to obtain a sum closer to ten than the Player Dealer’s sum without exceeding ten.

• Busting hands:  If the Player exceeds ten, then the Player must wait until the Player Dealer forms his/her hand, then resolves the Player’s wager as follows: If the Player exceeds ten but the Player Dealer does not exceed ten, the Player loses his/her wager, if both the Player and the Player Dealer exceeds ten, but the Player Dealer is closer to or an equal distance from ten than the Player, the Player loses his/her wager (e.g. Player loses with a 3♥ 9♣ or a 3♣ 8♦ if the Player Dealer has a 2♥ 9♠); if both the Player and the Player Dealer exceeds ten, and the Player is closer to ten than the Player Dealer, the Player pushes on his/her wager, i.e. the wager is returned (e.g. Player pushes with a 2♥ 9♠ if the Player Dealer has a 2♥,10♣).
• Double Aces are automatic win (pays 3 to 2):  If the Player forms a final hand consisting essentially of only two Aces, the Player automatically wins and is rewarded 3 to 2 (3:2).  However, if the Player Dealer’s final hand also consists of two Aces a push is declared.  Additionally, a push hand is declared if both the Player and the Player Dealer’s final hands have identical sums without exceeding 10.
• Double Down:  In an optional embodiment, if the Player’s first dealt card is an Ace, the Player may have the option of increasing (double down) his/her base wager in exchange for a single additional card (one additional card only). The Player automatically wins if the single additional card dealt to the Player is an Ace (if the Player Dealer without 2 Aces (Double Aces)).
  • For example, if the Player receives an initial hand, A♣, he/she may opt to increase his/her base wager, if the single additional card dealt to the Player is an A♠ to form a hand of A♣ A♠ (Double Ace), the Player is rewarded based on the increased (double down) base wager. In the event that the Player Dealer also forms his/her final hand A♥ A♦, a push is declared and the Player’s base and double down wager is neither collected nor rewarded. In another example, the increased base wager of the initial hand A♣ and the single additional card dealt to the Player is 2♠ to form a final hand 3, the increased base wager is resolved as described below. (The House may have the option to allow the Players to increase (double down) their base wager either on an Ace only or on any initially dealt card).
• House Way:  After each Player forms a final hand, the Player Dealer forms a final hand. In forming the final Player Dealer hand, the Player Dealer optionally plays according to predetermined set of House rules. For example, in an optional embodiment, the Player Dealer receives additional cards until his/her total is greater than or equal to six (hits on 5 or less and stands on 6 or higher).  Once the Player Dealer has formed a final hand, the Player Dealer sums the values of the cards in the Player Dealer’s final hand and compares his/her final hand with each Player’s final hand. The hand having a sum closer to ten, without exceeding ten, is the winning hand. In the event that the Player and the Player Dealer have identical sums, a push is declared and the wager is neither collected nor rewarded.
  • For example, if the Player Dealer has the final hand 2♥ 6♦ = 8 and the Player has a final hand 5♣ 4♠ = 9, the Player is declared the winner and rewarded according to his/her base wager. Conversely, if the Player Dealer has a final hand A♥10♣ = 10 (with a 10 an Ace, an Ace has a value of zero) and the Player has a final hand 3♣ 6♥ = 9, the Player Dealer is declared the winner and the Player’s base wager is collected.  If the Player has the hand 2♥ 6♦ = 8 and the Player Dealer also has the hand 3♦ 5♣ = 8, a push is declared and the Player’s base wager is neither collect nor rewarded.  If the Player Dealer forms the final hand 2♣ 3♥ 6♣ = 11 or A♥ 3♥ 7♣ (an Ace has a value of 1) =11, which exceeds ten (a busting hand), all the remaining Players who have not exceeded the target value of ten or received an automatic winning hand are rewarded based on their base wagers.

Double Ace, No Bust Community Side Bet

Five Card Poker Bonus Hand

Game plays without Face cards, Jack, Queen and King had been removed

Player places the side bet in the circle D that mean player plays the Dealer Poker bonus hand, such as below:

1. After the dealer stands on his/her first card initially dealt or done hitting his/her final hand then the Dealer compare his/her hand to each player final hand,  after  the Dealer done paying the winning or takes the losing wagers.
2. Then the Dealer draws his/her hand to the total of 5 cards to create 5 cards Poker bonus hand. For example: Dealer hand first dealt card is a 4, he/she has to hit until 6 or higher. (hits on 5 or less and stands on 6 or higher) Dealer hits the second card is a 3 (4+3=7), Dealer draws 3 cards from the shoe ( the drew cards (Supplemental cards) are 3,4 and 10) and places it a little low to the right side of the Dealer final hand.  The Dealer Poker hand are 4,3 + 3,4,10 is a two pairs, this hand is matched one of the 5 Cards Poker Bonus Payout Table below, any Player who places the side bet in the circle D has to be paid as the two pairs payout.

Fortune Double Ace, No Bust Bonus Payout Table: plays with five cards, Dealer 1 or hitting cards Plus 1 or 4 of drawing cards (supplemental cards) from the shoe.

Double Ace, No Bust Individual Side Bet

Five Card Poker Bonus Hand

Game plays without Face cards, Jack, Queen and King had been removed

Player places the side bet in the circle P that mean the player draws his/her own Poker bonus hand  such as below:

1. After Dealer deals one cards to each player and to him/herself then the Dealer deals 4 community cards (Supplemental Cards) in order, the first card place at  number 1, the second card at 2, the third card at 3 and the fourth card at 4 on the  layout at the right side of the Dealer. Player may stand on any of his/her first card  initially dealt, but the Dealer has to hit on 5 or less and stands on 6 or higher. If  the Player exceeds 10, then the Player must wait until the Dealer forms his/her final  hand, then resolves the Player’s wager as follows: If the Player exceeds 10 but the  Dealer does not exceed 10, the Player loses his/her wager, if both the Player and the  Dealer exceeds 10, but the Dealer is closer to or an equal distance from 10 than the  Player, the Player loses his/her wager (e.g. Player loses with a 3♥ 9♣ or a 3♣ 8♦ if the  Dealer has a 2♥ 9♠); if both the Player and the Dealer exceeds 10, and the Player hand  is closer to 10 than the Dealer, the Player pushes on his/her wager, i.e. the wager is  returned (e.g. Player pushes with a 2♥ 9♠ if the Dealer has a 2♥,10♣). After the Dealer is done paying the winning or collecting the losing wagers. Then the Dealer will form the 5 cards Player Poker Bonus hand, such as below:
2. If any player whose final hand with 5 cards, his/her hand need no any supplemental card. If his/her final 5 cards match one of the 5 Cards Poker Bonus  Payout Table below then he/she wins that amount otherwise his/her side bet wager has to be collected.
3. Then the Dealer turn over the first community card at the number 1 on the layout to combine it to the Player whose final hand with 4 cards ( 4 + 1 cards = 5  cards) if his/her 5 cards match one of the 5 Cards Poker Bonus Payout Table then  wins that amount, after the Dealer paying the winning or takes the losing wagers.
4. Then the Dealer turn over the second community card to combine it to the player whose final hand with 3 cards…
5. Then the 3^rd card to combine it to the final hand with 2 cards…
6. Then the 4^th card to combine it to the final hand with 1 cards…

If any player whose final hand + 1 or 4 of the community cards (supplemental cards) (total 5 cards) which mention above and match one of the 5 Card Poker Bonus Payout Table below then win that amount.

Fortune Double Ace, No Bust Bonus Payout Table: plays with five cards, Player 1 or hitting cards Plus 1 or 4 of Community cards (Supplemental cards)

ANALYSIS

No Bust Double Ace is a new casino table game similar to blackjack. It is played with 6 standard decks of cards with all face cards removed from each deck. So, each deck has 40 cards.

Rules of Play

The object of the game is to get as close to 10 as possible in order to beat the dealer’s hand. 2s through 9s count as their face value, and aces count as 1 or 0. Only in an initial two-card hand composed of an ace and a 10 can the ace count as 0, in which case the hand’s total is 10 instead of 11.

The game begins with each player making a blackjack-style primary bet against the dealer. The player also has the option to make a Bonus side bet. The Bonus side bet has two versions. One is based on five cards and one is based on six cards. The casino operator has the option of offering either one.

Once all players have made their bets, the dealer deals one card face up to each player and one card face down to himself. Depending on the version of the Bonus side bet pay table in use, the dealer will also deal four (the five card version) or five (the six card version) community cards to the left of the chip rack. Each community card will be placed face down in the community card area with card spaces numbered from 1 to 4 (or 5).

The player now has the option of drawing more cards, standing or doubling down. The player can double down only on the first card. When doubling down, the player must put up a second bet equal to his original bet and then the dealer will deal him one card.

After all players have made their decisions concerning their primary bets, the dealer will expose his card and play out his hand to settle the primary bets. The dealer must stand on 6 or above and draw more cards otherwise. Two aces are the highest hand.

If neither the dealer nor the player hand has gone over 10, then whoever has the higher total wins the hand and ties are pushes. If the player hand exceeds 10 and the dealer hand is 10 or below, then the player loses. If the dealer hand exceeds 10 and the player hand is 10 or below, then the player wins. If both the dealer hand and the player hand exceed 10, then:

• the player loses if the dealer hand is closer to 10 than is the player hand;
• the bet pushes if the player hand is closer to 10 than is the dealer hand;
• the player loses if the player hand and the dealer hand tie.

A player’s AA (two Aces) pays 3 to 2 and all other winning hands are paid even money.

Note that a player’s AA pushes the dealer’s AA.

Once all primary bets have been settled, the dealer will expose the community cards to settle the Bonus side bets. Players who made the Bonus side bet will use all the cards in their hand plus as many community cards as necessary to form a five (or six) card poker hand. For example, if the player has three cards in his hand, then community cards 1 and 2 will be used to complete the player’s poker hand for the five card Bonus side bet.

If the poker hand matches any winning hand combination according to the Bonus pay tables below then the player wins the Bonus side bet:

NOTES

(A) A flush can be composed of pairs or triplets, which are ignored. For example, the following are valid flushes:

(B) There are six instead of ten straights: A2345, 23456, 34567, 45678, 56789 and 678910.

(C) The six card Bonus pay table includes two winning hand combinations that use all six cards: the 6 of a kind and 3 pair. Otherwise, only the best five of the six cards are used.

Five Card Bonus Side Bet

There are C_240,5 = 6,363,048,048 ways to deal a 5 card hand from a 240-card deck. The probability distribution is shown below:

The win frequency for both pay tables is 19.14%.

Six Card Bonus Side Bet

There are C_240,6 = 249,219,381,880 ways to deal a 6 card hand from a 240-card deck. The probability distribution is shown below:

The win frequency for both pay tables is 19.83%.

Primary Bet

A combinatorial analyzer was written to determine the player’s optimal strategy. The analyzer cycled through all possible player-dealer hand combinations and determined the best play for the player at each decision point.

d … double              h … hit          s … stand

6 decks

The player should double down on an Ace. The house advantage is 0.84% of the initial wager or 0.76% per total wager.

No study was conducted to ascertain whether the game could be vulnerable to card counting.

Presented By: Stanley Ko
GAMBOLOGY – PO Box 82225 – Las Vegas, NV 89180 – (702) 258-9685
February 13, 2007