BACKGROUND OF THE INVENTION

Blackjack or twenty-one is a well-known casino card game. Blackjack is played with one or more standard decks of 52 cards between a dealer and one or more players. The object of the game is for a player to accumulate a hand of cards having a point total exceeding that of the dealer, without exceeding twenty-one. For numbered cards, the point value equals the number value. Face cards (kings, queens, and jacks) have a point value of ten. Aces are assigned a point value of either one or eleven as determined by the person holding the hand that included one or more aces. A two-card hand having a total point value of twenty-one is known as blackjack.

Blackjack play is commenced by a player making an initial wager (â€œthe anteâ€ ) on the outcome of his or her upcoming hand. Players typically indicate their bet or wager by placing an appropriate number of chips or markers in a designated area of the blackjack table.

After the wagers have been placed, the dealer deals two cards to each player and to him or herself. Each of the players' cards is dealt face up or face down depending on the number of decks being used. The dealer's initial two cards are typically dealt one face down and the other face up. The dealer deals one card at a time to each player and then to the dealer before repeating the process with the second card.

After the dealer and the players have been dealt an initial hand of two cards, each player in turn elects to receive additional cards (â€œhitâ€ ) or to wait (â€œstandâ€ ). A player may elect to take additional cards until he or she decides to stand or until the total point value of the player's hand exceeds twenty-one, known as â€œbust.â€ Once all players have either received their desired number of cards or have busted, the dealer turns over the face-down card. Based on the value of that card, the dealer takes additional cards or stands. Under most rules, a dealer must â€œstandâ€ if the dealer's hand is equal or greater than seventeen and â€œhitâ€ if the hand is less than seventeen.

Once the dealer has completed the play, the outcome of the game is determined. A player wins if either the dealer busts (dealer's hand exceeds twenty-one) or the player's hand has a greater point value than the dealer's hand. The winning player is paid at 1:1, i.e. receives an amount equal to the initial wager in addition to recovering the initial wager. If the dealer's hand exceeds that of a player's or if a player busts, the wager is lost. If a dealer and the player have equal hands (known as â€œtieâ€ or â€œpushâ€ ), the wager is returned to the player.

During the game, the players have a chance to increase their initial bet (â€œup the anteâ€ ). In addition, a player may split the hand in two hands each hand being supported by two wagers, each of an amount equal to the original wager. Another option is to â€œdouble downâ€ , i.e. double the wager in exchange for an additional card.

To increase the interest of the players, the blackjack game is often modified by various side wagers or side bets. Side wagers are attractive to players because they are perceived as â€œhedgingâ€ the player's chances. For example, a player may bet on a particular outcome of his or her hand. (U.S. Pat. No. 7,222,854). If the outcome is such that the main game is lost but the value of the hand matches the side bet, the player loses the main bet but collects money on the side bet. A similar bet may be placed on the outcome of the dealer's hand (U.S. Pat. Nos. 6,536,767 and 6,113,102). If the dealer receives a winning hand, but the hand also matches the player's side bet, the player loses the main wager but wins the side bet.

In a more exciting variation of side betting, the players bet on a particular card, such as the next card being dealt. For example, a player may bet that the next card he or she receives will have a particular value (Canadian Application No. 2,281,350). Alternatively, a player may bet on the dealer's face-up card (U.S. Pat. No. 6,796,898) or a dealer's face-down card (U.S. Pat. No. 5,743,532).

Most side wagers are placed at the same time with the main wager. At that time, before any cards have been dealt, the players cannot form any predictions regarding the outcome of the hands and rely only on luck. In a more attractive variation, the side bets are placed after one or more cards have been revealed. For example, a player may be allowed to place a side bet on the outcome of his or her own hand after the initial card has been dealt to the players and the dealer (U.S. Pat. No. 6,302,396).

Players generally perceive side bets placed in the middle of the game as â€œsaferâ€ because something about the hands is already known. A variation of such side bets is known as â€œinsuranceâ€ . An insurance wager may be placed only if the dealer's face up card is an ace. Traditionally, insurance bets are up to one half of the original bet amount. The insurance bet â€œinsuresâ€ the player against the dealer's face-down card being a ten. (In that case the dealer's hand equals twenty-one or blackjack). If the dealer indeed has twenty-one, the insurance is paid at 2:1. In other words, the player loses the original wager, but gets the money back (the insurance wager was one-half of the original wager but receives a 2:1 return). If the player also has twenty-one, the insurance wager is lost but the original wager is returned.

Some modifications of the traditional insurance wager have been described. For example, an insurance wager may be placed if the dealer's face up card has the value of ten (is a â€œtenâ€ or a face card). This bet insures the player against any selected outcome of the player's hand or the dealer's hand. If the actual outcome matches the insured outcome, the player wins the insurance bet. (See for example, U.S. Pat. No. 6,796,898). Such system of insurance provides poor odds for the house. Compared to traditional insurance, the modified version may be placed more often and allows betting on any outcome. With proliferation of card counting, such a system offers players many opportunities to place bets that have a good chance of winning.

The goal of the house is to ensure maximum participation of the players, while keeping the odds in favor of the house. Side wagers generally attract players because they are perceived as an extra chance. Side wagers placed after some cards have been revealed are even more attractive because players feel more in control. It would be especially beneficial for the house to have a side bet with very low chance of winning, which nevertheless would be very attractive to players.

SUMMARY OF THE INVENTION

The invention is an improved blackjack game with a side wager. The side wager may be placed only if the sum of dealer's first two cards equals ten or eleven. The side wager is betting on the next dealer's card being â€œany tenâ€ , i.e. a ten, king, queen or jack. The side wager is resolved independently of the outcome of the main game.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is a blackjack game with a side wager. The game requires a dealer and one or more players. Generally, the game proceeds according to the traditional rules of blackjack. First, the players place their wagers. These are â€œtraditionalâ€ blackjack wagers that will be resolved according to the traditional rules of the game. Then the dealer deals the first card. The dealer starts from one side (preferably the left of the dealer) and passes a card to each player and then to him or herself. Then the process is repeated with the second card. The players' cards are placed face up. The first dealer's card is placed face down and the second dealer's card is placed face up.

At this stage, some players may already win the game if they receive a hand that equals twenty-one. If not, the game continues as the players choose to â€œstandâ€ , i.e. not receive any more cards, or â€œhitâ€ , i.e. request another card from the dealer. Next, the dealer must reveal his face-down card. If the total value of the dealer's hand equals ten or eleven, the players are allowed to place a side wager. The side wager is betting on the dealer's next card having the value of ten. Four cards are included in this outcome: â€œnatural tenâ€ , king, queen and jack.

After the dealer receives his or her next card, the side wagers are resolved. If the dealer receives one of the four cards covered by the wager, the players are paid on their side wagers. Notably, this also means that the dealer has received either twenty or twenty-one and in most instances, the â€œtraditionalâ€ blackjack wagers are won by the house.

If the dealer's card is not ten, the side wagers are collected and the round of blackjack is completed according to the traditional rules, i.e. the cards are dealt until all of the players and the dealer have either received a desired number of cards or have â€œbustedâ€ . If the dealer busts, the players are returned their wagers and get paid an amount equal to the wager. The same amount is paid if a player's hand exceeds the value of the dealer's hand. If a player busts or has a hand smaller than the dealer's, the player loses the wager. Finally, if the player's hand and the dealer's hand are equal in value, the wager is returned to the player.

The side wager on â€œany tenâ€ can be, for example, any amount up to 100% of the â€œtraditionalâ€ blackjack wager (including all increases of the main wager such as splitting and doubling down). The side wager pays in accordance with the original amount allowed for the side wager. The purpose of this limitation is not to allow players more than the recovery of their main wager. If the player wins the side wager, this most likely means that the house won the main wager. If the player is allowed to bet 100% of the main wager as a side wager, the side wager should pay at 1:1. If the player is allowed to bet 50% of the original bet as a side wager, the side wager should pay at 2:1. With such rules, the players at best, break even (i.e. lose the main wager but recover the loss through the side wager).

Preferably, the side wager is 50% of the total wager and pays at 2:1. As explained in further detail below, psychologically, such a side wager would be very attractive to the players as a chance to â€œsave the situationâ€ . Optionally, side bets with higher stakes and higher odds are also possible as explained in the subsequent section.

Another option, is to open the side wager only to those players whose hands are active (i.e. players who are not â€œstandingâ€ and have not â€œbustedâ€ ) when the dealer turns their face-down card.

The side wager offered by the present invention holds a special attraction to the players in several ways. First, the wager incorporates an â€œactive flopâ€ , i.e. betting on the turn of the next card that is resolved instantly. The excitement generated by such bets is well known from poker.

Second, the side wager of the present invention is perceived as a way out of a bad situation. When the dealer's hand is ten or eleven, the players fear that they will lose the round. If the dealer's next card is valued at ten, the dealer's hand will be either twenty or twenty-one. The players fear that the chance of the dealer getting a card valued at ten is higher than getting a card of any other value. Justifiably so: in each suit, ten is assigned to four separate cards: â€œnatural tenâ€ , king, queen and jack. When the player is allowed to bet on â€œany-tenâ€ as the dealer's next card, the player perceives that he or she is hedging against a likely negative outcome. However, as explained in detail below, the odds still favor the house.

Psychology plays an important role in decisions made at the blackjack table. Specifically, it is known that most players perceive that the dealer's face-down card is a ten. This is illustrated by the way in which most players react to the dealer's face-up card.

For example, if the dealer's face-up card is six, the players often stand. This is because they perceive that the dealer has sixteen (six plus the face-down ten). This requires the dealer to take an additional card and the dealer will likely bust and the players will win. This illusion often hurts players: if the dealer had less than sixteen, the dealer does not bust. However, the player's hand now is too low to win because the player decided to â€œstandâ€ and not take additional cards.

Similarly, if the dealer's face-up card is ten, the players perceive that the dealer has a total of twenty. In reaction to the dealer's ten, players usually hit. This is because they are trying to beat twenty, i.e. get twenty-one. This way players bust when they could have won by just â€œstandingâ€ .

Finally, if the dealer's face-up card is low (between two and six), the players perceive this as a winning situation. In response, players double up or split to increase their bets. This is because they perceive that the dealer has between twelve and sixteen. Then the dealer will definitely have to take another card and will likely bust. The perception changes dramatically when the dealer reveals the face-down card and it turns out that instead of twelve to sixteen, the dealer's hand is ten or eleven. The players know that ten is the most frequently occurring value of the card. A ten-value card will bring the dealer's hand to twenty of twenty-one. Such a situation is perceived as losing for the players.

When a perceived winning situation is turned into a losing situation, players want a way out. The present invention offers a way to hedge against the most dreaded outcome: dealer's next card having the value of ten (â€œany tenâ€ ).

The present invention is reminiscent of the traditional insurance side bet. An insurance bet is placed when the face-up card is an ace. Then the players are allowed to bet that the face-down card is a ten. As is explained below, psychologically, the present invention is different from insurance in several critical ways.

First, when the dealer has an ace, the players habitually expect to lose the round, become passive and prefer to wait for the next round. In contrast, the present invention anticipates that the round starts with the dealer having a low card (two-to-six). The players perceive this as a winning situation. They split, double up or otherwise increase bets. When suddenly the â€œluck turnsâ€ , the players actively seek a way to save the situation. Instead of remaining passive, as is often the case with insurance, the players are likely to place the side wager.

Second, in the case of insurance, the side wager is betting on the value of the dealer's face-down card. That card is already been drawn. Psychologically, betting on a card that has not yet been drawn is more exciting and inspires more hope of winning.

Finally, insurance bets are well known in the art. Many blackjack guides and strategy manuals warn players against insurance (see for example www.blackjackinfo.com, section â€œBlackjack Rulesâ€ and en.wikipedia.org/wiki/Blackjack, section â€œInsuranceâ€ ).

Thus the side bet of the present invention holds a strong attraction for the players. As is shown below, the side wager of the present invention also has the odds that favor the house. The calculation of the odds is as follows¹:

In a 52-card deck, the chances of a two-card hand that equals ten is 4% or 1:25. The calculation is shown in Table 1.

TABLE 1DEALERS HANDS THAT EQUAL 10CombinationOdds2 + 84/52 Ã— 4/51 = 0.0063 + 74/52 Ã— 4/51 = 0.0064 + 64/52 Ã— 4/51 = 0.0065 + 54/52 Ã— 3/51 = 0.0046 + 44/52 Ã— 4/51 = 0.0067 + 34/52 Ã— 4/51 = 0.0068 + 24/52 Ã— 4/51 = 0.006Total0.006 Ã— 6 + 0.004 = 0.04,4% or 1:25

In a 52-card deck, the chances of a two-card hand that equals eleven is 4.8% or 1:20.8. The calculation is shown in Table 2.

TABLE 2DEALERS HANDS THAT EQUAL 11CombinationOdds2 + 94/52 Ã— 4/51 = 0.0063 + 84/52 Ã— 4/51 = 0.0064 + 74/52 Ã— 4/51 = 0.0065 + 64/52 Ã— 3/51 = 0.0069 + 24/52 Ã— 4/51 = 0.0068 + 34/52 Ã— 4/51 = 0.0067 + 44/52 Ã— 4/51 = 0.0066 + 54/52 Ã— 4/51 = 0.006Total0.006 Ã— 8 = 0.048,4.8% or 1:20.8

Based on these odds, the frequency with which the side wager of the present invention will become available (the dealer's hand is ten or eleven) is 1:11.4 or 8.8% of the time. (0.04+0.048=0.088 or 1:11.4).

As explained above, for psychological reasons, the side wager looks most attractive when the dealer's first card is between two and six. This may be taken as the minimum number of times that the players will place the side wager. In reality, the players may place the side wager more often.

Of the thirteen possible dealer's hands that equal ten or eleven, there are ten combinations where the first card is between two and six, as shown in Table 3.

TABLE 3DEALERS HANDS THAT EQUAL 10 OR 11 AND THE FIRSTCARD IS 2-6CombinationOdds2 + 94/52 Ã— 4/51 = 0.0063 + 84/52 Ã— 4/51 = 0.0064 + 74/52 Ã— 4/51 = 0.0065 + 64/52 Ã— 3/51 = 0.0066 + 54/52 Ã— 4/51 = 0.0062 + 84/52 Ã— 4/51 = 0.0063 + 74/52 Ã— 4/51 = 0.0064 + 64/52 Ã— 4/51 = 0.0065 + 54/52 Ã— 3/51 = 0.0046 + 44/52 Ã— 4/51 = 0.006Total0.006 Ã— 9 + 0.004 = 0.0585.8% or 1:17.2

Adding these odds, the side wager of the present invention will be available approximately 8.8% of the time. At the least, the players will be motivated to place the wager 5.8% of the time or 66% of the time that the wager is available.

Generally, the frequency of a ten-value card in a deck is 16/52=0.31 or 1:3.25. Since two cards are on the table, the chance that the dealer's third card will have the value of ten (player wins the side wager) is 16/50=0.32 or 1:3.1. The chance that the dealer's card will not have the value of ten (house wins the side wager) is 34/50=0.68 or 1:1.5, or 2:3.

In summary, the side wager of the present invention will become available in about 9% of all blackjack rounds. The players will be extremely motivated to place the side wager in approximately 6% of all blackjack rounds. The house has 2:3 (or 68%) odds of winning each side wager placed. Accordingly, at the least, the side wager of the present invention will bring additional winnings to the house in approximately 4% of all blackjack rounds (68%Ã—6%). If every available side wager is placed, the house will receive additional winnings in 6% of all blackjack rounds (68%Ã—9%). Due to the side wager, the house will have additional losses in between 1.3% (32%Ã—4%) and 2.9% (32%Ã—9%) of all blackjack rounds.

One can estimate the net benefit of the present invention to the house by subtracting the losses from the winnings. In a simplified version, such a calculation is possible when the side wager allows the players no more than the recovery of the lost main wager. (This however does not exclude the possibility of payouts, which are greater than the main wager.) The side wager will become available in approximately 9% of all rounds. In the best-case scenario, the players will place the side wager every time. At 68% chance of winning, the house will win in 6% of all rounds and lose in 3% of all rounds. Therefore, in the best-case scenario, the net gain will be a win in 6âˆ’3=3% of all rounds. In the worst-case scenario, the players will place the side wager only in only 6% of all rounds. Then the house will win in 4% and loose in 2% of all rounds. The net gain will be additional win in 4âˆ’2=2% of all rounds.

Optionally, one can offer a higher-stake side wager. Instead of betting on any card with a value of ten, a player can bet on a particular subgroup or even a single card within the â€œany tenâ€ group. As explained above, there are 16 value ten cards in the 52-card deck, giving the player the odds of winning equal to 16/52=0.31 or 1:3.25. If the player is restricted to a particular suit, the odds of winning drop four-fold to 4/52=0.08 or 1:13. The same 4/52 odds apply if the player is betting on â€œany kingâ€ or â€œany queenâ€ . If the player bets on an individual card, e.g. â€œqueen of spadesâ€ , the odds of winning drop sixteen-fold to 1/52=0.02. An attractive variation may be betting on â€œany black jackâ€ , i.e. a jack of spades or clubs. In a 52-card deck there are two such cards and the odds of winning are 2/52=0.04 or 1:25.

As shown in Table 4, each of these options is advantageous to the house. The higher risk bets may attract more players with the promise of the higher reward, making these bets especially beneficial to the house. The table shows an example of a game where the main wager was $20 and the side wager was $10. In each case (except when the dealer has 20 and the player has 21), if the player wins the side wager, he or she loses the main wager.

TABLE 4APPROXIMATE ODDS OF WINNING AND VALUE OF BETS IN DIFFERENTSIDE BETS: A HYPOTHETICAL PLAYER BETS $20 IN THE MAIN BETAND $10 IN THE SIDE BETANY SUITANYONE CARDAMONGBLACKAMOUNGANY TENANY TENJACKANY TEN(PAYS 2:1)(PAYS 4:1)(PAYS 8:1)(PAYS 16:1)HOUSEPLRHOUSEPLRHOUSEPLRHOUSEPLRWINSWINSWINSWINSWINSWINSWINSWINSODDS OF36/5216/5248/524/5250/522/5251/521/52WINDECIMAL0.690.310.920.080.960.040.980.02ODDSMAX WIN$10$20$10$40$10$80$10$160LOSS OF$20$20$20$20MAIN BETNET WIN$10$0$10$20$10$60$10$140NET VALUE$6.9$0$9.2$1.6$9.6$2.4$9.8$2.8OF SIDEBET

In each example shown in Table 4 the side wager is advantageous to the house. Furthermore, in each example, the house will still have an advantage if the payouts on higher-stakes wagers are doubled to 8:1, 16:1 and 32:1 in each respective column.

The modified blackjack of the present invention may be played on a blackjack table that has an additional space for placing side wagers. An example of such a table is shown on FIG. 1.

In addition, as is common with other card games, the modified blackjack of the present invention may be played between at least one player and an automated device. The device may represent one or more additional players and a dealer. Such devices include a display; means of making selection, such as for example, a touch-screen display, a set of keys or a keyboard; means of collecting and dispensing actual or virtual wagers, for example, an opening for depositing and dispensing coins or tokens, or reading a magnetic card; and a data processing unit. Such a device may be programmed to offer the side bet of the present invention as a part of a blackjack game. If in the course of the blackjack game, the dealer's hand does not equal ten or eleven, the game proceeds as usual. If the dealer's hand equals ten or eleven, the automated device displays an invitation to place a side wager. If the player places the side wager, the device displays the next dealer's card and determines the resolution of the side wager.

While the foregoing describes the exact steps of playing the game of the present invention, it is understood that it is not intended to limit the invention to the exact steps described herein. On the contrary, it is intended to cover all alternative modifications and equivalents that may be included in the spirit and the scope of the invention as defined by the appended claims.