Patent Application
20080026812
A wagering game based on sequences of cards is played by one or more players a) against a paytable, b) against a dealer or house hand, or c) against both a house hand or dealer hand and a paytable. A player makes an initial wager to play in the wagering game. Each player placing an initial wager has at least three playing card placement positions. A partial hand or initial hand is dealt to each player. The player evaluates the first two cards received and determines what is the best arrangement that can be made with the cards. The cards are arranged by the player by positioning them in two of the three playing card holding positions. The player selected (or automatic position selection) is made to offer a best likelihood or highest probability of a third card forming a consecutive rank sequence of cards when the third card is dealt to a third card position oriented with respect to the positions taken up by the first two cards that were dealt to a player and then positioned by a player. If the third card “fits” sequentially into the ordered arrangement of the cards, then the player wins on the initial wager or qualifies to play against the dealer.
The player positions the initial two cards dealt to create the largest vector space in which a third card will fit. The term vector space will be described graphically and by example to explain the concept. It must first be established that the first two cards may be arranged in any combination of three positions among the three playing card placement positions (I, II and III). Identifying a filled position as X and an empty position as O, the three choices for the playing cards would be:
Orientation 1—I-X, II-X, III-O
Orientation 2—I-X, II-O, III-X
Orientation 3—I-O, II-X, III-X
The various orientations are to be read in a single direction, usually left to right, but right to left may also be used. One objective of the game is to construct hands of at least three cards with the rank or value of the cards in sequence, preferably ascending sequence, from one direction to the other, as from position I to position II to position III. For example, playing cards of rank 2 5 J are in ascending order from left to right, as are cards 6 Q K. On the other hand, cards K 8 Q are not in sequence left to right as cards cannot be read “around the corner.” A player must therefore arrange the initial two cards in a sequence and orientation of rank to maximize the likelihood of another card (the third card dealt) being in the proper orientation to form a sequence of ranks or values in the proper order. It is here that the concept of vector space is considered.
In placing the cards in two of the three placement positions, the desire to form a sequence of cards must be considered in terms of probability for the rank of the third card. The orientation for purposes of the invention shall be considered from left to right in ascending value as follows, with the size of the boxes indicating the relative rank or value of the cards and the arrows showing the relative direction of reading the cards.
Vector space would be considered the unoccupied space from one pair of boxes towards a third box or between the two end boxes. There are therefore three vector spaces to be considered. Those vector spaces are:
The two initial cards are positioned so that the vector space remaining from the positioning of the two initial cards offers the greatest probability of the third card forming a sequence when placed in the third slot or available card position. Referring to the identified vector spaces, for example, if the initial cards were a 2 and a 3, Vector space 1 would be used with the 2 in position I and the 3 in position II so that a third card of a 4, 5, 6, 7, 8, 9, 10, J, Q or K would be a winning card. Similarly, if the first two cards were a 2 and K, vector 2 would be used with the 2 in position I and the King in position III, so that a third card of a 3, 4, 5, 6, 7, 8, 9, 10, J, or Q would be a winning card. If the first two cards were a Q and K, vector 3 would be used with the Q in position II and the King in position III, so that a third card of a 2, 3, 4, 5, 6, 7, 8, 9, 10 or J would be a winning or qualifying card.
A game played according to the rules described herein is referred to as “Roo” and is a new card game based on the concept of a kangaroo straight. A kangaroo straight, or roo straight for short, is a row of cards in ascending order from left to right. Specifically, the first card is less than the second card, the second card is less than the third card, and so on. For instance, 2-3-4 and 6-9-K are both valid roo straights. Any set of cards that is not in the correct order or contains a pair is an invalid roo straight. Some examples of invalid roo straights are 4-3-2, 6-K-9, and 8-8-9.
In the game Roo, the object is to form a roo straight using 3 cards. To do so, players initially receive 2 cards that they must place in a specific configuration. They must designate their 2 cards as the low and middle, the low and high, or the middle and high cards of their final roo straight. They will then be dealt a third card to the remaining position in their roo hand. Next, the dealer will also attempt to form a 3-card roo straight in a similar fashion. To win, a player must first form a roo straight and then beat the dealer's hand if the dealer also forms a roo straight.
These rules are intended to be exemplary and are not to be taken as absolute limits on the scope of play of games envisioned herein.
Ante Bonus
To analyze the game, a combinatorial program in Java analyzed the game using a brute force approach. The following describes the steps that the program executed.
After executing the steps above, the program calculated the expected values1 (EV) of each of the 3 possible ways to play each of the initial 2-card deals. The program then compared these values and took the highest of the 3. The average of all the highest EV's of all possible hands gives the expected value of a single ante wager. The negative of this figure is the house advantage. 1 The expected value is defined as the weighted average of all possible outcomes of an event. Suppose there are n possible outcomes of an event. Let xi=value of the ith outcome and pi=the probability the ith outcome. Then expected value=Σxi*pi, for i=1, 2, . . . , n.
The following table shows the ante bonus portion of the expected value:
In the Pocket Roo side bet, players win if they successfully form certain types of roo straights. They automatically lose if they do not form a straight or if they are dealt a pair. The following list describes each of the winning straights:
The amount paid for each of the roo straights above varies depending on the hand. See tables 3 and 4. The outcome of the Pocket Roo side bet does not affect the outcome of the ante wager and vice versa.
To analyze the Pocket Roo side bet, I created a combinatorial program in Java that analyzed each of the 3 possible ways to play any given 2-card deal. The following describes the steps that the program executed:
The next table shows one version of the Pocket Roo side bet pay schedule and gives a summary of its expected value of −2.6968%. The corresponding house advantage is 2.6968%.
The following table shows another version of the Pocket Roo side bet pay schedule and gives a summary of its expected value of −4.5068%. The corresponding house advantage for the pay schedule below is 4.5068%.
Appendix B shows the expected value of each of the 3 ways to play any 2-card player hand. It also shows the optimal playing strategy.
In the Pairs Insurance bet, players win if their first 2 cards form a pair or their 3-card hand contains a pair. Table 5 below shows the different winning hands and their corresponding pay outs.
To analyze the Pairs Insurance bet, I used combinatorics counting techniques to determine the number of each type of winning hand. I then used this information to calculate the expected value of the Pairs Insurance bet. The following table summarizes these results.
The following table gives the expected values of all 3 ways to play any 2-card player hand for the ante wager. The second column of the table gives the optimal playing strategy.
Optimal Strategy Key:
The following table gives the expected values of all 3 ways to play any 2-card player hand for the Pocket Roo side bet. (The values below apply for the pay schedule shown in Table 3.) The second column of the table gives the optimal playing strategy.
Optimal Strategy Key:
Also available in the game is the Joey Roo event and side bet wager.
The Joey side bet is similar to the Pocket Roo side bet in that its 2 highest paying hands are the Royal Roo and the Royal Flush Roo. However, with the exception of these 2 hands, the Joey side bet does not penalize players for not making a valid roo straight. The following list describes each of the winning hands on the Joey side bet pay table:
The Joey side bet was analyzed using the same methodology to analyze the Pocket Roo side bet. The next table shows one version of the Joey side bet pay schedule and gives a summary of its expected value of −4.3258%. This corresponds to a house advantage of 4.3258%.
The following table shows another version of the Joey side bet pay schedule and gives a summary of its expected value of −2.5882%. This corresponds to a house advantage of 2.5882%.
In addition to the play of the underlying game of ROO™ poker in which players attempt to achieve a kangaroo straight in the sequential order of the three cards and beat the dealer's ROO™ poker straight, the Roo™ game described herein may be used as a side bet game or ancillary games when other games (blackjack, Baccarat, Three Card Poker® games, etc. are being played. For example, in addition to the underlying bets already made on Three-Card Poker® game hands, as described in U.S. Pat. Nos. 5,885,774; 6,056,641; 6,237,916; 6,345,823; and the like, a side bet wagers may also be made on the first two cards, with a third card later delivered in the game. It may be adapted with more difficulty to blackjack where a third can might not ordinarily be dealt to particular hands. In that event, either a community third card may be used for any Roo wagers, or cards may be dealt after conclusion of the blackjack hand to avoid card usage that would interfere with the underlying strategy of blackjack.
These and other aspects of the invention are alternatives appreciated by one of ordinary skill in the art to be within the scope of the generic teachings of the present technology and game structure. In this vein, automated table systems, automated bet recognition and automated card reading and monitoring systems may be used to implement play of the present games and technology.
