1 Localization System for Roulette and other Table Games Christoph Ruland 1 1 University of Siegen, Hoelderlinstrasse 3, D Siegen/Germany; Tel.: ; Fax: Abstract: With many board games, it is desirable to uniquely and electronically identify the position of the game pieces, irrespective of whether the game is played locally or remotely via communication networks. This paper describes a technology which performs an exact localization of game pieces, tokens, jetons or chips on the game board or table. In order to achieve this, antennas which emit independent code sequences are integrated into the board or table. The game pieces, jetons or tokens detect the code sequences and may either use them to determine their position themselves and send this to a controller or only signal to the controller which code sequences they have received, on which basis the controller then calculates the position of the game pieces. This results in alternating localization and data phases. Power to the game pieces can be supplied passively, e.g. by induction, via a power supply layer in the board or table. The methods used are based on proven technologies such as CDMA, RFID or cryptography in order to securely transmit and archive the information. Keywords: Game Piece Localization, Table Games, Online Gaming, Orthogonal Sequences 1. State of the Art Game pieces are used in board games of all kinds, e.g. by party games played for entertainment, games practiced as sport such as chess, or games of chance played for profit. Sometimes game pieces are used which differ more or less in their artistic and valuable design, but also plastic chips of different colors or shapes which each represent a certain win value. While some games are only played by one player, e.g. Solitaire, others involve two players playing against each other, e.g. chess, and some even have several players who all participate in one round at the same time, such as with roulette. Board games may also be played by multiple players over the internet. In some board games, the game pieces or game chips must be placed on a certain number of predefined fields, as with chess, while other table games do not require fixed positions but also permit the selection of intermediate positions, such as on roulette tables on which jetons may also be placed on lines and intersections. It is often hard to determine onto which admissible or inadmissible position a game piece has actually been placed (see Figure 1). This is already difficult when playing locally, but when playing remotely via networks where the game table or board is located at the remote game partner s site and cannot be seen, this is even harder. It is very important in each instance to be able to clearly and consistently determine the actual position of each game piece: does the piece touch a line or does it partly lie on the line? Does the actual position correspond to the intended one? The determination of the actual position prior to the round beginning is important for the players and the game master in order to be able to verify whether the game piece has been placed on the position onto which it was supposed and is allowed to be placed, and following the round, it is important for the game master who then determines the result. Thus,
2 technical means are required which objectively and bindingly determine and reliably record where the game pieces or tokens are located on the game table or board. This requirement applies independently of whether the players are physically present or whether the game is played online, e.g. over the internet. Figure 1: Jetons on a Roulette Tableau 2 A common method applied in casinos is the use of video cameras employed to record the position of the placed jetons so that, when in doubt, the video recordings can be used to verify which player placed which jeton on which position and whether the position is within a field, on a line or probably even on the cross of two lines. This method may also be used for other board games which are, for example, played online and where the players are informed of the position of the other players game pieces by means of a video signal. However, the verification of video recordings always means an interruption of the game and the participants concentration on the game. Moreover, video recordings are often unclear and do not allow for objective decisions. One electronic method by which the position of the game pieces is determined in a wireless manner is known from the game escrabble das intelligente Brettspiel [escrabble the intelligent board game] . This is an integrated circuit board laminated with a game board foil. The wireless transmission of information to identify the player, letter and game piece occurs via RFID at a frequency of MHz, the communication between the game board, casino and laptop occurs via a 2.4 GHz radio interface, see also RFID ortsgenau auslesen [Precise RFID position scanning] . This means that each square is in principle provided with an RFID reader which wirelessly reads the identifier from the placed game piece. 2. Orthogonal Signal Technology The method described in this paper uses orthogonal code sequences transmitted simultaneously via a number of antennas. The technology of orthogonal code sequences is particularly commonly used in wireless transmission. Two signals x(t) and y(t) are orthogonal if their correlation is 0, i.e. if Φ(x(t), y(t)) = xt () ytdt () 0 (1)
3 Orthogonality means that the two signals are independent. In mobile radio communication, e.g. UMTS, these signals are used to simultaneously transmit the signals of different users. Each user is assigned a code sequence which is orthogonal to the code sequences of the other users. Each user spreads and links the data it wants to send to the code sequence assigned to it. If multiple users send data at the same time, this results in an aggregation of signals. Each user can then determine whether the composite signal contains data linked to its code sequence by correlating its code sequence with the composite signal and isolating it from the composite signal. Many textbooks refer to this technique as the CDMA (Code Division Multiple Access) method. The code sequences used are, for example, socalled Walsh codes or Gold codes ,. Compared to the above, the localization system for board games described here works far more simply as it does not involve spreading of user signals and multiplying with code sequences but only by emitting code sequences to be detected. The localization phase in which the game pieces detect their position is followed by a data phase in which they transmit their information to the controller Localization of Game Pieces by means of Orthogonal Code Sequences The localization of game pieces is carried out with antennas, with each antenna being assigned an orthogonal code sequence. A particular code sequence is only emitted via the assigned antenna. The antennas are spatially distributed, e.g. in a (Cartesian) coordinate system, in parallel or perpendicularly to each other. The number M of antennas chosen depends on the number and accuracy of the game piece positions to be detected and the antenna ranges. For example, the antennas may correspond to boundary lines defining the board or table squares if the transmission range of the antennas is half the width of an individual square. The transmission range of the antennas and the reception range of the receiving antennas in the game pieces are also adjusted accordingly. This is exemplified in Figure 2 for a section of a chess board and a roulette tableau. Each game piece or token contains a receiver, configured to simultaneously receive each of the M code sequences. In other words, the receiver receives the composite signal of several antennas within the range where it is located and then verifies which of the orthogonal code sequences have been received. Thus, the electronic circuit in the pawn on b2 receives the sequences 2, 3, 6 and 7 (Figure 2) and the jeton covering the numbers 32, 33, 35 and 36 receives the sequences 3 and 7. In the electronic circuit of a game piece, a table is stored in which a unique identifier is allocated to each of the M orthogonal code sequences. Based on the identifiers, the electronic circuit in the game piece can derive the position of the piece relative to the M antennas as the identifiers are each assigned to one of the code sequences and therefore to one of the antennas. This means that the game piece position is not determined externally but by the game piece itself. The position detected by the game piece, or the antenna identifiers whose code sequences have been identified, is transmitted via a radio interface, e.g. an RFID, NFC (Near Field Communication), Bluetooth interface or an infrared transmitter.
4 4 Figure 2: Examples of Positions of Game Pieces This information can be transmitted via the same antennas via which the code sequences have been emitted. In this case, localization phases and data transmission phases alternate. The simultaneous reading of the positions of multiple game pieces is facilitated by MAC (Media Access Control) protocols such as those used for reading RFIDs (multi-tag protocols) . If the localization phases are not to be interrupted by the reading phases, e.g. with mobile game pieces or very quick operations, both processes can also take place simultaneously. In order to achieve this, an additional reception system is required for the information emitted by the game pieces, e.g. use of a second frequency band.
5 If, in the future, games are played three-dimensionally, the antennas and game pieces may also be arranged three-dimensionally. Power can be supplied to the electronic circuits of the game pieces by means of induction via the same antennas used to emit the code sequences or, alternatively, of course also via a separate inductive power supply system, e.g. antennas or a power supply layer in the game table. The game pieces would then be considered passive. The game pieces can also be equipped with capacitors or batteries to temporarily store energy, in which case the game pieces are referred to as semi-active Localization System for Roulette Tables The localization method will be described using the roulette table as an example. Figure 3: Transmission Antennas and Code Sequences Figure 3 shows the section of a roulette table in which 6 antennas are installed that mark the boundary lines between the individual squares. The antennas are configured as dipole antennas, their position defining a coordinate system, namely a Cartesian coordinate system. The antennas 3, 4 and 5 extend in the x-direction at the y-coordinates y = 0, y = 1 and y = 2, respectively, whereas the antennas 0, 1 and 2 are in parallel to the y-axis at the x-coordinates x = 0, x = 1 and x = 2, respectively. Each of the antennas is uniquely assigned to an orthogonal code sequence. More specifically, code sequence A is uniquely assigned to the antenna 0 at x = 0, code sequence B to the antenna 1 at x = 1,
6 code sequence C to the antenna 2 at x = 2, code sequence a to the antenna 3 at y = 0, code sequence b to the antenna 4 at y = 1 and code sequence c to the antenna 5 at y = 2. Underneath the game table, there is a transmitter which is connected to the antennas. The purpose of the transmitter is to simultaneously transmit the 6 code sequences during the localization phase. In this process, only the 6 code sequences are transmitted via the respective antennas assigned to the code sequences, i.e. no other useful information is transmitted in addition to the code sequences. Proven RFID technology can be used for the communication between the transmitter via the antennas and the game pieces, i.e. standard modules for RFID readers and RFID tags in the game pieces. In this case, the code sequences are correspondingly encoded and modulated. The RFID technology also ensures that the pieces are supplied with power for the communication ,. For example, if the game piece receives code sequence a, it is allocated to identifier a by table 1. The same applies to the other code sequences. The game piece can receive all code sequences simultaneously which means that it receives a composite signal resulting from the superimposition of the code sequences emitted by the antennas in the reception range in which the game piece is located. Depending on the position, one, two or more code sequences are simultaneously received via the receiving antenna of the game piece. The electronic circuit determines (by correlation with all admissible code sequences) which code sequences are contained in the received composite signal. The game piece determines the coordinates of the transmitting antennas; and from these its own position, by means of an allocation table. Table 1: Allocation Table Identifier of the Code Sequence Coordinate of the Antenna A x = 0 B x = 1 C x = 2 A y = 0 B y = 1 C y = 2 6 The game piece now knows in which antenna ranges it is located. For example, if the antennas run in parallel at distance A, the range of each antenna would be adjusted to A/2. If the game piece is located at the intersecting point of antennas 1 and 4, i.e. only in the range of these two antennas, as shown in Figure 3, it therefore only receives the code sequences emitted by these two antennas, namely code sequences b and B. The game piece then saves the identifiers of the received code sequences, i.e. 1 and 4, completing the localization phase. In the subsequent reading phase, the game table computer uses the RFID reader to read the storage contents of the game pieces, meaning that, with respect to Figure 4, the identifiers 1 and 4 are received. The program in the game table computer also includes allocation tables and determines the coordinates of the identifiers. For identifier 1, this yields the x-position x = 1, and for identifier 4, the y-position y = 1, at the same time yielding the coordinates and thus the game piece position in the coordinate system defined by the antennas, namely the coordinates x = 1 and y = 1. The game pieces could also perform the localization themselves and transmit the determined coordinates directly in the reading phase.
7 The game piece position detected by the game table computer can then be issued via a user interface, network connection, stored and shown on a display. The localization phase can be performed simultaneously for all game pieces and the reading phase may be quasi-simultaneous as there are anticollision procedures for simultaneous reading of RFIDs . 7 Examples Figure 4 shows, as an example, antennas a and b with their intersecting area of the respective ranges R illustrated as shaded areas. Here, the range R can be significantly smaller than the distance A between the antennas (cf., e.g., Fig. 3) such that the position of the object can only be determined if the object is in the immediate vicinity of or above one of the antennas. Note: in the following, no differentiation is made between the designation of the antenna and the identifier of the assigned code sequence, e.g. antenna a corresponds to identifier a. Figure 4: Intersection of 2 Antennas Figure 5 shows the intersecting area of antennas a and b if a code sequence a is transmitted via antenna a and a code sequence b via antenna b. If the game piece is located in the intersecting area between antennas a and b, it identifies the identifiers a and b. Depending on the position, it may also only transmit identifier a or b or no identifier at all if it is outside of the antennas reception area. Figure 5: Jetons in the Intersection Area of 2 Antennas
8 Figure 6 shows a corresponding illustration for four antennas, e.g. antennas a, b, c and d, with the parallel antennas having the distance A between each other. The antenna ranges R are indicated in Figure 6 as shaded areas: here, each range R is A/2. Figure 6: Overlapping areas of 4 Antennas 8 The possibilities for unique position detections resulting from Figure 6 are shown in Figure 7. For example, if the game piece is located at the intersecting point of antennas a and d, it receives the code sequences with the identifiers a and d. If the game piece is located over antenna d, i.e. between antennas a and b, it receives the code sequences of antennas a and b between which the game piece has been placed in addition to the code sequence d. The illustrated area can be part of a game board or table, e.g. of a roulette tableau. Figure 7: Possible Positions exploiting 4 Antennas If the game piece is located at the center, it is within the range of all antennas a, b, c, d and therefore receives the code sequences with the identifiers a, b, c and d.
9 As can be seen from Figure 7, the game piece thus receives a characteristic combination of identifiers at each of the nine different positions shown, from which the position can be derived. In contrast to Figure 7, Figure 8 shows an additional antenna per coordinate direction. In the case of the design form being considered here, the code sequences a, e, b and c, f, d are transmitted via antennas a, e, b and c, f, d, respectively. The position-dependent combinations of code sequences which can be received by a game piece are shown in Figure 8 for the selected section. Figure 8: Positions using 6 Antennas 9 The above examples only use 2 or 3 parallel antennas per direction and therefore only encompass up to 9 squares. However, a chess board or roulette table consists of many more squares and lines defining those squares. The concept illustrated could therefore be generalized according to the requirements. A corresponding number of antennas and different code sequences would then be required. However, a more effective solution for larger game boards or tables is to group n transmitting antennas (Figure 9). In the y-direction, there are four equidistant parallel antennas emitting code sequences with the identifiers a, b, c and d, respectively. In the x-direction, there are a number of n equidistant parallel antennas transmitting code sequences with the identifiers 1, 2, n. Figure 9: Grouping of Antennas
10 This allocation of code sequences to antennas is repeated per group of antennas extending in the x- direction pursuant to a predetermined spatial pattern as shown in Figure 9. Despite this repetition of code sequences, clear position detection is still possible if the group affiliation is known and the antenna ranges are limited. Also with respect to adjacent antennas of two groups placed next to each other and extending in the x-direction, here the antenna used to transmit code sequence n and the antenna used to transmit code sequence 1, unique position detection is possible as the same sequence from 1 to n has always been chosen in the individual groups regarding the spatial allocation to the antennas of a group. The repetition of groups of antennas may also be applied in the x-direction; but with a roulette tableau, repetition in the y-direction is sufficient (Figure 9). In the localization phase, the N groups may, for example, be selected one after the other in a fixed predefined order to transmit the relevant code sequences. Figure 10 shows a further development of Figure 9 in which the number of antennas has been increased in both the x- and the y-direction in order to enlarge the areas or improve the precision of the position detection. Figure 10: More Positions by Group Sampling 10 Figure 11 illustrates the possibility to use patch antennas for the antennas used to transmit the code sequences. A particular code sequence with an allocated identifier from 1 to 25 is emitted via each of the patch antennas.
11 11 Figure 11: Positioning by Patch Antennas x Figure 12 shows the various positioning options resulting from the superimposition of the emitted code sequences. Figure 12: Positions using Patch Antennas The patch antennas may also be grouped. In this case, the signal distribution ranges need to be taken into account with respect to the repeat distances of the codes in order to avoid superimpositions of two transmissions of the same code by two antennas. In order to increase accuracy even further, panel antennas with several patch antennas on their surface may be used instead of patch antennas. The selection of the antenna type to be used depends on the frequency range (the side length of a patch antenna is typically defined as, wherein is the wavelength), the distances and the accuracy requirements.
12 12 7. Online Gaming and Social Network Gaming The methods presented above are also suitable for board games played online or in social networks. The boards are then not only shown electronically on displays on which the game pieces are also moved electronically but exist in reality, with the real game pieces being moved by hand. Traditional games played on real game boards are combined with new electronic methods in order to make these games even more secure and to be able to play them remotely. This will open up new dimensions for games bound to playing surfaces. 8. Security Aspects The authenticity and integrity of the position data transmitted by the electronic game pieces are particularly important. It must be ensured that they actually originate from the indicated game pieces and cannot be modified. The information must be trustworthy and verifiable. This does not only apply for the moment of position detection but also for transmission and archiving. Moreover, the security functions are particularly important for online and social network gaming. In order to achieve this security, cryptographic and security features must be used which are known from literature, e.g. digital signatures  or message authentication codes (MAC)  or, as an option, encryption for online games . 9. Conclusion and Future Work Further practical studies will have to be conducted, particularly with respect to antenna tuning and design. Moreover, instructions need to be drawn up as to how the signal strength of the transmitting antennas, the reception range of the receiving antennas and the distances between transmitting antennas are to be coordinated with each other in order for each position on the game board or table to be clearly identified. It would also be interesting to test the technology described with a game in which the game pieces are arranged three-dimensionally. References  (accessed on )  (accessed on )  J.-R. Ohm, H.D. Lüke, Signalübertragung, Springer-Verlag: Berlin-Heidelberg, Germany, 2002  K. David, T. Benkner, Digitale Mobilfunksysteme, B.G. Teubner: Stuttgart, Germany,1996  K. Finkenzeller, RFID Handbuch, Carl Hanser Verlag: München, Germany, 2008  ISO/IEC 14443: Identification Cards Proximity integrated circuit cards  ISO/IEC 15693: Identification Cards Contactless Integrated Circuit Cards Vicinity Cards  ISO/IEC 14888: Information Technology Security Techniques Digital Signatures with Appendix  ISO/IEC 9796: Information Technology Security Techniques Digital Signatures giving Recovery  ISO/IEC 9797: Information Technology Security Techniques Message Authentication Codes  ISO/IEC 18033: Information Technology Security Techniques Encryption Algorithms