Scalable Multi-Player Game with a Strategic Component

Abstract

The present invention provides methods and an apparatus for transmitting and collecting data in order to administer a lottery-like game between a host computer and a plurality of peripheral user interface devices. The invention further generates and utilizes automated host players (bots) to set a minimum prize level for the winner in a way that assures the house still has an edge or benefit. The prize amount can reliably be announced before the game begins and before the actual number of human players is known.

Claims

1. A method of administering an interactive game between a host computer and a plurality of peripheral user interface devices comprising the steps: a) transmitting from the host computer to the plurality of peripheral user interface devices: an opening time of an entry period, a closing time of the entry period, an opening time of a selection period, a closing time of the selection period, a minimum winning prize amount, and a discrete ordered selection set, wherein the discrete ordered selection set comprises a plurality of selectable ranked items; b) providing on each user interface device a number of electronic type 1 tokens and electronic type 2 tokens; c) opening the entry period where players are able to join the game during the entry period through the user interface devices and wherein a fee is collected from said players; d) generating a number of automated host players, wherein each automated host player is provided with a number of electronic type 1 and type 2 tokens; e) opening the selection period, wherein during the selection period the type 1 and type 2 tokens associated with each user interface device and automated host player, independently from one another, are able to be linked with one or more of the selectable ranked items; f) closing the entry period wherein after the entry period is closed, no further players are able to join the game; g) closing the selection period wherein after the selection period is closed, no further type 1 and type 2 tokens are able to be linked to one or more of the selectable ranked items through the user interface devices, and wherein the closing of the selection period occurs after the closing of the entry period; h) transmitting data from each user interface device to the host computer when the selection period is closed, wherein the transmitted data comprises which selectable ranked items are linked to the type 1 and type 2 tokens from each user interface device; i) identifying via the host computer the smallest or lowest ranked item of the selectable ranked items having the least nonzero number of linked type 1 tokens from the transmitted data from the user interface devices and from the automated host players and no linked type 2 tokens from the transmitted data from the user interface devices and from the automated host players, and designating the identified smallest or lowest ranked item as the winning item; j) determining via the host computer one or more winning players for the game, wherein the one or more winning players are automated host players or human players who linked a type 1 token to the winning item through the user interface devices, and wherein some or all of the winning players may be automated host players; and k) broadcasting results of the game to the plurality of peripheral user interface devices and displaying a summary of the results on the plurality of peripheral user interface devices.

2. The method of claim 1 wherein the number of automated host players generated by the host computer is determined by the formula: b=P.sub.0/(1−p)C, where b is the number of generated automated host players, P.sub.0 is the minimum winning prize amount, C is total player fees collected from the players , and p is a fraction of the total player fees retained by an administrator or the host computer .

3. The method of claim 1 wherein the number of automated host players generated by the host computer is determined by the formula: $b=\max \left(0,\frac{P_0}{\left(1-p\right)C}-N\right),$ where b is the number of generated automated host players, P.sub.0 is the minimum winning prize amount, C is total player fees collected from the players, p is a fraction of the total player fees retained by an administrator or the host computer, and N is the number of human players.

4. The method of claim 1 further comprising electronically separating the players into two or more groups; identifying via the host computer the smallest or lowest ranked item of the selectable ranked items for each group having the least nonzero number of linked type 1 tokens and no linked type 2 tokens, and designating the identified smallest or lowest ranked item as the winning item for each group.

5. The method of claim 1 wherein each automated host player randomly links a number of electronic type 1 and type 2 tokens with one or more of the selectable ranked items during the selection period according to a probability distribution; and data is transmitted to the host computer, wherein the transmitted data comprises which selectable ranked items are linked to the type 1 and type 2 tokens by the automated host players.

6. The method of claim 5 wherein the probability distribution function is a Nash equilibrium strategy, or a probability distribution function that is approximately equal to the Nash equilibrium strategy.

7. The method of claim 1 wherein during the selection period, each linked type 1 and/or type 2 token on the user interface devices are able to be unlinked from the selectable ranked items and linked to a different item from the selectable ranked items, and wherein data comprising the selectable ranked items linked to the type 1 and type 2 tokens when the selection period is closed is transmitted to the host computer.

8. The method of claim 1 comprising administering a plurality of simultaneous subgames having common entry periods and selection periods and having separate sets of selectable ranked items, wherein the type 1 and type 2 tokens associated with each user interface device are able to be linked to one or more of the selectable ranked items in any of the sets of selectable ranked items associated with said subgames, wherein the number of type 1 and type 2 tokens able to be collectively linked to the sets of selectable ranked items is finite, and when the common selection periods close, a winning item is determined for each subgame, and the winning players are players who linked type 1 tokens on the winning items in one or more of the subgames.

9. The method of claim 1 further comprising displaying on the user interface devices, the current total number of players that have joined the game during the entry period, the final player count after the entry period ends, and time remaining before the entry period, selection period, or both, are closed.

10. The method of claim 1 further comprising displaying on the user interface devices, the number of automated host players participating in the game.

11. The method of claim 1 further comprising paying each of the one or more winning players a percentage of the collected fees.

12. The method of claim 1 wherein the selection set is a set of whole numbers, or a set of alphabetical symbols in alphabetical order, or a set of Roman numerals, or a set of whole numbers using the reverse ordering (largest to smallest).

13. The method of claim 1 further comprising constructing a histogram on the host computer from the transmitted data from the user interface devices, where the bar in the histogram associated with each item in the selection set shows the number of players that linked a type 1 token to said item and the number of players that linked a type 2 token to said item, and electrically communicating the histogram to the user interface devices.

14. The method of claim 1 further comprising determining a second place item, wherein said second place item is determined by an algorithm after the winning item is identified, and determining an n-th place item, wherein said n-th place item is determined by the same algorithm after the (n-1)-st place item is found.

15. A method of administering an interactive game comprising of one or more rounds between a host computer and a plurality of peripheral user interface devices, wherein each round comprising the steps of: a) transmitting from a host processor a discrete ordered selection set to the plurality of peripheral user interface devices, wherein the discrete ordered selection set comprises a plurality of selectable ranked items; b) providing on each user interface device a number of electronic type 1 tokens and electronic type 2 tokens; c) opening an entry period where players are able to join the game during the entry period through the user interface devices; d) opening a selection period, wherein during the selection period the type 1 and type 2 tokens associated with each user interface device, independently from one another, are able to be linked with one or more of the selectable ranked items; e) closing the entry period wherein after the entry period is closed, no further players are able to join the game; f) closing the selection period wherein after the selection period is closed, no further type 1 and type 2 tokens are able to be linked to one or more of the selectable ranked items through the user interface devices, and wherein the closing of the selection period occurs after the closing of the entry period; g) transmitting data from each user interface device to the host computer when the selection period is closed, wherein the transmitted data comprises which selectable ranked items are linked to the type 1 and type 2 tokens from each user interface device; h) identifying via the host computer the smallest or lowest ranked item of the selectable ranked items having the least nonzero number of linked type 1 tokens from the transmitted data from the user interface devices and no linked type 2 tokens from the transmitted data from the user interface devices, and designating the identified smallest or lowest ranked item the winning item; i) determining via the host computer one or more winning players for the round, wherein the one or more winning players are players who linked a type 1 token to the winning item through the user interface devices; and j) determining if there is a single unique winning player in the round, in which case said unique winner is awarded a prize; wherein if there is no single unique winner in the round, the prize is not awarded, and another round is scheduled.

16. The method of claim 15 wherein the provided selection set is larger in successive rounds.

17. The method of claim 15 wherein the prize for a round is increased by a fraction of fees collected in a previous round.

18. The method of claim 15 wherein a consolation prize is awarded to multiple winning players in rounds when there is no single unique winning player.

19. An apparatus for providing an interactive game between a plurality of players, where said system comprises: a) a host computer programmed for collecting and processing input data, and outputting data and information relevant to the game; and b) one or more user interface stations connected to said host computer, said one or more user interface stations able to send player selection input to said host computer, and said host computer able to send data and information to the user interface stations; wherein said host computer is programmed to: i) transmit to each user interface station: an opening time of an entry period, a closing time of the entry period, an opening time of a selection period, a closing time of the selection period, a minimum winning prize amount; and a discrete ordered selection set, wherein the selection set comprises a plurality of selectable ranked items, and also provide to each user interface station a number of electronic type 1 and electronic type 2 tokens; ii) open an entry period where the players are able to join the game during the entry period through the user interface stations and wherein a fee is collected from said players; iii) generate a number of automated host player, wherein each automated host player is provided with a number of electronic type 1 and type 2 tokens; iv) open a selection period, wherein during the selection period the type 1 and type 2 tokens associated with each user interface station and automated host player, independently from one another, are able to be linked with one or more of the selectable ranked items; v) close the entry period wherein after the entry period is closed, no further players may join the game; vi) close the selection period, wherein after the selection period is closed, no further type 1 and type 2 tokens are able to be linked to one or more of the selectable ranked items through the user interface stations, and wherein the closing of the selection period occurs after the closing of the entry period; vii) transmit data from each user interface station to the host computer when the selection period is closed, wherein the transmitted data comprises which selectable ranked items are linked to the type 1 and type 2 tokens from each user interface station; viii) identify which selectable ranked items in the selection set, among those that did not contain type 2 tokens, contained the least number of type 1 tokens with at least r type 1 tokens, where r>0, and designate the identified selectable ranked items as the winning items; ix) determine the one or more winning players for the game, wherein the one or more winning players are the players who linked a type 1 token to the winning items, wherein some or all of the winning players may be automated host players, wherein the number of automated host players generated by the host computer is determined by the formula: b=P.sub.0/(1−p)C, where b is the number of generated automated host players, P.sub.0 is the minimum winning prize amount, C is total player fees collected from the players, and p is a fraction of the total player fees retained by an administrator or the host computer.

20. The system of claim 19 wherein each of the one or more user interface stations comprise one or more computer processors connected to a network able to transmit data to the host computer.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0048] FIG. 1 illustrates the high-level functionality of a preferred embodiment of the present invention. Players, using a specially designed app on their smartphones (or other electronic device connected to the internet), pay a fee and register to play in a round of the lottery-like game of the present invention. During the selection period of the round, the app allows players to independently choose which numbers from the selection set they want to place their type 1 and type 2 tokens, and then uploads their choices to the host computer when the selection period ends. The host computer takes all the player choices together, determines the winners, constructs a color-coded histogram that summarizes the results of the round (how many type 1 and type 2 tokens on each number, which number was the winning number, 2.sup.nd place, etc.), and sends the histogram back to the players, which are displayed on their apps, along with notifications of prizes for winning players.

[0049] FIG. 2 shows an embodiment of a player interface screen that players use to place their Type 1 and Type 2 tokens. In this example the selection set is {1,2, . . . , 100}, and the players are allotted three Type 1 tokens (displayed as coins) and two Type 2 tokens (displayed as bombs). In this example the players click and drag the icons for Type 1 and Type 2 tokens to the numbers they choose. Players can change their minds about their choices by moving the icons, until the selection period ends. The positions of the coins and bombs when the selection period ends determines the players' final choices.

[0050] FIG. 3 shows an embodiment of (hypothetical) results of a round of the game of the present invention in histogram form. The number of players is small in this example to keep things simple. The horizontal axis lists the elements of the choice set {1,2, . . . , 9} and the vertical axis shows how many tokens of each kind were placed on the choices, by the players collectively. The blue squares making up the vertical bars correspond to type 1 tokens, and the “bombs” correspond to type 2 tokens; so for example there are four type 1 and two type 2 tokens on choice “2”. In this example the winning number is “6” since it is the smallest number with one type 1 token on it that does not have any type 2 tokens on it. The player that chose number “6” in this example is a unique winner.

[0051] FIG. 4 shows the results of another hypothetical round of the game of the present invention in histogram form with the same embodiment as FIG. 3. This time there is no unique winner since there are no numbers with exactly one type 1 token and no type 2 tokens. The winning number is “5” since there are no bomb-free choices with one type 1 token, and “5” is the smallest bomb-free choice with two type 1 tokens on it. The two players that chose “5” are both winners and split the prize. In this example, if another player had placed a type 1 token on “7” then he/she would have been a unique winner.

[0052] FIG. 5 shows the timeline for a round of the game in an embodiment of the present invention. At time e.sub.0 the entry period opens, allowing players to register to play in the round. New players can register up to time e.sub.1. After that they must wait until the next round to play. Between times s.sub.0 and s.sub.1 registered players choose where to place their type 1 and type 2 tokens. (FIG. 2 illustrates an embodiment of a player interface screen for placing type 1 and type 2 tokens.) Preferably, registered players can change their minds about their choices right up until time s.sub.1. If players wait until time e.sub.1 to make their choices then they will know exactly how many players are in the round (and therefore the number of type 1 and type 2 tokens played) since no new players can register after that time. In one embodiment e.sub.0=s.sub.0, meaning that players can begin to make their choices as soon as they register. Preferably e.sub.1<s.sub.1 so players have time to make (or re-think) their choices after the final player count is set. The showdown time t* must be after the selection period ends, but the gap between them can be small. At time t* the winning number and winning players are determined, and a message summarizing the round (e.g., FIGS. 3 and 4) is sent to all the players.

[0053] FIG. 6 shows the timeline for a progressive jackpot version of the game in an embodiment of the present invention. Each round follows the timeline described in FIG. 5, but there will typically be multiple rounds. The game continues until there is a round with a unique winning player, at which time the progressive jackpot (accumulated over the previous rounds) is awarded. Preferably the choice set for the i-th round {1 ,2, . . . , M.sub.i} increases each time so there will eventually be a unique winning player, no matter how many total players there are.

[0054] FIG. 7 is a flow diagram showing the tasks of the host computer in an embodiment of the present invention, e.g., FIG. 1. The embodiment illustrated in FIG. 7 also includes automated host players (or “bots”). The number of bots is set to a number so the house can guarantee that if a human player wins, the prize will be at least as big as some predetermined level, P.sub.0.

[0055] FIG. 8 is a flow diagram showing the determination of the winning number and winning player(s) in a preferred embodiment of the present invention.

[0056] FIG. 9 is a flow diagram showing an embodiment of the placing algorithm for the present invention (first place, 2.sup.nd place, etc.). The algorithm for first place is the same in preferred embodiments of the present invention, however alternate algorithms are available for how the other places are determined.

[0057] FIG. 10 is a flow diagram showing how the payoffs to the winning players of a round are determined in an embodiment of the present invention.

[0058] FIG. 11 is a flow diagram showing how automated host players (bots) select numbers for their Type 1 and Type 2 choices in an embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

[0059] As used to describe the present invention, the following terms are defined as follows.

[0060] A “lottery” is a means of raising money by selling numbered tickets and giving prizes to the holders of numbers drawn at random (Google dictionary). In other words, the winning numbers in a lottery are chosen at random (Le., by chance). A distinctive feature of many popular modern lotteries (like Power Ball) is the potentially unlimited number of players that can play, and the option for players to choose their own numbers. Herein, a “lottery-like game” is a game where players choose numbers (or other items from a “selection set”) as they would in a lottery, but the players that win prizes are determined by a fixed function of the players' collective choices, and not by chance. The game of the present invention is therefore a lottery-like game.

[0061] A “house” is the generic name for person or entity administering the game of the present invention. The house may be a bricks and mortar casino or business, or a web site on the internet, or the Multi-State Lottery Association, which runs large scale lottery games in the United States like Powerball. “House rules” are rules that have no effect on the logical operation of the game of the present invention, such as the size of the selection set, or the amount of time players have to make their choices, or the fees charged for playing.

[0062] A “Nash equilibrium strategy” for a multi-player game such as the game of the present invention, is a strategy where a player makes a choice randomly from a certain probability distribution. Said probability distribution has the property that if every player is using the strategy to make their choices, then no player would do better by changing to a different strategy (thus, an equilibrium). Very often Nash equilibrium strategies are good strategies, but there is no guarantee that it is the best response to every other strategy. Knowing the Nash equilibrium strategy does not guarantee winning, or even having an advantage over the other players. For the games of the present invention it is difficult, but not impossible, to compute or approximate the Nash equilibrium strategies. If the Nash equilibrium strategy cannot be calculated (e.g., if the allocated numbers of type 1 and type 2 tokens, n and m, are large), or if for any reason the house does not want to use the Nash equilibrium strategy for its bots, the bots can be programmed to make their choices in some other way, e.g., choose uniformly between a lower and upper bound set by the house.

[0063] A “unique winning player” or “unique winner” is a player that chose the winning number with a type 1 token, and was the only player that chose the winning number.

[0064] “Places” refer to 1.sup.st place, 2.sup.nd place, 3rd place, and higher place numbers or winners.

[0065] “Bots” are automated (virtual) players provided by the house to compete along with the (human) players. Bots preferably play by the same rules as the human players, i.e., they are allotted the same number of type 1 and type 2 tokens. Bots can use the Nash equilibrium strategy to make their choices, but do not have to.

[0066] The “entry period” of a round of the present invention is an interval of time when potential players can register and pay any fees to play in the round.

[0067] The “selection period” of a round of the present invention is an interval of time when registered players can choose where to place their type 1 and type 2 tokens. In preferred embodiments of the present invention, the entry period ends before the selection period ends so that in the time between the end of the entry period and the end of the selection period, players can make their choices with knowledge of exactly how many players registered for the round. When the selection period ends, all the players' choices are communicated to the host computer.

[0068] The “showdown” occurs after the selection period ends in an embodiment of the invention. The showdown is when the host computer processes the players' choice data, determines the winner(s), constructs the summary histogram, and broadcasts the summary histogram to the players and/or spectators.

[0069] A “summary histogram” is the way the results of a round of the present invention are communicated to the players in a preferred embodiment. The horizontal axis of the histogram lists the items from the selection set. The histogram bars above each item show the number of type 1 and type 2 tokens that were (collectively) placed on that item by the players. By using various coloring schemes for the histogram bars, it is possible to show the winning number and other places, in addition to the numbers of type 1 and type 2 tokens on each item.

[0070] Overview

[0071] The present invention provides a method and system for administering a lottery-like game where the players select numbers (or other identifiers) similar to typical lottery games, but where the winning number is the smallest number chosen by at least one player with the property that no other number chosen by at least one player was chosen by fewer players, and the number is eligible to win. Players each choose n numbers to potentially win (using type 1 tokens), and m numbers to be ineligible to win (using type 2 tokens), where n is a fixed number greater than or equal to one, and m is a fixed number greater than or equal to zero. (The values of n and m can be considered “house rules”.) In other words, in addition to selecting numbers players believe may be winning numbers with type 1 tokens, players can also place “bombs” or “mines”, with type 2 tokens, on numbers they believe may otherwise be winning numbers, thereby preventing those numbers from winning, and thereby increasing their own chances at winning. The present invention therefore does not need or utilize random number generators or any other source of randomness to determine winners, and this fact alone makes the present invention different in kind from lottery games in the prior art. The present invention can be played by any number of players (greater than 2), and the players can optionally include virtual players (bots) controlled by the house.

[0072] The present invention provides an apparatus that allows players to play the game of the present invention. The apparatus a) allows players to register, pay fees, and choose where to play their allotted type 1 and type 2 tokens; b) communicates the players' choices to the host computer in specially formatted data packets; c) processes the data packets received from the players; d) summarizes the processed data in a specially formatted electronic histogram; and e) broadcasts the electronic histograms.

[0073] The present invention also provides a method, utilizing bots, for the house to announce a minimum prize amount that a human player will win if said human player wins, before the game of the present invention begins, and without jeopardizing the house's profit.

[0074] FIGS. 3 and 4 illustrate the outcome of a round of the game of the present invention (with a small number of players) using histograms. A histogram is a very good way to summarize the results of a round of the present invention. In the embodiment of FIGS. 3 and 4, above each number is a bar representing the total number of type 1 tokens that players collectively placed on that number, along with bombs representing the total number of type 2 tokens the players collectively placed on that number. From the histogram it is easy to determine the winning number by sight, and this is why preferred embodiments of the present invention produce them from the raw player-choice data and broadcast them to the players and potential spectators.

[0075] Entry fees can be collected for a round of the game of the present invention, similar to common lottery games, and prizes distributed to the winners. The prize amounts can depend on the number of players, e.g., a fraction of the total fees collected from the players for that round; or a fixed amount; or a progressive jackpot based on what happened in previous rounds, or any of a number of other possibilities.

[0076] Preferably, the game of the present invention is provided to players using computers or other electronic devices like smart phones (their game interface devices) connected to a network, such as the internet. The game interface devices run a program or app specially designed for the game of the present invention. As shown in FIG. 1, a host computer is used to administer the game. A plurality of players therefore use game interface devices to connect to the host computer over the network. Players are able to pay entry fees and register for the round of the game during the entry period, and select where to place type 1 and type 2 tokens on the selection set during the selection period, using the interface devices. A screen shot of an embodiment of a game interface device for making type 1 and type 2 selections is illustrated in FIG. 2. The players' selections are communicated to, and confirmed by, the host computer at the end of the selection period, which then processes the data (FIG. 7). After processing the data the host computer sends summary histograms and personal results to each player, which are displayed on their game interface device.

[0077] The user interface devices can be any device able to connect to the host computer. For example, different players can make selections and pay fees using the same authorized kiosk at different times (similar to buying tickets for common lottery games at a convenience store), or players can log into the host computer using a personal computer or handheld electronic device (such as a smartphone). For personal computers or handheld devices, a specific application or website is needed to access the game. Allowing players to use computers or handheld devices encourages greater participation of the game, and also enables the game to be operated efficiently at small social setting such as at sports bars or restaurants.

[0078] In one typical embodiment of the game of the present invention, generally illustrated in FIG. 7, the host computer announces the rules of the upcoming round, such as what numbers or items can be selected, e.g., {1,2, . . . , M} (the selection set), the number n of type 1 tokens each player is allowed to choose from the selection set, the number m of type 2 tokens each player is allowed to choose from the selection set, the number of bots that will play, b, the starting time of the entry period (when players can register for the round), the starting time of the selection period (when players can choose their numbers), the ending time of the entry period (no more players can register for that round), the ending time of the selection period (choices locked in), and the showdown time, when the winners are determined.

[0079] After the entry period ends the host computer preferably informs all the players of the total number of players in the round (human and bot) and the total number of type 1 and type 2 tokens that will be placed on the selection set by said players. The players can use that information to help them finalize their choices before the selection period ends. The host computer is also allowed to use that information in to determine the strategy and actions of the bots.

[0080] In one embodiment, the host computer determines what numbers the b bots will place their type 1 and type 2 tokens on after the entry period ends, according to a probability distribution (an embodiment is shown in FIG. 11). The type 1 tokens for each bot is placed on a number randomly from a probability distribution depending on N, n, m, and b ensuring that no number is chosen more than once. The type 2 tokens for each bot are placed on numbers randomly from another probability distribution depending on N, n, m, b, and the elements where the type 1 tokens were placed, ensuring that no type 2 tokens are placed where type 1 tokens are already placed. Optionally, the probability distribution for placing type 1 and type 2 tokens is based on the Nash equilibrium for the game of the present invention.

[0081] After the selection period ends, the game of the present invention enters the showdown phase where the host computer determines the winning numbers and players (possibly bots) and sends a summary of the round in histogram form (e.g., FIGS. 2 and 3) to all the players. Optionally, the histograms sent to the players are “personalized”, showing each player's choices color coded on the histogram, showing what place the player came in, and how much the player won. The timeline of a typical round of the game of the present invention is illustrated in FIG. 5.

[0082] Further non-limiting variations of the present invention are explained and described in the examples presented below.

EXAMPLES

Example 1—Minefield Limbo

[0083] In an embodiment of the lottery-like game described in U.S. Pat. No. 8,727,870 (Burton Simon), each of N players chooses a single number in the range {1,2, . . . , M}. When all the choices are in, the system determines the winner(s) by the following steps:

[0084] Determine k.sub.i, i=1,2, . . . , M, the number of players that chose i.

[0085] Determine k*, the minimum of {k.sub.1, k.sub.2, . . . , k.sub.M}, excluding those that are 0.

[0086] Determine w, the smallest index such that k.sub.w=k*. w is the winning number.

[0087] Determine the player(s) that chose w. These are the winning player(s).

[0088] It is a mathematical fact that if players do not communicate with each other and M is large enough compared to N, e.g., M>N/ln(N), then k* will almost always be 1, i.e., there is a unique winner. There are four issues with the lottery-like game described in U.S. Pat. No. 8,727,870 that are addressed in the game of the present invention.

[0089] Firstly, the rules of the U.S. Pat. No. 8,727,870 game implicitly assume that players keep their choices secret from the other players, but there is often no way to enforce secrecy. If some players disregard this convention of secrecy then the nature of the game is subtly changed. For example, suppose M>N/ln(N) so there will (almost certainly) be a unique winner. Now suppose a player (a “cheater”) announces over social media that he is going to choose item #1. Then the other players find themselves in an uncomfortable position. If they choose #1 then they know they will not win because the cheater already chose it. But if nobody “volunteers” to thwart the cheater, then the cheater will win. Of course, it is also possible the cheater is lying about his choosing item #1. This possibility makes the other players uncomfortable too. It would be preferable in a new game if cheating in this way could not benefit the cheater, and thereby players would not be tempted to cheat.

[0090] Secondly, the preferred embodiments of lottery-like game U.S. Pat. No. 8,727,870 are very simple since players choose a single number. It would be preferable in a new game if players choose multiple numbers and/or numbers with more than one purpose.

[0091] Thirdly, it would be advantageous to allow players the opportunity to play in rounds of the game where N (the number of players) is very large. But there may not always be large numbers of people available to play in every offered round. It would be preferable in a new game if the total number of players could be set at any level.

[0092] Fourthly, in the U.S. Pat. No. 8,727,870 game there is a winning number, and associated winning player(s), but there is no second place, third place, etc. It would be advantageous to have a method to assign placing besides first place.

[0093] An embodiment of the game of the present invention, called Minefield Limbo, addresses all four issues described above. Minefield Limbo incorporates “bots”, which are virtual players, so (in principle) any number of players N is possible. In the game of the present invention there are two kinds of tokens, called type 1 tokens and type 2 tokens. Each player (including bots) gets n type 1 tokens (n≥1) and m type 2 tokens (m≥0), where n and m are set by the house. Each player places their n type 1 and m type 2 tokens on the M items in the selection set any way they want. When the players all make their choices the system determines the winner(s). The steps for determining the winner(s) in the game of the present invention are as follows: Remove all numbers from {1,2, . . . , M} that have at least one type 2 token on them; and for or each of the remaining numbers, determine k.sub.i, the number of players that chose i with a type 1 token; determine k*, the minimum of the k.sub.i's, excluding those that are 0; determine w, the smallest item in the selection set such that k.sub.w=k* (w is the winning number); determine the player(s) that chose w (these are the winning Player(s)) (FIG. 8); determine the placing of the non-winning numbers by sequentially removing the winning numbers and rerunning the winning number algorithm (FIG. 9.)

[0094] In the Minefield Limbo embodiment of the present invention, the type 2 tokens are called “bombs”. Any number with one or more bombs on it cannot be a winning number.

[0095] Minefield Limbo addresses and solves the problems identified above since if a player tries to “cheat” by announcing one or more of his choices, other players can place their type 2 tokens (bombs) on those choices without sacrificing their chances of winning (with their type 1 tokens). Cheating like this is obviously not a viable strategy in any embodiment of the game of the present invention. Additionally, since players place bombs, they must simultaneously decide where to put their own bombs, and how to avoid bombs placed by other players when they place their type 1 tokens. These strategic issues are multiplied in Minefield Limbo by increasing n and/or m. Furthermore, in every embodiment of the game of the present invention (including Minefield Limbo) the use of bots allows an unlimited number of players.

[0096] Thus, in addition to the selection of potential winning numbers (with type 1 tokens), this game allows each player to place a mine or bomb (with type 2 tokens) which prevents other players from winning with that designated number. If one player believes that another player may select (say) the number 13, placing a bomb on that number will prevent that number from being the winning number. If there is a bomb on some number, nobody can win with that choice.

[0097] A unique winning player in Minefield Limbo is therefore one that picks (with a type 1 token) the smallest bomb-free (type 2 token free) number that nobody else picks. There may not be a unique winning player in every game. If there is no unique winning player then the winning players are those that choose the winning number as defined above.

[0098] In Minefield Limbo there are second place and third place winners as well as (first place) winning players. One embodiment of an algorithm that assigns places to items in the choice set is illustrated in FIG. 9. The amounts that first place winners, second place winners, and other place winners are paid in prizes can be considered house rules.

[0099] Good strategies for Minefield Limbo are much more involved than strategies for the game described in U.S. Pat. No. 8,727,870. Placing bombs and avoiding bombs add additional variables successful players must take into consideration, and allotting multiple type 1 and type 2 tokens opens up a large variety of strategies concerning how the tokens should be spread out. A few simple strategies may be obvious: it is unwise to place a type 1 token on the same number twice, or to place a bomb where you have a type 1 token. Beyond that, each player must try to predict what numbers other players (and bots) are likely to select with their type 1 tokens and bombs.

[0100] In a further embodiment, there are multiple instances, s, of Minefield Limbo occurring simultaneously, i.e., with common entry period and selection periods, wherein players place their n type 1 tokens and m type 2 tokens on the selection sets for one or more of the s selection sets as they please. The players are constrained to a total of n type 1 tokens and m type 2 tokens, but otherwise they can distribute them among the s selections sets any way they want to. The winning number on each selection set is the smallest of the numbers with the least nonzero number of type 1 tokens that do not have any type 2 tokens on them, consistent with the usual rules of Minefield Limbo. Likewise, second place (and so on) are optionally determined for each selection set. Optionally, there are different prizes awarded to the winning players (players that chose the winning number, or placed) on each of the s Minefield Limbo games.

Example 2—Top Limit limbo

[0101] It is a mathematical fact that there is almost always a unique winner in games with a large number of players if the number of items in the selection set is sufficiently large. However, this is not true if players have to choose a number between 1 and M, where M is small enough so that every choice will (probably) be chosen by more than one player. For example, if M=100 and there are N=1000 players, each with n=5 type 1 tokens, then it would be expected that about (1000)(5)/100=50 type 1 tokens will be placed on each choice. As a result, there will probably be no unique winner. Of course there is always a unique winning number (unless every item in the selection set has a type 2 token on it) but the winning number almost always has multiple players that picked it when M is small. M in this scenario is called the Top Limit. The winning number in this embodiment would be the smallest of the least-popular-choices, consistent with the winning number for all embodiments of the present invention, i.e., the algorithm in FIG. 8. The winning players are those that chose the winning number. The rules for Top Limit Limbo are consistent with the rules described for Minefield Limbo.

[0102] If M (the Top Limit) is sufficiently large compared to N (the number of players), e.g., M>N/ln(N), then there is probably a unique winner, so the probability an average player wins is about 1/N (the number of players). In a Top Limit Limbo game with a smaller M, the probability of winning is about 1/M. It is therefore much easier to win at Top Limit Limbo, 54but the individual prizes are smaller since the prize is shared by all the players that chose the winning number.

Example 3—Jackpot Limbo

[0103] Top Limit Limbo can further be turned into a progressive jackpot game, as illustrated in FIG. 6. In Jackpot Limbo the contest starts with an initial jackpot, and the jackpot increases every round until somebody wins it. To win the jackpot in a given round, a player has to be the unique winner in that round.

[0104] To maximize the fun and suspense in Jackpot Limbo, the house sets the initial Top Limit small enough so that it is very unlikely there will be a unique winner, and increases Top Limit slowly in each subsequent round until finally there is a unique winner that wins the jackpot.

[0105] When there is no unique winner in a round of Jackpot Limbo, the round is like a normal round of Top Limit Limbo, i.e., the players that pick the winning number (the smallest least popular choice with no type 2 tokens on it) split the daily prize. The daily prize is some fraction of the ticket sales for the day (FIG. 10). Some of the remainder goes to increasing the jackpot for the next round.

[0106] Having now fully described the present invention in some detail by way of illustration and examples for purposes of clarity of understanding, it will be obvious to one of ordinary skill in the art that the same can be performed by modifying or changing the invention within a wide and equivalent range of conditions, elements and other parameters without affecting the scope of the invention or any specific embodiment thereof, and that such modifications or changes are intended to be encompassed within the scope of the appended claims.

[0107] When a group of materials, compositions or components is disclosed herein, it is understood that all individual members of those groups and all subgroups thereof are disclosed separately. When a Markush group or other grouping is used herein, all individual members of the group and all combinations and subcombinations possible of the group are intended to be individually included in the disclosure. Every combination of components described or exemplified herein can be used to practice the invention, unless otherwise stated. In the disclosure and the claims, “and/or” means additionally or alternatively. Moreover, any use of a term in the singular also encompasses plural forms.

[0108] The terms and expressions which have been employed are used as terms of description and not of limitation, and there is no intention that in the use of such terms and expressions of excluding any equivalents of the features shown and described or portions thereof, but it is recognized that various modifications are possible within the scope of the invention claimed. The invention illustratively described herein suitably may be practiced in the absence of any element or elements, limitation or limitations which is not specifically disclosed herein. All headings used herein are for convenience only.