Amusement devices and games including means for processing electronic data where ultimate outcome of the game is dependent on relative odds and/or where chance is a factor

Abstract

Games related to the provision of information are described. Games may be formulated to exploit biases such as long shot bias and favorite bias. Games related to the provision of information are described. Games may be formulated to exploit biases relating to the Monty Hall paradox. Games related to the provision of information are described. Games may include wagering on hands of cards, e.g., poker wagering games.

1 - 28 . (canceled) 
     
     
         29 . A machine implemented method, comprising:
 providing, by at least one processor, first information about a set of possible outcomes of an event to users, wherein at least a part of the first information identifies a characteristic of a true outcome of the set of possible outcomes;   receiving, by the at least one processor, second information, the second information being based on at least first wagers placed by the users, the first wagers being placed following provision of the first information;   determining, by the at least one processor, a first set of likelihood values corresponding to the set of possible outcomes using the second information, wherein each likelihood value of the first set of likelihood values corresponds to a respective possible outcome of the set of possible outcomes;   determining, by the at least one processor, that a first likelihood value of the first set of likelihood values is greater than a first threshold value or less than a second threshold value, the first likelihood value corresponding to a first possible outcome of the set of possible outcomes; and   performing, by the at least one processor, one or more first actions or one or more second actions responsively to determining that the first likelihood value is greater than the first threshold value or less than the second threshold value.   
     
     
         30 . The method of  claim 29 , wherein the method is performed by one or more servers, the one or more servers configured to communicate with one or more devices via a communications network; and
 wherein the first information is provided by the one or more servers via one or more devices.   
     
     
         31 . The method of  claim 30 , wherein the one or more devices comprise one or more mobile gaming devices. 
     
     
         32 . The method of claim  1 , further comprising:
 if the first likelihood value is greater than the first threshold value, performing the one or more first actions.   
     
     
         33 . The method of  claim 32 , wherein performing the one or more first actions comprises:
 determining a second likelihood value, the second likelihood value being less than the first likelihood value and greater than or equal to the first threshold value;   associating the second likelihood value with the first possible outcome; and   providing one or more users of the users with the second likelihood value and an opportunity to wager on the first possible outcome.   
     
     
         34 . The method of  claim 32 , wherein performing the one or more first actions comprises:
 providing one or more users of the users with an opportunity to wager on the first possible outcome at a lower premium than would be provided if the opportunity to wager had been based on the second information and the first likelihood value.   
     
     
         35 . The method of  claim 32 , wherein performing the one or more first actions comprises:
 grouping one or more possible outcomes of the set of possible outcomes other than the first possible outcome together to produce a combined possible outcome;   determining a second likelihood value;   associating the second likelihood value with the combined possible outcome; and   providing one or more users of the users with the second likelihood value and an opportunity to wager on the combined possible outcome.   
     
     
         36 . The method of  claim 32 , wherein performing the one or more first actions comprises:
 grouping one or more possible outcomes of the set of possible outcomes other than the first possible outcome together to produce a combined possible outcome;   providing one or more users of the users with an opportunity to wager on the combined possible outcome; and   providing at least one user with separate opportunities to wager on respective possible outcomes of the one or more possible outcomes, the separate opportunities to wager being based on the second information and the first set of likelihood values.   
     
     
         37 . The method of claim  1 , further comprising:
 if the first likelihood value is less than the second threshold value, performing the one or more second actions.   
     
     
         38 . The method of  claim 37 , wherein performing the one or more second actions comprises:
 determining a second likelihood value, the second likelihood value being greater than the first likelihood value and less than or equal to the second threshold value;   associating the second likelihood value with the first possible outcome; and   providing one or more users of the users with the second likelihood value and an opportunity to wager on the first possible outcome.   
     
     
         39 . The method of  claim 38 , wherein providing the one or more users with the opportunity to wager comprises:
 providing the one or more users with the opportunity to wager at a higher premium than would be provided if the opportunity to wager had been based on the second information and the first likelihood value.   
     
     
         40 . The method of  claim 37 , wherein performing the one or more second actions comprises:
 providing one or more users of the users with an opportunity to wager on the first possible outcome at a higher premium than would be provided if the opportunity to wager had been based on the second information and the first likelihood value.   
     
     
         41 - 46 . (canceled) 
     
     
         47 . A machine implemented method comprising:
 providing, by at least one processor, first information about a set of possible outcomes of an event to users, wherein at least a part of the first information identifies a characteristic of a true outcome of the set of possible outcomes;   determining, by the at least one processor, a first set of likelihood values corresponding to the set of possible outcomes using first wagers placed by the users following provision of the first information, wherein each likelihood value of the first set of likelihood values corresponds to a respective possible outcome of the set of possible outcomes;   determining, by the at least one processor, at least one second likelihood value responsively to comparing the first set of likelihood values to one or more predetermined values, the one or more predetermined values being derived from data regarding expected biases of the users; and   providing, by the at least one processor, the at least one second likelihood value to at least one user of the users.   
     
     
         48 . The method of  claim 47 , wherein the at least one second likelihood value corresponds to two or more possible outcomes of the set of possible outcomes. 
     
     
         49 . The method of  claim 48 , further comprising:
 grouping the two or more possible outcomes together to produce a combined possible outcome; and   associating the at least one second likelihood value with the combined possible outcome.   
     
     
         50 . The method of  claim 47 , wherein the expected biases of the users comprise at least one of a long shot bias or a favorite bias. 
     
     
         51 - 52 . (canceled) 
     
     
         53 . An apparatus comprising:
 at least one processor; and   at least one memory having instructions stored thereon which, when executed by the at least one processor, direct the at least one processor to:
 provide first information about a set of possible outcomes of an event to users, wherein at least a part of the first information identifies a characteristic of a true outcome of the set of possible outcomes; 
 receive second information, the second information being based on at least first wagers placed by the users, the first wagers being placed following provision of the first information; 
 determine a first set of likelihood values corresponding to the set of possible outcomes using the second information, wherein each likelihood value of the first set of likelihood values corresponds to a respective possible outcome of the set of possible outcomes; 
 determine at least one second likelihood value responsively to comparing the first set of likelihood values to one or more predetermined values, the one or more predetermined values being derived from data regarding expected biases of the users; and 
 provide third information based on the at least one second likelihood value to at least one user of the users.