as skill may be interpreted as a form of knowledge , the following definitions are used : “ skill ” refers to a decision ( in betting , playing , or both ) such that long term performance is maximized . on an individual - trial basis , however , adopting “ skillful ” play may or may not yield a desired result , as an element of randomness remains . as an example consider , the discussion of playing a hand of blackjack already described . “ knowledge ” refers to a decision that , on an individual - trial basis , yields necessarily a desired result . an example is the decision of how to respond to the question , “ which united states state is the geographically smallest ?” clearly , a correct answer has no associated uncertainty . the approach applied herein is especially suitable for games wherein the player has a high level of knowledge or skill . as will be explained , the concept includes apportionment of the pay out , or value , of the bonus , jackpot , progressive or otherwise including the underlying game via a remainder funded escrow or some variant thereof . that is to say that , the preferred embodiment is a bonus game with apportionment to fix the house advantage , or essentially so , but any game including the underlying game can have an apportioned pay out to protect against skillful or knowledgeable play . consider a bonus game testing player &# 39 ; s knowledge . the knowledge - based bonus game could be atop an underlying conventional slot machine . the slot machine can be a standard stepper - reel or video - reel which includes a bonus feature . the overall game is the underlying game of chance plus the bonus game . the knowledge - based bonus game could be achieved upon reaching a win or other random event during primary play of the underlying slot machine . without loss of generality , assume that with x units wagered , the player is eligible for the knowledge - based bonus game with frequency f . the expected return is r units for the game without the bonus , and during the bonus participation , on average , garners a bonus value of b units . the formula for calculating the house advantage may be written as : for example , consider a slot machine in which the player ( with max bet , x , of 3 coins - in ) is eligible for a knowledge - based bonus game with frequency of 0 . 01 ( 1 in every 100 spins ). furthermore , the expected return r , on the conventional underlying game of chance without the bonus , is 2 units or ( 66 . 7 %). assume a desired house advantage of 8 %. solving formula 1i , the desired b = 76 units . it is important to note that the value of b represents an average award of 76 units . each individual visit to the bonus round may award the player with more , or less , than 76 units so long as on average , 76 units are paid . to allow play by a player with perfect knowledge while maintaining a house advantage , one form of this invention occurs as the machine distributes b . for example , when an incorrect answer to a knowledge - based game is given , the player receives just a portion of b , the remainder of b being deposited to a player &# 39 ; s escrow account . at such time as any player triggers the escrow ( in a manner to be described ), the current value of the players &# 39 ; escrow account is awarded . for example , in one embodiment , a correct answer triggers the escrow ; the correctly answering player receives b plus the current value of the escrow . as used herein players &# 39 ; escrow is an accumulating , or progressive , fund available for future players . in this example , although an individual player may or may not receive the entire value of b , a portion of b has been awarded upon each visit to the bonus round ; the remainder of which has been “ awarded ” to escrow . from the casino or house operator &# 39 ; s point of view , a constant house advantage is thus ensured . the casino , house or operator , in fact , does not care if the current or a future player ( via escrow ) receives the escrowed portion of b . what is important to the casino , house or operator is that all of b has been paid ( either immediately or to escrow ), and in this sense is no longer on the machine &# 39 ; s “ books .” more importantly , the player with perfect knowledge can , at best , instantaneously win just the awarded portion of b , since the escrow represents prior “ awards ” from the operator &# 39 ; s point of view . for example , consider a game with the parameters as described already , and with a knowledge - based bonus game that functions in the following manner . a touch screen is employed and the player is presented with a question and three possible answers . if the player answers correctly , 76 units plus the current value of the escrow are awarded . if the player answers or guesses incorrectly , a portion , 50 units , is awarded and the remainder , 26 units , is added to escrow . in this way , the value b for the knowledge - based bonus game is preset at 76 units , whether or not the player answered the question correctly thus , a method has been disclosed for maintaining the house advantage constant , regardless of the player &# 39 ; s knowledge level . the game has the appealing feature that should a player fail to answer correctly , the escrow value grows , prompting the player to continue in an effort to revisit the bonus and “ unlock ” the accumulated award . note that the player need not be prompted with possible responses . a keyboard or voice recognition mechanism can be employed to input answers . for example , the query “ what is the present population of las vegas ?” might be given . the closer a player guessed at the correct answer , the greater the fraction of b that would be awarded . any remaining units would be credited to the escrow meter . furthermore , stipulations such as “ player cannot be higher than the answer ” or “ player cannot be lower than the answer ” can be put in place as an added twist to the game . also , a series of questions could be utilized to challenge individuals with superior knowledge . thus , a player answering correctly may be rewarded and queried with another question , and so forth , until missing a question . alternatively , a quiz comprising , e . g . seven questions might be given and the player rewarded a portion of b based on the percent of correct answers of the total answers . the remainder of b would be credited to the escrow meter . should a player answer all seven questions correctly , the player would win the collected escrow award in addition to the value of b . in addition , a time limit may be placed on the player . this time limit may be such that after time expires , the player is awarded as if he had answered incorrectly . alternatively , a timer may be employed such that a player who answers correctly quickly is awarded a larger prize than a player who answers correctly albeit more slowly . too , a timer may be employed such that any quick answer ( whether correct or incorrect ) receives a larger award than the corresponding ( correct or incorrect ) slow answer . the awarding step includes the step of basing the amount of the award on the length of time taken to complete the knowledge - based game . the awarding step includes the step of yielding generally higher awards for a shorter length of time , and lesser awards for a longer length of time . also , clues may be given to help the player determine the correct answer . these clues may be given as a function of time ( e . g ., every 5 seconds , another clue is revealed ). alternatively , the clues may be “ bought ” by the player , either literally or in the form of reduced awards . for example , consider the query “ which state in the united states has the largest area ?” assume a bonus value b of 50 coins . should the player want to buy a hint , it may cost an additional wager of 10 coins . hence , the puzzled player may literally buy a hint for 10 coins . hints such as “ the state begins with the letter ‘ a ’” or “ the state is not part of the continental u . s .” may be given to help the player determine the correct answer , albeit at a lesser net than if the player had correctly determined the answer without buying any hints . the awarding step includes the step of yielding generally higher awards for a lesser number of clues , and yielding generally lesser awards for a greater number of clues . the step of awarding further includes the step of a player buying a clue . questions may also be utilized which may have several correct answers ( e . g ., survey questions ), or may have answers that can be scaled to responses ( e . g ., how “ close ” the player guessed at the actual answer ). furthermore , puzzles , etc . can also be provided in which logic and / or knowledge results in a known method of solution with no uncertainty . whether used as a bonus or as a part of a game , the means of initiating the bonus or entering the part of the game is immaterial to this invention . what is material is that during a bonus game , as explained , the algorithm described ( or something similar ) is used to ensure either a constant house advantage or essentially so . the exact nature of the bonus game could be one of many possibilities , some of which have been described . it is important to note that while the teachings of this invention are suitable for knowledge - based gaming , the invention can be applied to non - knowledge - based gaming as well . for example , the player may , upon visiting a bonus game of value b , roll two dice . if the total is 12 , the player wins the value of b plus the escrow award . if the player rolls 7 through 11 inclusive , he wins ¾ of b , the remainder going to escrow . if the player rolls less than 7 , he wins ½ of b , the remainder going to escrow . in this fashion , the current invention can be applied to a game with no skill or knowledge . in this case , the advantage is that a player who did not unlock the escrow is encouraged to continue to play . similarly , the game may be applied to a game of skill , but not knowledge . we note that the house advantage is constant when the escrow begins anew at zero immediately after being won . however , the house may wish to “ re - seed ” the escrow at a non - zero value to encourage additional play immediately after an escrow amount has been won . below we discuss two methods by which a non - zero reset may be accomplished . a first method of accomplishing a non - zero reset is for the house simply to provide that reset value for a new escrow after an escrow is won . in so doing , the house foregoes a constant house advantage , since the actual house advantage will be a function of how often the escrow is won . however , the house will encourage additional play since the escrow never resets to zero . a second , preferred , method is for the house to further set aside a portion of each escrow contribution to a reserve . in this case , the players &# 39 ; escrow account is further divided into a current escrow and a reserve escrow . each contribution is apportioned to either the current or reserve escrow . when the current escrow fund is won , the value of the reserve escrow becomes the new reset value of the current escrow . the advantage herein is that additional play is encouraged , even immediately after an escrow has been won , while maintaining a constant house advantage . the method may have the step of adding to the at least one escrow account includes the steps of dividing into a current escrow account and a reserve escrow account . the method could also have the step of dividing includes putting a bigger share into the current escrow account and a smaller share into the reserve escrow account . for example , consider a bonus game of average value b equal to 100 . a player not winning the bonus round is awarded an average of 40 , the remaining 60 being distributed in the following manner : 40 to the current escrow , and 20 to the reserve escrow . as before , a player winning the bonus round is awarded 100 plus the current escrow . if , on average , it requires 5 visits ( 4 unsuccessful plus 1 successful ) to the bonus round to unlock the current escrow , then the average reset value will be 80 coins , and the average value of the current escrow , when successfully won , will be 240 coins . note that while this example contributes to the reserve escrow only when a player is unsuccessful in winning the current escrow , this need not be the case . indeed , a contribution to the reserve escrow may be made upon each visit to the bonus round , or based upon some other criteria , such as randomly , upon every successful visit to the bonus round , upon every other visit to the bonus round , and so forth . too , the portion contributed to the reserve escrow need not be fixed . to summarize , the exact nature by which the reserve escrow is funded is not material to this invention . what is material is that there is a reserve escrow suitable for re - seeding the current escrow after being won . while the foregoing has been discussed in terms of a bonus game , the teachings herein are equally applicable to a standalone configuration . consider a game in which x = 10 units must be wagered . the award for the game is randomly selected from the following weighted pay table : the average potential award is thus 0 . 1 × 5 + 0 . 2 × 8 + 0 . 6 × 10 + 0 . 1 × 15 = 9 . 6 units = b . a player is given a question and two possible responses . should the player answer correctly , he is awarded the potential award plus any escrow . should the player answer incorrectly , he is awarded nothing , the potential award being added to escrow . it is clear , based on the discussion above , that the house , in effect , is paying an amount equal to b on every play . if the player is correct , the house is paying the player directly ( plus any escrow ). if the player is incorrect , the house is paying the player indirectly through escrow . hence , the house advantage for this game ( using formula 1 with r = 0 and f = 1 ) is simply : ( x − b / x = 4 % it should be clear that the teaching above of current and reserve escrows is equally applicable in the case of a standalone game . note that the foregoing example is illustrative only and not meant to limit the teachings of the invention . the use of questions and answers is also illustrative , and any suitable game could be employed . the following represents an illustrative example under the teachings of the present invention of implementing a knowledge - based game as bonus game atop underlying games of chance . although a preferred embodiment , this in no way should be interpreted to limit the scope of the invention . instead , it is meant to indicate possibilities under the teachings of this invention . consider a slot machine with a knowledge - based bonus game in which , periodically , the player gets to participate in family feud . as in the game show , a question given to 100 people will be presented to the player . seven possible answers will be shown to the player , comprising in random order the top five actual answers and two bogus answers . the object of the game is for the player to choose the five correct answers while avoiding the two incorrect answers . upon beginning , and during each subsequent turn after a correct guess , the player selects an answer believed to be one of a top five or most popular actual answer . if chosen correctly , then the number of people ( between 1 and 100 ) that gave the player &# 39 ; s response is credited or awarded to the player , and another guess is allowed . if guessed incorrectly , then the knowledge - based bonus game ends , with any unclaimed credits ( i . e ., the sum of the actual answers not chosen ) deposited to the progressive or escrow account . e . g ., the query “ name something everyone complains about ” might be accompanied by these responses : the actual survey results of 100 people show in parentheses . for the example given , they total 100 but could be slightly less . the actual survey results would be invisible to the player as the answers are sought . for exemplary purposes , assume the escrow progressive is presently at 300 coins . if the player selects ( d ), he is awarded 11 coins and another guess . the choice ( 0 ) is no longer displayed , or otherwise denoted as already having been guessed . thereafter , if the player selects ( b ), he is awarded 35 more coins and another guess . again , choice ( b ) is no longer displayed . thereafter , if the player picks ( c ), the knowledge - based bonus game is over since this is a bogus answer . the player receives a total of 35 ÷ 11 = 46 coins . the remaining 26 + 21 + 7 = 54 coins are added to the escrow , for a new progressive total of 354 coins . upon a player ( the same one or another at that machine ) again entering the bonus round , the escrow would show the new total of 354 coins . the game continues this way until a player correctly guesses the five actual answers while avoiding the two bogus answers . doing so awards the player not only the values for the actual answers , but also the current value of the escrow . thereafter , the escrow resets to zero coins , or if desired , some other initial value that is a design choice . alternately , under the teachings herein as described above , a reserve escrow may also be employed so as to reseed an escrow after being won . the example above is illustrative only and not meant to limit the teachings of this invention . a method of a house apportionment of a bonus value is used to pay during play of a bonus game . fig1 shows a flow diagram for the house apportionment of the bonus game bonus value . entry of the bonus game is achieved during play of an underlying game of chance . the method of house apportionment includes steps of awarding the player a portion of the bonus value and adding the remainder of the bonus value to at least one escrow account available to reward the player or subsequent players . the awarding step is based on the bonus game including the step of knowledge - based playing . the awarding step of the knowledge - based bonus game includes the step of knowledge - based playing by answering , selecting or guessing the appropriate responses to queries . the step of knowledge - based playing includes the step of selecting or guessing the appropriate answers to multiple choice questions . the step of knowledge - based playing by answering , selecting or guessing includes the step of challenging the player with questions having a common theme . the knowledge - based playing step of the bonus game includes the step of asking the player questions the value of which is measured against survey responses . the knowledge - based playing by the step of answering , selecting or guessing includes the step of asking questions of varying difficulty . the step of awarding includes the step of first achieving a predetermined yet random event in the underlying game of chance to begin play of the bonus game . the expected value of the bonus game is fixed regardless of player proficiency in the bonus game . the awarding step of the bonus game happens with the wagering of x units to be eligible for the bonus game with a frequency f and with the expected return r units for an underlying game without the bonus , and with bonus participation , on average , garnering the expected bonus value of b units and wherein the step of calculating the house advantage as equal to −[ r + fb − x ]/ x . the step of adding to the at least one escrow account includes the steps of dividing into a current escrow account and a reserve escrow account . the step of dividing includes putting a bigger share into the current escrow account and a smaller share into the reserve escrow account . the method of house apportionment including the steps of awarding the player a portion of the bonus value and adding the remainder of the bonus value to at least one escrow account available to reward the player or subsequent players . the step of predetermining the bonus value paid by the house follows . the step of awarding the bonus value is with a step of selecting the bonus value randomly . the awarding step includes fixing the expected bonus value of the bonus game regardless of player proficiency in the bonus game . the method of house apportionment includes the steps of , awarding the player a portion of the bonus value and adding the remainder of the bonus value to at least one escrow account available to reward the player or subsequent players . the average bonus value paid by the house remains constant . thus the house advantage is fixed regardless of player proficiency in the bonus game . the steps of awarding and adding will be steps that over time provide a constant house advantage . the steps of awarding and adding are performed in connection with the step of playing a knowledge - based bonus game . the step of predetermining the bonus value paid by the house is followed . the step of determining randomly the bonus value paid by the house is practiced . the step of determining the bonus value paid by the house is predetermined . the step of determines randomly the bonus value paid by the house . a method of playing a casino game has the steps of accepting a wager and determining a value . fig2 shows the flow diagram for the house apportionment for a casino game value . fig3 shows a flow diagram of a method of house apportionment of a value disclosed for a knowledge - based game of the present invention . then the step of awarding the player a portion of the value . the step of adding a remainder of the value to the at least one escrow account available to reward the player or subsequent players is followed . the average value paid by the house remains constant and the house advantage is fixed regardless of player proficiency in the game . the steps of awarding and adding happen while playing a knowledge - based game . what is useful about the described approach is that , from a casino or house operator &# 39 ; s point of view , every time the bonus round begins , a known average number of coins are awarded . the credits are awarded either to the player immediately , to the escrow account ( to be dispensed later ), or between the two . some known average bonus round award , from the casino , house or operator &# 39 ; s point of view , is distributed , either to the current player or a players &# 39 ; escrow account . as such , the house advantage for the slot machine and knowledge - based bonus game remains predetermined . while the knowledge - based game for bonus , jackpot , progressive , or otherwise including the underlying game , has been described with variations and in connection with at least several particular embodiments , it should be understood that the details given are not meant to limit the teachings of the invention . in particular , the manner in which the knowledge - based game may be conducted may vary greatly . in the case of knowledge - based questions , the manner in which they are asked can also be varied greatly . the manner in which a player may win the escrow amount may also be by design choice , as is the fractional division of the award round between immediately awarded to the player and that saved to escrow to be awarded later . the approach applies to all casino games , and is especially well suited to games wherein the player may have a high level of knowledge or skill . in the claims , the concept includes apportionment of the value via a remainder funded escrow or variants thereof .