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.