Stochastic Recurrences of Jackpot Keno Sugden, Stephen J; Noble, Chris

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Sugden, Stephen J ; Noble, Chris
recurrence; Jackpot; simulation
We describe a mathematical model and simulation study for Jackpot Keno, as implemented by Jupiters Network Gaming (JNG) in the Australian state of Queensland, and as controlled by the Queensland Office of Gaming Regulation (QOGR) qogr. The recurrences for the house net hold are derived and it is seen that these are piecewise linear with a ternary domain split, and further, the split points are stochastic in nature. Since this structure is intractable brockett, estimation of house net hold obtained through an appropriately designed simulator using a random number generator with desirable properties is described. Since the model and simulation naturally derives hold given payscale, but JNG and QOGR require payscale given hold, an inverse problem was required to be solved. This required development of a special algorithm, which may be described as a stochastic binary search. Experimental results are presented, in which the simulator is used to determine jackpot payscales so as to satisfy legal requirements of approximately 75% of net revenue returned to the players, i.e., 25% net hold for the house (JNG). Details of the algorithm use to solve this problem are presented here, and notwithstanding the stochastic nature of the simulation, convergence to a specified hold for the inverse problem has been achieved to within 0.1% in all cases of interest to date.
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