document: Stochastic recurrences of Jackpot Keno We describe a mathematical model and simulation study for Jackpot Keno , as implemented by Jupiters Network Gaming -LRB- JNG -RRB- in the Australian state of Queensland , and as controlled by the Queensland Office of Gaming Regulation -LRB- QOGR -RRB- -LRB- http://www.qogr.qld.gov.au/keno.shtml -RRB- . 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 -LRB- Brockett and Levine , Statistics & Probability & their Applications , CBS College Publishing , 1984 -RRB- , 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 pay-scales so as to satisfy legal requirements of approximately 75 % of net revenue returned to the players , i.e. , 25 % net hold for the house -LRB- JNG -RRB- . Details of the algorithm used to solve this problem are presented , 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
doc_bio_tags: B I O B I O O O B I O B O O B I O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O B I O O B I I O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B I I O O O O O O O O B I I O O O O O O O O O O B O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B I O O O O O O O O O O O O O O
extractive_keyphrases: stochastic recurrences jackpot keno mathematical model simulation jupiters network gaming house net hold piecewise linear ternary domain split random number generator inverse problem stochastic binary search probability experimental results
abstractive_keyphrases: legal requirement chinese lottery game