A 2010 UNLV Master’s thesis by Ghaharian [Ghaharian, Kasra Christopher. “A mathematical approach for optimizing the casino slot floor: A linear programming application.” (2010)] used linear programming to perform an optimization of an unspecified Las Vegas casino floor, using coin-in and win data for 1812 slot machines, divided into 19 types and denominations. Realistic constraints were specified, corresponding to the maximum change to the number of each machine type/denomination that the management might be willing to implement. Ghaharian presented results that separately maximized the total slot floor coin in and win values for the property.
nQube specializes in multi-objective optimization and data-modeling, which allows us to simultaneously optimize both coin-in and win objectives. This figure shows the trade-off surface for these competing objectives, defined by the property that win cannot be improved without sacrificing coin-in, and vice-versa. The blue dots represent the trade-off surface; the red star is the initial point representing the casino’s current mix of machines; and the green circles represent a selection of representative optimal solutions. The delta values are the total number of machines that need to be swapped to achieve the representative solutions shown.
We have used the same linear model as Ghaharian here, hence the linear appearance of the trade-off curve. However, our software is capable of very large non-linear multi-objective optimization problems. A non-linear model may be justified by finer scale data on individual machine performance than the aggregate data used here.