Dr. R. Robinson 04/18/2014

PROBLEM STATEMENT

This report presents an analysis of whether for this casino, giving free-play on slot-machines (called promo-play below) motivated casino patrons to play their own funds after the free-play was exhausted. Given that the average hold for this casino was 9%, the coin-in per $1 of promo-play redeemed must exceed $11.11 if players gambled with their own funds after their promo-play was exhausted. (See the appendix to this report for an explanation of this $11.11 figure.) To explore this return to promo-play, the day-of-the-week effects, seasonality effects, and holiday effects were measured and controlled for, and the returns to promo were measured independent of these effects.

In addition, the days with significant negative and positive outliers are identified. Also, a forecast for the next day’s coin-in is presented. This forecast assumes $20,000 of promo redeemed.

DATA ANALYZED

Daily data for total coin-in and free-play for 150 days was analyzed for the G21 casino. The recorded data began on 12/18/2009 and ended 05/16/2010. Table 1 presents the basic statistics for this data. Table 2 presents the mean statistics per day-of-the-week and shows the mean statistics of seasonality and holiday.

Table 1

Basic Statistics for Coin-In and Promo-Play

For 12/18/09 Through 05/16/10

Mean

Maximum

Minimum

Standard Deviation

Coin-In

$2,297,821

$4,026,877

$1,251,546

$592,194

Promo

$19,451

$61,144

$3,729

$11,803

Table 2

Mean Statistics Per Day-of-the Week For Coin-In and Promo-Play

For 12/18/09 Through 05/16/10

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Coin-In

$2,516,218

$1,760,379

$1,795,949

$2,032,996

$2,153,796

$2,877,025

$2,882,557

Promo

$12,233

$20,683

$19,265

$25,533

$15,121

$32,079

$11,367

STATISTICAL METHODS

OLS regression was used to estimate model equation (1) where ∈ is the random-error term with the usual OLS assumptions applying.1 The regression coefficients m, t, w, r, f, s, are for the respective day-of-the-week dummy variables (0 or 1), and where the coefficient for Sunday was not included in order to avoid the dummy variable trap. N and H are depicted for seasonality effects and holiday effects respectively An F-statistic was used for testing hypothesis (i) given below.

A t-statistic was also utilized for testing the magnitude of the coefficient β1, as presented in hypothesis (ii) given below. To test whether the t-test is appropriate, a χ2 test for normality of the residual errors associated with the OLS estimate of model equation (2) is presented as hypothesis test (iii). To test for the randomness of the residual errors, a non-parametric runs test is presented to test hypothesis (iv). An F-statistic was also used to test hypothesis (v) given below, i.e., whether model (2) has greater explanatory power than model (1).

Equation (3) gives the predicted value for coin-in given a prediction for promo, and (4) gives the confidence interval for that prediction.

Coin-int = β0 + m(0 or 1) + u(0 or 1) + w(0 or 1) + r(0 or 1) + f(0 or 1) + s(0 or 1) +

+ N(0 or 1) + H(0 or 1) + ∈t (1)

Coin-int = β0 + m(0 or 1) + u(0 or 1) + w(0 or 1) + r(0 or 1) + f(0 or 1) + s(0 or 1) +

+ N(0 or 1) + H(0 or 1) + β1Promo-Playt + ∈t (2)

E(Coin-in) = β0 + … + β1 E(Promo-Play) (3)

95% confidence interval: E(Coin-in) t2.5% (S.E.of Prediction) (4) (i) H0: m = t = w = r = f = s = N=H= 0.

Tested with an F-statistic, α = 5%.

(ii) H0: β1 > 11.11.

Tested with a t-statistic, α = 5%.

(iii) H0: The residual errors associated with the OLS estimate of (2) are normally distributed. This is tested with a χ2 statistic, α = 5%.

(iv) H0: The residual errors are randomly distributed. This is tested with a non-parametric runs…