UNITED STATES TAX COURT

FRANCIS M. GAGLIARDI )

)

Petitioner, ) Docket No. 23912-05

)

v. )

)

COMMISSIONER OF INTERNAL REVENUE, )

I, Mark C. Nicely, hereby provide the following expert witness report on behalf of

Petitioner, Francis M. Gagliardi:

I. QUALIFICATIONS.

I am trained as a mathematician and computer engineer, having graduated with a

Bachelors of Science in Electrical and Computer Systems Engineering degree from Renssalear

Polytechnic Institute. I am currently a casino gaming consultant and director of gaming design

for a casino software company. I have extensive experience in the casino and gaming industry,

as reflected in my curriculum vitae attached as Exhibit 1, including working as a director of

mathematics and director of product development for a multi-media slot machine manufacturer,

as well as past and ongoing consulting to gaming and slot machine manufacturers.

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Mr. Gagliardi could actually have achieved financial “break even” or better from casino machine

Mr. Gagliardi’s casino gaming machine play resulted in respective losses of approximately

$638K, $678K, and $507K, with an error range of plus or minus $65K, $72K and $83K,

respectively (with a 95% confidence level). The probability that Mr. Gagliardi achieved financial

break even or better in those years under the described betting circumstances/assumptions is

astronomically unlikely (greater than 1 in a trillion).

III. DISCUSSION OF CALCULATIONS AND BASIS.

A. Summary.

My calculations are summarized in the accompanying Data and Calculations Chart,

attached hereto as Exhibit 2. One sample curve is illustrated in the accompanying Graph

attached hereto as Exhibit 3. Below I discuss my approach, assumptions, and calculations.

the casinos he frequented and the calendar years involved, I then drew upon my own industry

experience and relevant literature to determine the appropriate Return to Player (“RTP”) ratios

and related standard deviation. As discussed more fully below, I utilized an average RTP

assumption as well as a “best case” and “worst case” assumptions to illustrate the likely range of

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outcomes. I then calculated the expected financial outcomes, the normal range of these

C. Assumptions.

Mr. Gagliardi indicates that he gambled almost every day for stretches up to 15 to 20

hours, and that his level of gambling increased from 1999 through to 2001. The following

conservative assumptions, based on information from Mr. Gagliardi, were used for the analysis.

I accounted for 250, 275 and 325 full days of gambling for each of the years 1999, 2000 and

2001 respectively. For each full day of gambling, I accounted for 7 hours of effective gambling,

at a rate of 250 games per hour, or just over 4 games per minute.

Mr. Gagliardi indicated that he would vary his bet, with low bets in the $3.75 and his

highest bets being $20 for Keno and $16 for video slots. I used average bet values of $9.00,

$9.50 and $10.00 for each of the years 1999, 2000 and 2001 respectively. These figures seem

reasonable within the context of my industry knowledge and experience of serious gamblers.

were they required to do so during the years at issue.

My own online research and industry experience were used to derive appropriate RTP

ratios. In 2003, The Weekly Standard and Wall Street Journal both reported a 70% RTP for

Native American casinos in California. The keno machine Mr. Gagliardi played has operator

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selectable RTP, in 5% increments, between 55% payback and 90% payback, with a default

likely RTP for San Diego County Native American casinos during the years in question. The

RTP has likely increased at Native American casinos within the last few years with the increased

expansion in Nevada-style slot machines. Other published sources indicate 90% as the highest

expected payback for more recent times. For these reasons, I created three scenarios based upon

three different RTP assumptions: 90% for best case (best possible player payback), 70% for

worst case (worst possible player payback), and 83% for average case (the most likely player

payback).

Similarly, I relied upon a range of industry standard top award allocation percentages to

analyze only the base-game effect (since the top awards were captured via W-2G filings.) Even

this range is conservative as I have seen game models with 1% or lower allocated to top awards

and as high as 6%.

D. Calculations.

confidence intervals to determine expected outcome range, per the standard statistical technique

for predicting wins or losses in the casino industry. Confidence intervals were also used to try to

quantify the likelihood of Mr. Gagliardi having a break-even or better results, per the standard

statistical method for analyzing actual wins or losses in the casino industry.

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In the casino industry, a confidence level of either 90% and 95% is the typically used. I

1999 using the “average” assumptions.

The reported wins, $131,281, was indicated from the W2-Gs. The total number of

games, 437,500, is the product of bets/hour x hours/day x days of gambling in 1999, or

250 x 7 x 250. The total money wagered, $3,937,500, is the product of the number of

games x the average bet size of $9. As I already knew the winning from top awards, I therefore

had to calculate the expected base-game awards (all awards excluding those which would trigger

a W2-G filing) based on a base-game RTP of 80.5%. = 83.0% - 2.5% for top awards. The

product, $3,937,500 of total wagers x 80.5%, is the expected base-game awards $3,169,688.

Adding the $131,281 of known top awards with the $3,169,688 of expected base-game awards

yielded a total expected awards of $$3,300,969. The expected total win was therefore -

$3,937,500 + $3,300,969 = -$636,532, or in other words, a loss of $636K

normal variation range = (z σ /√n)

where:

z = normal distribution z-score. For a 95% confidence level, we use z=1.960

σ = standard deviation of the base game, or 5.6

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√n = square root of the total number of games

To calculate the odds that the overall winnings matched or exceeded the wagers, I used

the same confidence interval equation as above, but I determined the value of z needed to

produce the normal variation range required to include the break-even point. Specifically, I

calculated that the base-game would have needed an RTP of 96.7% in order for the base-game

winnings to be $ $3,806,219 = total money wagered of $3,937,500 – top award wins of

$131,281. This would require a normal variation range of 16.2% = 96.7% required – 80.5%

expected. Solving the confidence interval equation of 16.2% = (z x 5.6) / √960,000, yields a

value of z=19.1.

Normal distribution z-score tables published in statistics books and mathematical

handbooks usually only publish the probability equivalent of z values up to 3.0 (also known as

“3 sigma”). One statistics book did list the odds for z=5 in excess of 1 in 3 million. The

wins for those years. For the other best case and worst case scenarios, the alternate RTP

assumptions are used as described therein.

To visually represent the impossibility of an overall win, I constructed a graph of the

probability curve for the overall expected results using the most optimistic assumptions. Marked

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on the graph is the average expected loss of $775K, as well as the high and low ranges of $647K

expected range is from the break even point.

Dated: August ____, 2006 Respectfully Submitted,

MARK C. NICELY

EXHIBIT 1

CURRICULUM VITAE

OF MARK C. NICELY