Plaintiffs' Expert Witness Affidavit featuring testimony from Professor Robert C. Hannum

8/10/2019 Plaintiffs' Expert Witness Affidavit featuring testimony from Professor Robert C. Hannum

1/22

STATE OF WISCONSIN CIRCUIT COURT DANE COUNTY

STEVE VERRETT,8162 Stagecoach Road Case No: C!oss "#a$%s, WI &'&28(

a%d

)AR* *ROON+'1 -!ee% A.e%/e)ad$so%, WI &'0+

"#a$%t$s,Dec#a!ato! 3/dg4e%t

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RAD SC7I)E,Atto!%e -e%e!a#10 West )a$% St!eet)ad$so%, WI &'0'

Dee%da%t5

PLAINTIFFS EXPERT WITNESS AFFIDAVITOF PROFESSOR ROBERT C. HANNUM

STATE OF WISCONSIN 99 SS

DANE COUNTY 9

I, ROERT C5 7ANNU), he!e de;ose a%d sa /%de! oath:

15 I ha.e ee% !eta$%ed as a% e$%se!t add!ess he!e?5

Qualificati!" a!# Bac$%&u!#

1


2/22

25 I a4 a "!oesso! o R$s@ A%a#s$s -a4$%g at the U%$.e!s$t o De%.e!5

'5 I g!ad/ated !o4 the U%$.e!s$t o Dato%, =$th a ache#o!Bs Deg!ee 5S59 $%

)athe4at$cs $% 10+ a%d !o4 F#o!$da State U%$.e!s$t =$th a )aste!s )5S59 $% Stat$st$cs $%

106, o##o=ed a Docto!ate "h5D59 $% Stat$st$cs $% 105 I% 2+, I eca4e a F/## "!oesso! o

Stat$st$cs at the U%$.e!s$t o De%.e! cha%ged $% 21 to F/## "!oesso! o R$s@ A%a#s$s

-a4$%g9 a%d a4 a 4e4e! o the E


3/22

a%d the /s$%ess o cas$%o ga4$%g9( Gaming $a% a co/!se he#d $% as Vegas, =$th ha#Gdoe%

=o!#dGc#ass e


4/22

Edge: )athe4at$ca# A%a#s$s o Cas$%o -a4es5 Va%c/!a, Ead$%gto%, a%d Co!%e#$/s, eds5,

U%$.e!s$t o Ne.ada Re%o "!ess5

05 I he#d a Sess$o% Cha$! at the 10, 2, a%d 2 I%te!%at$o%a# Co%e!e%ce o%

-a4#$%g a%d R$s@GTa@$%g5 I =as a !ee!ee o! t=o ;a;e!s $% the 20 .o#/4e O;t$4a# "#a:

)athe4at$ca# St/d$es o -a4#$%g5 I ha.e a#so a;;ea!ed as a eat/!ed s;ea@e! at a %/4e! o

ga4$%g co%e!e%ces, $%c#/d$%g:

a5 J"o@e! a%d S@$##,K 1+th I%te!%at$o%a# Co%e!e%ce o% -a4#$%g R$s@ Ta@$%g,

a@e Tahoe, )a, 25

5 JS/;e! "a% : U%!a.e#$%g the )ste! o the 0L a%@$%g R/#e,K 1+th

I%te!%at$o%a# Co%e!e%ce o% -a4#$%g R$s@ Ta@$%g, a@e Tahoe, )a, 25

c5 J-a4$%g )ath: 7o= Cas$%os )a@e )o%e,K 3oh%s 7o;@$%s Co%e!e%ce o!

Ed/cato!s, as Vegas, NV, 3a%/a! 25

d5 J"o@e! a%d the a=,M -a4$%g a= S4;os$/4, D!a@e a= Schoo#, Se;te4e!

285

e5 MTa#e -a4es a%d "!o$ta$#$t: )o%e, )ath, a%d )ths,M -a4$%g O;e!at$o%s

S/44$t, as Vegas, NV, A;!$# 20

5 M*%o=$%g Whe% to 7o#d BE4 a%d Whe% to Fo#d BE4: The )athe4at$cs o "o@e!,M

NSF "!og!a4 o% -a4es o Cha%ce, U%$.e!s$t o Utah, 3/# 2&5

g5 MA )athe4at$ca# A%a#s$s o Cas$%o Dead Ch$; "!og!a4s,M I%te!%at$o%a# Acade4

o /s$%ess a%d Eco%o4$cs Co%e!e%ce, Octoe! 2'5

h5 M)athe4at$cs a%d -a4$%g Reg/#at$o%,M U%$.e!s$t o Ne.ada Schoo# o a=,

Octoe! 2'5

4


5/22

$5 MStat$st$ca# Sta%da!ds $% -a4$%g Reg/#at$o%: Fact a%d F$ct$o%,M I%te!%at$o%a#

)aste!s o -a4$%g a= S4;os$/4, Se;te4e! 2'5

5 M-a4$%g a= a%d )athe4at$cs,M U%$.e!s$t o Ne.ada Schoo# o a=, Se;te4e!

225

@5 M7o= Cas$%os )a@e )o%e,M As$aG"ac$$c -a4$%g Cas$%os Wo!#d Co%e!e%ce,

S$%ga;o!e, 3/%e 225

#5 MCas$%o )athe4at$cs,M Se4$%a! o! cas$%o e


6/22

o!a# a!g/4e%ts $% the case o% Octoe! 1, 215

5 Common%ealth o! (entuc"y v' )*) Internet +omain ames 2895 Th$s case

co%ce!%ed a go.e!%4e%t eo!t to se$e 1+1 se;a!ate do4a$% %a4es assoc$ated =$th o%#$%e

ga4#$%g5 The "o@e! "#ae!s A##$a%ce $#ed a% a4$c/s !$e a!g/$%g that the ;o@e!G!e#ated

do4a$% %a4es d$d %ot !e#ate to ga4#$%g eca/se ;o@e! $s %ot a ga4e o cha%ce5 Test$4o% .$a

a$da.$t59

c5 Peter #' Stone v' Commissioner o! Revenue Services, State o! Connecticut2695

Th$s case co%ce!%ed =hethe! o! %ot: 19 the ;#a$%t$ =as a ;!oess$o%a# ga4#e! $% the t!ade o!

/s$%ess o ga4#$%g /%de! the I%te!%a# Re.e%/e Code, 26 D5S5C5 162a9( 29 the De;a!t4e%t

o Re.e%/e Se!.$cesB $%co4e ta< =as d$sc!$4$%ato! as a;;#$ed to "#a$%t$ a%d othe! $%d$.$d/a#s

catego!$ed the Co44$ss$o%e! as %o%G;!oess$o%a# ga4#e!s( '9 the State $4;e!4$ss$#

d$sc!$4$%ated aga$%st $%d$.$d/a#s ased /;o% the t;e o ga4#$%g act$.$t e%gaged $%( a%d +9

the State se#ect$.e# e%o!ced $%co4e !e;o!t$%g !eP/$!e4e%ts aga$%st those =$%%$%g #a!ge! s/4s

o 4o%e $% ga4#$%g act$.$t$es5

d5 Thomas Cala%ay v' -isconsin +epartment o! Revenue 2&95 Th$s case

co%ce!%ed a ;et$t$o%e! =ho =as a##eged to ha.e ee% e%gaged $% a t!ade o! /s$%ess $% ;#a$%g

s#ot 4ach$%es $% as Vegas a%d At#a%t$c C$t5

15 I s;ec$a#$e, a%d a4 a% e


7/22

115 I ha.e ee% as@ed the "#a$%t$s $% th$s case to 4a@e th$s A$da.$t a%d to test$

o% the$! eha# to ;!o.$de $%de;e%de%t e


8/22

1+5 ett$%g $% ;o@e! ;!oceeds $% J!o/%ds5K I% a !o/%d o ett$%g, the ;#ae!s act $%

seP/e%ce, a%d ca% 4a@e o%e o se.e!a# 4o.es5 I %ood has et, the% the ;#ae! =hose t/!% $t $s

to act 4a e$the! Jchec@,K =h$ch 4ea%s that he chooses %ot to et, a%d to a##o= the %e


9/22

A%othe! !o/%d o ett$%g the% ta@es ;#ace5 Ne


10/22

cha%ce ass/4$%g the o!de! $% =h$ch ;#ae!s 4o.e $s dec$ded a !a%do4 4echa%$s495

25 eca/se e.e% $% the 4ost s@$##/# o ga4es, s/ch as go#, asea##, a%d chess, a

cha%ce e.e%ta !ea@$sh g/st o =$%d that ca!!$es a ;e!ect# st!/c@ go# a## $%to a haa!d, a%

/4;$!es ad ca##, o! the a!$t!a!$# a=a!ded ad.a%tage o ;#a$%g the =h$te s$de o the

chessoa!d4a !eP/e%t# a#te! the o/tco4e o the ga4e, $t 4a@es the 4ost se%se to as@ %ot

=hethe! s@$## a#=as a%d e


11/22

!et$!e o! good, o! he ca% ;#a tho/sa%ds o ha%ds o.e! the co/!se o a #$et$4e5 Th/s, a%od

a%a#$%g the %at/!e o ;o@e! 4/st dec$de =hethe! to co%s$de! o%# a s$%g#e o! a e= ha%ds o

;o@e!, o! $%stead co%s$de! ;o@e! o.e! the #o%g !/%5

2+5 The #o%g !/% $s the 4ost a;;!o;!$ate !a4e=o!@, o! t=o !easo%s5

a5 F$!st, a #o%g .$e= $s the 4ost co%s$ste%t =$th the sc$e%t$$c 4ethod5 I% sc$e%ce, a%d $%

stat$st$cs es;ec$a##, #a!ge sa4;#e s$es a!e c!/c$a# to e%s/!e that the !es/#ts o a t!$a# acc/!ate#

!e#ect !ea#$t5 S4a## sa4;#e s$es, o% the othe! ha%d, c!eate a s$g%$$ca%t !$s@ o e!!o!, as o%e

!$s@s ge%e!a#$$%g !o4 $d$os%c!at$c acts5 Fo! e


12/22

that a!e dea#t5 Th$s $%de;e%de%ce d!a=s a !$ght #$%e et=ee% s@$## a%d cha%ce, a%d a##o=s /s to

test the $%#/e%ce o e$the! acto! o% a ;#ae!s s/ccess o! a$#/!e9 $% the ga4e o Te


13/22

S@$## 1 269, htt;:HH===5ta/5ac5$#H%ogaaH"DFSHs@$##+5;dJA#o%K9 J;o@e! $s ;!edo4$%a%t# a

ga4e o s@$##K95

25 The .a#$d$t o th$s co%c#/s$o% $s /%de!sco!ed the act that $t $s has ee%

a!!$.ed at a host o scho#a!s e4;#o$%g a =$de .a!$et o e4;$!$ca# a;;!oaches5 I% 4 4ost

!ece%t st/d, /s$%g a dataase o 4o!e tha% o%e $##$o% ha%ds o !ea# o%#$%e ;o@e! $%.o#.$%g 158

4$##$o% ;#ae!s, I a%d the othe! a/tho!s ;!ese%t a !eg!ess$o%Gased 4ethod o! $so#at$%g a%d

4eas/!$%g the sste4$c cha%ce a%d s@$## e#e4e%ts $% Te


14/22

'15 To ;/t th$s 4a!g$% o .$cto! $%to ;e!s;ect$.e, co%s$de! that 4a% ;o@e! ;#ae!s

;#a ga4es $% =h$ch o%e J$g etK $s 2 P/$te a e= ;!oess$o%a#s ;#a ga4es =$th 4/ch

h$ghe! sta@es95 I% th$s s$4/#at$o%, the st!ateg$c ;#ae! =o/#d ha.e =o% a% a.e!age o '2 ;e!

ha%d !o4 the !a%do4 ;#ae!5 I% 4a% ;o@e! !oo4s, a dea#e! 4$ght dea# ' ha%ds ;e! ho/!5 Th/s,

a ;#ae! o##o=$%g a .e! as$c st!ateg co/#d e


15/22

7o#dE4 to/!%a4e%ts et=ee% 21 a%d 2& data $%c#/ded 8 ;#ae!s $% 81 se;a!ate

to/!%a4e%ts95 Co4;a!$%g ;o@e! to go# /s$%g data !o4 ;!oess$o%a# go# to/!%a4e%ts9, a ga4e

/%$.e!sa## he#d to e ;!edo4$%a%t# s@$##Gased, the a/tho!s ose!.e that Js@$## d$e!e%ces

a4o%g to; ;o@e! ;#ae!s a!e s$4$#a! to s@$## d$e!e%ces ac!oss to; go#e!s5K The 4a$% co%c#/s$o%

$% th$s st/d $s that Jthe!e a;;ea!s to e a s$g%$$ca%t s@$## co4;o%e%t to ;o@e!: "!e.$o/s $%$shes

$% to/!%a4e%ts ;!ed$ct c/!!e%t $%$shes5K It $s 4 o;$%$o% that the co%c#/s$o%s o that ;ee!

!e.$e=ed st/d a!e co!!ect ass/4$%g the acc/!ac o $ts /%de!#$%g data5

'&5 Othe!s Dedo%%o Dette!4a%, 289 e


16/22

'05 Us$%g a ga4eGtheo!et$c a;;!oach to st/d the !e#at$.e !o#es o s@$## a%d cha%ce $%

ga4es, othe! scho#a!s o!4 .a% de! -e%/gte%, 219 co%c#/de that the #e.e# o s@$## $% the

th!ee ;o;/#a! .a!$a%ts o ;o@e!, Se.e% Ca!d St/d, Te


17/22

a#e to ose!.e =hethe! a ;#ae!s =$% !ate $%c!eased a#o%g =$th h$s s@$##, as 4eas/!ed h$s

$%de


18/22

++5 As %oted ao.e, e.e! ha%d o ;o@e! $%.o#.es 4/#t$;#e dec$s$o% ;o$%ts, a%d each

o those dec$s$o%s $s $%#/e%ced %/4e!o/s acto!s !eP/$!$%g s@$##/# e.a#/at$o%5 I% o!de! to

4a@e the !$ght dec$s$o%s at the ta#e, ;o@e! ;#ae!s 4/st eco4e s@$##ed ;!act$t$o%e!s $% a .a!$et

o d$sc$;#$%es, $%c#/d$%g:

a9 )athe4at$cs, $5e5, ca#c/#at$%g odds(

9 Ose!.at$o%, $5e5, !ead$%g ha%ds a%d !ecog%$$%g ;atte!%s a%d Jte##sK(

c9 "scho#og, $5e5, assess$%g a% o;;o%e%ts 4ot$.at$o%s(

d9 "e!s/as$o% a%d dece;t$o%, $5e5, co%.$%c$%g o%es o;;o%e%t to 4a@e a 4$sta@e(

e9 3/dg4e%t, $5e5, ;!ocess$%g $%co4;#ete $%o!4at$o% P/$c@# to !each the !$ght dec$s$o%(

9 S$t/at$o%a# a=a!e%ess, $5e5, se#ect$%g ;!o$ta#e ga4es a%d e


19/22

4/st e s/$c$e%t# ca;a#e o ;e!s/as$o% a%d dece;t$o% to $%d/ce the4 to /%=$tt$%g# 4a@e

those ad ets5 S@$##ed ;#ae!s 4a


20/22

ett$%g, a%d e$the! o#d the est ha%d o! a$# to e


21/22

eca/se the ho/se $s d$s$%te!ested $% the o/tco4e o a ;o@e! ha%d, the co%ce!%s a%$4at$%g

#eg$s#at$o% aga$%st ga4#$%g a!e 4/ted =he% $t co4es to ;o@e!5

c5 Seco%d, ets $% ;o@e! se!.e a d$e!e%t /%ct$o% tha% ets $% t!ad$t$o%a# cas$%o ga4es5 I%

t!ad$t$o%a# cas$%o ga4es, ets s$4;# esta#$sh the a4o/%t that a ;#ae! $s =$##$%g to =age!, a%d

cha%ce $s the ;!edo4$%a%t acto!$% 4a% cases the o%# acto!that dete!4$%es the o/tco4e

o the ga4e5 The ;#ae! ;#aces h$s et, a%d the% =a$ts o! the =hee# to s;$%, ;/##s the s#otG

4ach$%e #e.e!, !o##s the d$ce, =a$ts to hea! h$s %/4e!s ca##ed, o! =atches h$s ho!se c$!c#e the

t!ac@5 The s$e o! %at/!e o h$s et has %o $4;act o% the o/tco4e5

d5 Not so $% ;o@e!5 I% ;o@e!, the ets the4se#.es co%st$t/te the ;#ae!s 4ost $4;o!ta%t

too#s to a#te! the o/tco4e o the ga4e5 ett$%g at the !$ght t$4e a%d $% the !$ght a4o/%ts,

;#ae!s ca% =$% 4o!e ;ots #/$%g the$! o;;o%e%ts $%to o#d$%g, the ca% a/g4e%t the s$e o

;ots that the ;#a% to =$%, a%d the ca% othe!=$se 4a%$;/#ate the$! o;;o%e%ts $%to 4a@$%g

4$sta@es5 Th/s, /%#$@e a Jga4#$%gK et, a ;o@e! et $s %e.e! so#e# a =age! o% the o/tco4e o a

cha%ce e.e%t( $t $s $%stead a o!4 o st!ateg$c co44/%$cat$o%, #$@e a chess 4o.e, o! a $d $%

!$dge5

&'5 Fo! the !easo%s ao.e, I co%c#/de that s@$## ;!edo4$%ates o.e! cha%ce $% Te


22/22

cha%ce e#e4e%ts, TOP / O!!icial 0ournal o! the Spanish Society o! Statistics and Operations

Research, Vo#5 , No5 1, ;;5 1G11+5

' Caot, A5N5, 7a%%/4, R5C5 2&95 "o@e!: "/#$c ;o#$c, #a=, 4athe4at$cs a%d the /t/!e

o a% A4e!$ca% t!ad$t$o%5 T'' Cooley $' Rev', Vo#5 22, No5 ', ;;5 ++'G&1'5

+ C!oso%, R5, F$sh4a%, "5, "o;e, D5-5 2895 "o@e! s/;e!sta!s: S@$## o! #/c@ Chance, Vo#5

21, No5 +, ;;5 2&G285

& Dedo%%o, )5A5, Dette!4a%, D5*5 2895 "o@e! $s a s@$##5 Gaming $' Rev', Vo#5 12, ;;5 '1G

'65

6 7a%%/4, R5C5, Caot, A5N5 295 To=a!d #ega#$at$o% o ;o@e!: The s@$## .s5 cha%ce

deate5 Gaming Research & Revie% 0ournal, Vo#5 1', No5 1, ;; 1G25

0 7o;e, "5, )cC/##och, S5 295 Stat$st$ca# A%a#s$s o Te

Documents

Plaintiffs' Expert Witness Affidavit featuring testimony from Professor Robert C. Hannum