Get your taxes done using TurboTax

https://www2.illinois.gov/rev/forms/incometax/Documents/currentyear/individual/IL-1040-Schedule-CR.p...

you're wrong. it's done on the above schedule where non-illinois gambling winnings are included in both line  15 colums A & B

 

Do not include any amount in Column B except net operating loss (NOL) carryforwards,
other states’ gambling and lottery winnings, and recoveries of items
deducted in prior years.

 

line 43 column B is divided by colum A both include non-illinois gambkling winnings

skip lines 44 through 50 assuming your a full-year illinois resident

line 51 taxes paid out of state

line 52 tax due IL-1040 line 12

line 53 enter decimal from line 43

line 54 line 52 times line 53

line 55 compare lines 51 and 54 and enter the lesser amount. this  is your tax credit

 

 

Hope I made you happy by showing that you'll get credit in Illinois for taxes paid on out of state on gambling winnings. Say Thank You.