This Info here is rich with explanation as well.
Also here is what Google defines as A Game or Gaming...
lot·ter·y/ˈlädərē/ 
Learn to pronounce noun noun: lottery; plural noun: lotteries
(prize) draw sweepstake sweep bingo lotto tombola drawing of lots pools gamble speculation game of chance
The first recorded public lottery in the West was held during the reign of Augustus Caesar for municipal repairs in Rome. The first recorded lottery to distribute prize money was held in 1466 in Bruges, in what is now Belgium, for the announced purpose of providing assistance to the poor.
“The Lottery has given California public schools more than $39 billion since we began in 1985. We gave more than $1.8 billion to public schools in Fiscal Year 2020-21, which is about 1% of the state's annual budget for public schools.Aug 10, 2022
Here is what Google defines as A Game also known as Gaming:
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