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The economics general approach to defining expected value does NOT work in regards with lottery playing. Let’s, for example, analyze a case of a “neutral” draw (take aside organizers’ costs): if the ticket costs you, say, $5.00, and the odds to win the jackpot would be, for example, 1 in 15,000,000, then the expected value of the prize should be ($5.00 x 15,000,000 =) $75,000,000.- (disregarding secondary prizes). However – the actual jackpot prize is only, say, $20,000,000.-…
Does that mean that such draw is not “neutral”, or not “fair”? Obviously not. There are additional factors that make the player play such lotto games, regardless of the fact that the odds to win desired lotto results are not in their favor. Among such factors are thrill, excitement, relatively low ticket cost, etc. Also, there are good causes behind the lottery game (e.g. – authorities that use substantial portion of the revenue for good causes. see GOOD CAUSES here), as well as the legitimate need of the organizers to cover their costs and profit taking.