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Uh, except for some the equation is really

E[winnings] + (entertainment value) + (compulsion) > cost

even if E[winnings] + (entertainment value) < cost

That's true of anything though.

The only problem with your inequality is that for many “entertainment value” really means “addictive pull”.

Additionally, most people's budgets are not robust enough where entertainment costs can even be factored in, especially those who are most vulnerable to gambling.

The bulk of my budget goes to rent, car, and food :(

That’s definitely true, but I wonder what the ratio is between people like that and people who don’t have a good grasp of the odds.

I’m always amazed and appalled at just how bad most people I’ve met are with basic probabilities. Now that’s just my anecdote, but I think your ratio would strongly favor the casinos, which I guess explains why the casinos exist and thrive in the first place.