What is the expected return of this hypotetical lottery game? What is the expected return of this hypotetical lottery game?
There are 60 numbers and you must pick 6 different numbers.
Then they pick 6 numbers (that will be different from each other) at random and if your 6 numbers is equal to those 6 numbers (but dont need to be at the same order) you win $3,500,000$ dollars.
Each ticket cost $3.5$ dollars to buy.
This is a simplified version of mega sena from brazil

The expected return is $$\frac{3.5\cdot 10^6}{\binom{60}{6}}\approx 0.07$$ , which is very low compared to $3.50$. As Ant pointed out, that would mean
an average loss of $3.43$ dollars per game.
Moreover , only the jackpot allows a win, so in practice, one would very likely win NOTHING, making the game very unattractive.
The probability of winning would be $1 : 50,063,860 $
