At what jackpot minimum is playing Lottario rational?
I screenshot https://www.playsmart.ca/social-hub/ironing-out-lottery-odds.
The Main Jackpot: Starts at $250,000 and grows until it’s won. There is no capped maximum amount to the jackpot.
Two chances to win per \$1 play. Each \$1 play includes two sets of six numbers from 1-45.
Since Lottario's jackpot is uncapped, some minimum jackpot amount shall make Lottario's Expected Value positive? What's Lottario's break-even point?
This can't be answered with the information shown. -1 because that really should have been obvious.
First, you need to know the cost of acquiring one of those 4,072,530 chances. For simplicity, you could say that's the price of a ticket. If the cost of entry were free, then the expected value of that ticket is always positive. That's the obvious part.
The less obvious part is knowing how many people will enter the lottery for any round. The more people, the higher the chance that there will be multiple winners. You didn't say what happens then. They could have another round to pick a single winner, or could divide the payout equally among the winners, for example. Either way, though, multiple winners reduces the expected value of any one ticket.
Since it's impossible to know how many entries there will be when you buy a ticket, there is no way to know the expected value.
Also "rational" and "positive expected value" are two different things. Remember that you are not guaranteed expected value. That's only what you get averaged over an infinite number of attempts. Even if you bought a ticket every round, you are still far more likely to be worse off than if you never bought a ticket. You'd have to define very subjective goals to decide "rational", which really doesn't belong on this site.
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