House advantage is probably the wrong terminology for the lottery, but I don’t think expected value is. Expected value is how much you will get paid for how much you pay in.
Theoretically the odds for the lottery don’t change regardless of how many tickets are sold. Each ticket combination has a set likelihood for being pulled up.
The difference is in the payout. If the payout is 1 million, and you spent one dollar, and the odds are 1 in 1 million, then that is an even game. So if there is no winner, and next week the prize goes to 2 million, and the cost per ticket is still 1 dollar, then the expected value just doubled.
This is different than a lottery that uses purchased tickets such that the ticket receipt goes into a bucket, and then the drawing comes from the bucket. The odds of winning that are determined by the number of tickets purchased.
It doesn’t do you any good to buy two identical tickets. They are not going to pay you twice the money, once for each ticket. That might have been the case at one time, but it isn’t now. The pot is shared between the tickets, so if you have two tickets, you get two halves. Or if there are three independent winners, they split the win three ways. Or if there are two winning tickets, but one winning ticket was a pool of 5 people, then those 5 people will split half the pot 5 ways.
Whereas if the winner is picked from the ticket pool, then it is advantageous to buy multiple tickets. That changes your odds of winning more than it changes the number in the pool.
Say there are 100 people who buy a $1 ticket. That’s a $100 pool. Drawing picks the ticket stub out of a bucket. Assuming randomized bucket. Now buy two tickets. You’ve spent $2, for 2/101 chance of winning, instead of 1/100 chance of winning. That’s 1.98% chance of winning over 1% chance.
Of course, with lotteries running on millions of entries, that changes the percentages to tiny changes.
The thing is, for all the talk about how low your odds of winning actually are, somebody wins. That’s why people play.