Why don't 175,000,000 people (around half the us population) start a lotto pool, where each of them plays a unique combination of numbers, then split the winnings? Each person would get 7.42 million this way.
I think each person would get about eight dollars. Also coordinating this would require resources and therefore cost. Finally the government doesn't like it when people win so there are laws f-for your protection. Derp.
Let me explain it this way: let's say the winner gets $1300 one dollar bills. 175 people split the pot, they each get $7.42. But in actuality, scaled up to millions, the winner gets effectively 1300 one-million dollar bills, so each person gets 7.42 million
Your trolling attempt is completely boring at this point mate, sorry. You'll notice you didn't increase the amount of people splitting the money in your second example from 175 to 175,000,000.
lol, that's not even the cash received. the one time cash payment is probably around ~400 million for 1.3 billion. Of that 400 million, you are left with 200 million in cash after taxes.
According to game theory
Assuming everyone is risk neutral and has the same taxes (huge assumption, not sure if taxes is necessary assumption),
In the Nash Equilibrium for the lottery, the exact number of people will enter the lottery such that the expected payoff is the same as the cost of a ticket, hence everyone should be indifferent to joining the lottery and not joining the lottery.
In reality of course, way more people will join the lottery than is required to balance the expected returns with the cost and thus it is not worth it for a risk neutral person to invest in the lottery.
The reason for this is because it is profitable (with an expected return of around $2.25 per ticket) assuming there are no ties to split the jackpot. This is multiplied with a factor K (dependent on number of tickets bought, for the probability that two people DON'T tie) and hence if everyone is rational, the exact number of tickets will be bought such that K*$2.25 = $2.00 + tax.
Hence if you work purely off of game theory, one should be indifferent to buying a ticket and not buying a ticket.