I'm not a statistician, but I'm interested in how far I can push myself with my basic algebra skills, armed with a C# development background and Excel.
Suppose I have several lotteries, each with different payouts, and odds, what is the right way to go about comparing and ranking the various games?
What would a graph of that data look like? (Scatter with a logarithmic axis?)
I would start by looking at the expected value or expected return of a ticket. The expected value is essentially the average of the payouts, weighted by their odds. For example, suppose you bought a ticket for \$1, which gives you a 1 in 100 chance of winning \$100. The expected value of that ticket is $$ E(\textrm{Ticket})=\bigg(\frac{99}{100}\bigg)(\$0) + \bigg(\frac{1}{100}\bigg)(\$100)=\$1$$ Since the ticket costs \$1, your expected return (expected value - entry fee) is $\$1-\$1$, or \$0. I doubt you'll find odds that good in real life though. Off the top of my head, I think the expected value of a \$1 US lotto ticket is often about \$0.50 (so the expected return is -\$0.50), but it obviously varies with the jackpot and payout structure.
You're not plotting something like this, are you? :-)
Brief answer: Found this website which is looking at from simple statistical point of view, with poisson distribution.
http://users.stat.umn.edu/~geyer/lottery/
As a matter of fact, the above answer actually gives the basic calculation of expected payout of profit for 1$ ticket.
Try Stochastic Dominance, it is a means of comparing various gambles to see if one is better...
