Positive net expectation values and gambling

[Dauphin]

You know, I wish I had stayed in science. Doing accountancy and not using my mathematical brain for 5 years has left me a dullard.

[KrazyHorse]

It's a difficult calculation, but if we assume the same form of the lottery from previously, and that the rollover might occur again this week:

180 million + 1.2 * (t) = prize pool

prize pool distributed = prize pool * (1 - (1 - 1 / 76275360)^t)

your expected return = prize pool distributed / t

The breakeven point appears to be around 180 000 000 tickets sold (this is merely coincidence, by the way; it depends strongly on the percentage of money put from tickets into prize pool. At 50% it's more like 115 million tickets sold)

[KrazyHorse]

Assuming that buying one ticket is a good investment buying more will be a better investment. Guaranteed. So long as you choose distinct tickets, that is. Buying random tickets is a bad idea.

[KrazyHorse]

BTW, the factor

(1 - 1/x)^t used in the calculation was approximated as exp(-t/x) to avoid the roundoff error that was sure to result from using the exact form. The error should be sufficiently small to make this approximation valid, given the very high values of x and t