Okay, I'm the guy (above) with all the "historic" posts, but THIS time I feel I actually have the correct answer to the original "Is it better to play 1 dollar on 10 lottery draws or 10 dollars on one lottery draw?"-question!
As I understand how lotteries operate, there actually ARE 2 sets of statistical averages. The "raw, brute #'s" set that we're all familiar with ("1-in-175,000,000," etc.), and then, once again, the long-term "historic" set -- which is where the house's "historic pay-out" table comes in.
Take the following "short-term"-example, which in theory should be extrapolatable into a longer-term set: 1 person buys 1,000 tickets, 17 people buy 100 tickets, 593 people buy 5 tickets, and 8,756 people buy 1 ticket. Out of which group of people is the winning Grand Prize likeliest to come from? Clearly the 1-ticket group!
Now, while it may be true that the single 1,000-ticket buyer has a 1,000x better chance of beating any SINGLE member of the 8,756 1-ticket buyers, it's quite clear that, "overall," one of the 8,756 1-ticket buyers has a better chance of beating the single person holding the 1,000 tickets!
See, if I'm correct, then statisticians apparently forget to factor-in the brute reality that lotteries are COMPETITIONS, which are thus RELATIVE to different #'s of GROUPS of ticket buyers, NOT just a matter of "odds in a vacuum!" Again, if I'm correct here, then the smartest buyers of tickets in the above COMPETITIVE scenario would be the 1-ticket buyers, NOT the single 1,000 tickets buyer!
So, again I ask, since I'm sure major lotteries give each of their Grand Prize winners a form to fill-out which has a question on it to the effect, "How many tickets TOTAL did you buy at the time that you bought your winning ticket?," then it follows that these various lotteries know EXACTLY what the "smartest # of tickets to buy" (hence the "Golden #") is for any one of their particular games!!!
I imagine that, over time, said Golden # is relatively stable (let's guess 7-9 tickets), and this is why I surmise that a statistical mathematician can likely determine what said "historical" Golden # likely is WITHOUT necessarily having to consult the HQ of any given lottery (in order for THEM to state what the Golden # is)!
Please, either show me where I'm wrong here, else "get" how my line of reasoning makes total sense! Thank You.