Re: Calculate Last Digits

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dpb wrote:
Dave O. wrote:
....
... - if you extend a lottery to the end of time then every permutation will at some point be drawn)

Again, not necessarily. Eventually it becomes more and more likely, granted, but it isn't guaranteed. Every number has the same probability on every draw so it's possible some particular combination may just never happen to get selected, no matter how many drawings there are...

Or, playing the same combination for N lotteries (where N is the population size) _won't_ guarantee a winner even after the Nth drawing. Odds will start to be pretty good, as N increases, but never a sure thing.

As others have noted, the only way to ensure a win is to hold all N possible winners for a given drawing (which of course, even if practical from a physical standpoint, the oddsmakers now ensure is a losing proposition).

I'd have to go dig it up to find it again, but in one of my early probability theory courses in uni the prof brought up a story of a fella' in a national lottery who worked up a ploy to allow a consortium of his buddies to essentially do that. At the time, the odds weren't calculated correctly and he got caught, so to speak, by breaking the bank. As I recall, he hanged...

And, of course, much of the early theory was developed in support of such enterprises by guys like LaPlace, etc., ...

One of my all-time favorite prefaces is from an early treatise on gaming...to my great regret I failed to note the title and author when I clipped the reprint and saved it and I no longer recall whose it is, but enjoy. :)

"It is thought as neceffary to write a Preface before a Book, as it is judg'd civil, when you invite a Friend to Dinner, to proffer him a Glafs of Hock beforehand for a Whet: And this being maim'd enough for want of a Dedication, I am refolv'd it fhall not want an Epiftle to the Reader too. I fhall not take upon me to determine, whether it is lawful to play at Dice or not, leaving that to be difputed betwixt the Fanatick Parfons and the Sharpers; I am fure it is lawful to deal with Dice as with other Epidemic Diftempers; and I am confident that the writing a Book about it, will contribute as little towards its Encouragement, as Fluxing and Precipitates do to Whoring."

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