Probability of winning a scratch lottery ticket given that 95% have been sold

HokieBalla34

http://moneycentral.msn.com/content/...rly/P89288.asp

Here is an excerpt from the article, under HOW TO PLAY SMARTER
Beware the stale game.
People often don’t realize that scratch games aren’t finished when someone wins the biggest prize; the tickets are left out until they’re all sold. That means you might be buying a ticket to a game in which there’s no chance for a juicy payday, says Chris Gudgeon, co-author of “Luck of the Draw: True-Life Tales of Lottery Winners and Losers.” Gudgeon’s advice: Avoid scratch games that have been lingering near the Slurpee machine for ages. “If you’re buying the scratch-and-wins, particularly the seasonal ones, don’t buy a Christmas one at the following Halloween,” he says. “There’s a very good chance that all of the prizes are gone.”

Agreed, there is a VERY GOOD CHANCE that the prize is gone. But as this thread provides, since you don't know whether or not it remains, you should not be dissuaded from purchasing one of the remaining ones (Whether any ticket purchase is a good investment is not at all relevant to this discussion).


Thanks all for your input.

DaveC426913

THANK you. Durrr.

I've been trying to clarify that point all along: tickets are sold AFTER the big prize is won. Posts 3, 6 and 15 explicitly ask about this particular condition, or state it as an assumption.

That invalidates virtually ALL previous discussion about the odds (except mine that is hee.)

daveb

I believe your argument is that if there are n tickets that can be sold, the probability of any single ticket winning is 1/n. However, if m<n tickets have been sold, the probability the winning ticket has already been sold (assuming you don't know if this is the case) is m/n, or P(winner <=m). Is that what you mean?

0rthodontist

No, it still doesn't make any difference. Unless you actually KNOW of particular prizes in the game that have been sold already, it doesn't matter when you get the ticket, even if there are a thousand small prizes.

If you did somehow know what prizes were given out, and you noticed that there were a disproportionately small or large number of them for the number of people that have played the game, then that would be one situation where you actually could invest wisely by either not buying a ticket (if you know that disproportionately many prizes have been given out) or buying a ticket (if you know that disproportionately few prizes have been given out). But that happens extremely infrequently, ESPECIALLY when there are many small prizes.

If there is one big prize that someone already got, and even it's shown on the news that they got it, but so long as you didn't see that news report and you buy a ticket--then from the knowledge you have your odds are STILL the same as they were as if the news had not been shown.

HokieBalla34

DURRRR and post 1 states that a few logical assumptions have been made, namely that you don't know if the winning jackpot ticket has been sold or not. Therefore, it is a moot point whether or not the game is still played out after the ticket has been won.

DaveC426913

Of course you don't know if the winning ticket's been sold! The only way you could know that is if you're clairvoyent or cheating. Which is why is was a pointless assumption.

Or did you mean the winning ticket has already been announced?

HokieBalla34

Hence the word LOGICAL. This assumption was made merely to dissuade people who would inevitably make the argument that your chances would vary depending if you knew the winner had been sold (or not been sold). Since this information would not be relevant to our debate (which is whether the fact that 95% of the tickets had been sold affects your present odds, absent any other POINTLESS information), the assumption was made in order to determine the desired answer and eliminate extraneous debates/information.

And on a side note, you couldn't be more incorrect with your statement: "Of course you don't know if the winning ticket's been sold!" It is actually VERY simple for one to determine if the ticket had been sold--using the right resources, of course (Hint: It doesn't involve enlisting Mrs. Cleo or a cheat!!!). I may be letting the cat out of the bag here but it's called THE INTERNET An example of what I am talking about may be easiest for you to understandVirgina Lottery Results. I would imagine that Virginia isn't the only state that publishes their results but did not care to check. That may be a good exercise for the Santa Barbara School of the Clairvoyant or Cheaters Anonymous.

And no, I did not mean "the winning ticket has already been announced". Obviously you wouldn't assume that "the winning ticket has already been announced" because that would imply that the winning ticket no longer remains and P[x=winner] = 0. Talk about pointless assumptions.

But thanks everyone for your input. The situation has been clarified and the debate is closed.

DaveC426913

That was the clartification I've been asking for. A bit more clear than the initial one sentence.

RyanPMcBride

I just saw this post... even though it is quite old I wanted to input some statistics into the solution.

1. If you buy the 1st ticket sold out of 100 your chances are 1/100
2. If you buy the 44th ticket sold out of 100 your chances are now 44/56 assuming the winning ticket has not yet been sold. It is 56 because 44 tickets have already been sold that have not won (100-44).
3. The problem with this theory is that you will never know when the winning ticket is sold. But if you somehow did find out there were no winners yet, then obviously your chances are greater.

Just thought I would throw that in there.

Peace!

DaveC426913

This is wrong (as I'm sure you will quickly realize. Having a 44/56 chance of winning is ridiculously good odds.)

If you buy the 44th ticket out of 100 (and no ticket yet was the winner) your chances of being the winner are 1/57. (You have an equal chance of winning as any of the 56 subsequent players.)