If there is a jackpot that rises until there is a winner, is it a misunderstanding of statistics to assume that as the jackpot rises it is more likely that someone is going to win?
The size of the pot doesn’t matter directly. It is as simple as the number of tickets sold. Big jackpots tend to entice more people to buy tickets and those that have bought them to buy more. That does raise the odds of a winner on a given week. If there still is no winner then the process repeats so the cysvle feeds into itself to increase the odds of a winner on a given week. Eventually you have so many tickets sold each week that the odds of the streak continuing go down lower and lower.
That assumes that the distribution of numbers picked is somewhat random. The chances of anyone winning wouldn’t be very good if many people bought the same numbers.
10 million tickets sold on a $5 million jackpot have the same odds of winning as 10 million tickets on a $500 million jackpot.
To put Shagnasty’s comment in a more direct analysis - the stated odds of winning the Mega Millions jackpot is 1 in 175 million. If 10 million (randomly distributed) tickets are sold then the approximate probability of having a winner would be one in 17.5. If later, a drawing has sold 80 million tickets (the jackpot increases roughly by about 45-50% of the value of tickets sold) then the probability of a winner is about 1 in 2.1.
Powerball has become much more complex as they have now gotten to the point where the maximum amount that the jackpot can increase, between drawings, is 25 millions dollars and any additional monies goes into a second jackpot to provide additional payout to those holding tickets with the selected five regular numbers without the correct powerball number. (don’t know how this new twist plays out with the Power Play feature).
And to further clarify… A lottery drawing is an ‘independent event’. Asking if it’s more likely that someone will win if it goes a long time without a winner is like asking if it’s more likely that a coin flip will come up tails because it has come up heads 3 times in a row. The answer is no.
Now, in the real world of lotteries, the odds a winner happening do go up, for the reasons cited above. More people play when the jackpot is bigger, so there’s a greater likelihood that someone will hold a ticket with the winning numbers.
<nitpick>
Actually, I don’t think these numbers are quite right, unless there’s some rule that there can’t be two tickets sold with the same set of numbers on them. If it works the way I think it does, you need to use a Poisson distribution for the probabilities, which gives you a probability of about 1 in 18.5 for 10 million tickets bought and about 1 in 3.46 for 80 million tickets.
</nitpick>
Don’t know Poisson’s rule but it would also seem that the possibility of multiple tickets (which there is) would make the probability greater (i.e., lower number when expressing as “1 in x”). Does it not work this way?
No, because out of 10 million tickets sold, some will be duplicates. The duplicates don’t count as seperate chances of a winner having been sold; if the duplicates are winners, then only the first time the combination was sold would it be relevant. So you have somewhat fewer than 10 million combinations sold out of the 175 million total possible combinations. This gives a smaller chance that a winning combination was sold.