I was with my youngest getting a Red Box movie at the local grocery store, and there was a line of six people for the lottery ticket machine right next to it. One guy put in a $20 bill thinking he could get change, but that’s not how the machine works. First time I have ever seen a line for lottery tickets in my fairly well-to-do suburb.
I bought a ticket Sunday morning when I returned the movie, no line at all. If someone were at the machine I probably would not have bought one. Since chance works itself back to the mean, and you should match about 1 number per ticket, and I matched exactly zero numbers the past 5 times I bought a ticket, I figure my odds are about 99% that I get all six number this time. That’s why I can’t buy two tickets, it would be more likely to split those numbers 3 on each.
If 292M tickets are sold, via Quick Picks for computer random selection, the odds for the winning number not to be among the tickets sold seems to be (1- 1/N)^N = e^-1 = 37% where N=292M. If twice as many tickets are sold (584M), then the odds of not selling the winning number is (1-1/N)^2N = e^-2 = 13.5%.
In 2014 there were about 123.2M households in the USA (the Powerball is participated by 44 states+DC, PR, VIs) . If every household buys 3 tickets each drawing (as we did the past two times :)) ), then about 370M tickets will be sold each drawing and the odds of no winning number is between 15% and 35%.
If 33% of ticket sales revenue is added to the jackpot, then the increase of $400M (from 900M to 1.3B) suggests about 600M ticket sales. So, the odds of no wining number this Wednesday would be close to 13%. :))
Not that I am actually worried about winning, but I feel the same way. If I am going to win at all, a nice low million jackpot that no one cares about would do me just fine Of course with the odds of either ever happening, I don’t worry to much about it.
But do we know how many of the tickets were sold via random selection? That was my point. You can’t do the calculation about Bill Gates’ expectation if you don’t know how many tickets will be sold, and what the distribution of numbers will be in the tickets sold.
My sister called me this morning , convinced she bought one of the tickets that won $1M…she bought a ticket at a shop that had a winner , but since she heard no one won the jackpot , she tossed the ticket in the trash at the hotel she was staying at…ARGH!!!
She contacted the state lottery commission and they are sending her some kind of form to fill out and the store is checking their security cams…I thought without presenting a signed ticket , you were out of luck for collecting a prize ?
Backtracking on what I previously said, people are saying that there were k= 440 million tickets sold for the last jackpot. And we know that the number of possible combinations is N = 292 million. So if all the tickets were selected randomly, we’d expect that (1 - 1/N)^k, .778, of the combinations would be unselected. And that’s exactly what occurred, according to the Texas estimate. So people picking non-randomly isn’t making a difference, if the Texas estimate is true. http://www.txlottery.org/export/sites/lottery/Documents/jackpotestimates/pb20160109.pdf
I am looking at my numbers on my two tickets. They look like really good numbers. I mean REALLY good. So good that you can all back off and stop wasting your time.
^ k=1.5N=440M and the chances that the winning combination is not picked would be (1-1/N)^1.5N =[ (1-1/N)^N ]^1.5=[e^-1]^1.5= e^-1.5 = 0.223 = 1-0.777. Does this mean that when k=1.5N=440M tickets were sold or the combos were randomly picked for 440M times, in all those combos picked, some 0.223N=65M combos (of the possible 292M combos) were never selected? It sounds right (I’m confused ).
Right. ~22.3% of combos were not picked. (Sorry I mistyped in #127 above.) We just model using a binomial: each combination has an independent k * (n-1)/n chance of not being picked.
Well, I just bought my very first lottery ticket ever. Guess I should cancel my afternoon meetings and start interviewing investment advisers who will be able to handle the $850+ million coming my way. There’s probably some tax planning that should be done while my ticket is still nominally worth only $2 (even though of course I know its true value). Gift tax is much less on half a cent (1/400 of $2) than on the $1 million I plan to give my mom on Thursday. I’d better make that transfer now. Probably should get the estate planning lawyers involved now, too. Phew, there’s a lot to do before Wednesday night.
(LOL I’ve already gotten my $2’s worth of amusement out of the ticket. But it is strange how a tiny corner of one’s mind does start to consider the possibilty once a ticket is purchased).
One of my easy picks has my lucky number as the powerball so logically I’ve started searching for the land on which I’m going to open up my animal sanctuary for when I win. Colorado seems nice but I think I’d like to go somewhere a bit warmer.
Just in case you were wondering, H informs me that yes, it is possible to set it up so that a trust receives the annual payment and will continue to do so after your death. So to maximize your winnings, you can select the annuity. No matter how old you are.
I would advise not holding more than $1 million in any one account… so, the winner would have to open more than 800 accounts. sheesh! I don’t want to win! Too much trouble!!
AL is one of 6 states that doesn’t have a lottery, but a Republican is going to propose it at next session. Since I am 20 miles from TN ticket purchase, I decided the pot is sweet enough to give up an hour of my time. My 6 tickets are by my religious icons. The store has been owned by this couple for 5 years. Showed me where a guy won $1 M on TN lotto and some time later the same guy won $100,000 also from TN lotto.
Okay, so yeah we bought a couple of tickets. Not much thought to what we would do because we know we will not win. Haha. Would probably take the annuity. Less taxes, more pay-out and apparently heirs can inherit. First year, smallest, is about $14,000’000, after taxes. Could I live on that?!?
Of course with the odds of either ever happening, I don’t worry to much about it.
).
There’s probably some tax planning that should be done while my ticket is still nominally worth only $2 (even though of course I know its true value).