# For those that want to hit the PowerBall

Discussion in 'Math' started by WBahn, Jan 19, 2016.

1. ### WBahn Thread Starter Moderator

Mar 31, 2012
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With the recent huge jackpot in the PowerBall (in excess of \$1.5 billion), more and more people seem to think that this is a viable way to secure their fortune and/or retirement (which is very different than buying a handful of tickets for the entertainment value).

So what would it take to have a 50/50 chance of winning the PowerBall sometime during your life?

Let's make some assumptions -- you start playing PowerBall as soon as you are legally old enough and play consistently for the next fifty years. Then let's assume that there are twice weekly drawings that work out to 104 drawings per year, or 5200 drawings in your life. Let's assume that each PowerBall ticket is \$2 and remains that way throughout that entire timeframe.

How much would it cost you, each drawing, to buy enough tickets have an 50% chance of winning the PowerBall at least once?

Apr 30, 2011
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Less than \$300M; a bargain. Are you one of those naysayers trying to suck the joy out of life?

3. ### WBahn Thread Starter Moderator

Mar 31, 2012
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That's if you wanted to have a 50-50 chance of winning a given PowerBall drawing. My question is about what you would have to buy each week to have a 50-50 chance over a 50 year time span of winning at least once.

But let's look at the \$300M needed to have a 50-50 chance of winning on a single drawing.

Since that is firmly in the top tax bracket, you would have needed to earn somewhere in the range of \$600M to have the \$300M available for the tickets.

Then, if you were the sole winner of that ~\$1.6B jackpot you would have gotten about \$800M for the cash payout. Of that, over \$300M would have gone to federal income tax and, for most people, another \$40M to state income tax, leaving you with about \$450M. And that's IF you win (you only have a 50-50 chance) and IF you are the SOLE winner of the jackpot.

A clearer picture emerges if you look at what it would take to guarantee a win. If you have bought nearly \$600M worth of tickets it would have had to earn \$1200M (or \$700M if you got the money via long-term capital gains) in order to walk away with \$450M -- IF you were the sole winner. But at the kinds of ticket sales these jackpots produce, there is seldom just a single winner. In this last one you would have turned \$700M to \$1200M of earnings into less than \$150M of winnings. Which is why you almost never see anyone buy all possible tickets -- it HAS happened in some of the smaller state games, but I don't know if anyone has ever actually walked away ahead using that strategy.

Lotteries are great boons for government because, between federal and state taxation, they get to take and keep about 85% of the money people that play earned in order to play. No other form of gambling that I am aware of could attract players at anywhere near that outrageous take. Most forms of gambling can only take 5% to perhaps 25% before people walk away because they don't think they are able to win enough to justify the risk. Interesting psychologies at play.

4. ### GopherT AAC Fanatic!

Nov 23, 2012
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It depends. Take slot machines for example where odds can be carefully tuned and published for advertising purposes.

In the end, how much does the average player take home from each casino? Ultimately, they go home losing what ever they budgeted to lose (if they are responsible gamblers - assuming there is such a thing). So, what us the difference? The gamblers get to play twice as long at the second consino vs the first and 4 times as long at the third vs the first. The payback between the time gamblers arrive and leave is effectively the same.

So, discussing why people would play or would not play based on payback rates is as rediculous as a gambler's believe that they are going to win big someday. In the encoder, it is more about the marketing and setting the scene of a potential for a big win than the real odds or payback rates.

5. ### WBahn Thread Starter Moderator

Mar 31, 2012
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While casinos can and do advertise payback odds for a small number of games, that's not what I'm referring to.

If I were to run, for example, a dog track, I can tailor the odds calculations to result in an expected payback percentage. Even if I don't ever publish what that payback percentage is, I would find that if I set it too low that my business would fall off very rapidly and even though I was getting more of each person's bet, the number of bets would be down so much that I would make less money. Similarly, if I set it too high then I would get flooded by more people making bets but I would be making so little on each bet that I would make less money. The phenomenon you talk about -- that they will play until they lose the same amount of money and all that changes is how long it take that to happen -- is real but it isn't the dominant factor. For instance, if the payout percentage is so high that they would have to stay for 36 hours to lose their budgeted amount, then changes are they aren't going to end up losing their budgeted amount. But the bigger factor is not how much each person loses, but how many people come through the door to lose that amount in the first place. The point is that even without knowing the paypack percentage, people respond, on average, at a subconscious level to what it is and, for a given type of gambling, there is a pretty narrow range of paypack percentages that will result in maximum revenue to the house -- and casinos and horse tracks and dog tracks are very, very aware of what those ranges are. To the best of my knowledge, they are all significantly higher than the payback percentage for state lotteries, which are an out-of-the-park outlier. I think there are three factors that drive that: (1) It is an effectively isolated and distributed form of gambling -- the bets are small and spread out in time so you don't realize how much you are actually betting; (2) the headline payouts are big numbers; (3) it is marketed as being "good" because the money that is kept will be used for the children (or open space, or whatever).

6. ### Dr.killjoy Well-Known Member

Apr 28, 2013
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What ever happened to those mathematicians who won the lottery a couple times with a certain equation??

7. ### WBahn Thread Starter Moderator

Mar 31, 2012
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Could you find and post some information on it?

It's only meaningful if they provided the equation they used someplace archival BEFORE the drawing. It's trivial to come up with an equation that predicts the balls drawn afterwards.

Also, the archival method has to be such that there can't be other, hidden, archives. For instance, one of the classic con games in the stock market is for someone to make a bunch of predictions that cover all the basis -- for instance pick three stocks and then four outcomes for each (down >5%, down <5%, up <5%, up >5%) and then publish one prediction in the classified or personal section of 64 different newspapers. Then whatever happens you only point to the one that matches and hold it up as proof of your system's ability to accurately predict the market.

8. ### Tonyr1084 Active Member

Sep 24, 2015
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They say "You can't win if you don't play." However, I say "You can't lose if you don't play." And that's a winning move without all the math.

Honestly, I'll drop maybe \$20 to \$40 a year. After all, it only takes one set of winning numbers. And you know SOMEBODY has to win it. AND when the pot grows to stupidly high amounts - THAT is when I certainly WON'T go to play.

9. ### jpanhalt AAC Fanatic!

Jan 18, 2008
5,699
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I have never bought a lottery ticket and probably never will. The stock market is much the same, but the thrill takes longer to be dashed. Some people with a lot of disposable cash buy lottery tickets for fun. The sad fact is that many people with a lot less cash do it thinking they "might" win and be set for life.

On to the subject of math, I recall a PowerBall from several years ago in which a consortium calculated that the cost of buying every combination was less than the payout. Thus, they had a 100% change of winning. True. What I didn't read was how they compensated for the chance (based on the number of tickets sold) of multiple winners. In other words, it was still a gamble.

John

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10. ### Tonyr1084 Active Member

Sep 24, 2015
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I read (or heard) that to buy every possible winning combination (for the 1.5 billion) would have taken (I think I heard) 8 (or 18) years. You can't just walk in and say "I'll take one of every combination, the print-out alone would take years to process.

Now, if you want to buy a ticket for a drawing ten years in advance, then your hope for the lottery would be that it would be huge for that single night. Otherwise, you've spent many multiples of millions with the possibility of winning a few million. That'd stink!

11. ### WBahn Thread Starter Moderator

Mar 31, 2012
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There have been a few times that groups (or in one case an individual) have attempted to buy all the possible combinations. I don't think anyone has ever succeeded because I think all such lottery games require that tickets be purchased either in person or individually (except using the short cut of buying N quick-pick tickets) and either have to be paid for in cash or via debit card.

An Australian consortium attempted to corner the Virginia lottery a couple decades ago and were only able to purchase a couple million tickets (of the 7+ million needed) during the purchasing window.

For PowerBall, you have about 300 million tickets that have to be purchased in about a three day period, so you would have to average purchasing over 1100 tickets, each unique and therefore each filled out by hand, each second. Even if you could get your hands on the necessary ticket forms and you hired a thousand people to fill them out ahead of time and then go into a store that would let them stand there submitting the forms for eight hours each and each person did this each of the three days, each person would still have to submit the forms at the rate of one ticket every few seconds. You'd probably have to hire at least a hundred thousand people to each prepare enough forms for 3000 ticket to have a reasonable likelihood of getting them all submitted -- and you have to add the cost of this huge short-term payroll to the total cost. It would probably take at least a week to fill out all the forms in addition to the time standing in line to submit them, so let's call it about 100 hours per person. At, say, \$10/hour, that's another million dollars, which is chump change compared to the nearly \$600 million for the tickets themselves. But think of the logistics (and associated costs) of finding and hiring a hundred thousand people and then can you really count on them to accurate prepare their assigned range of tickets without duplicates and without any that are invalid (marked too lightly or smudged or some such)?

12. ### WBahn Thread Starter Moderator

Mar 31, 2012
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Smart man, you are.

A very disproportionate share of lottery tickets are sold to people that can least afford them. Worse is that many people on government assistance spend their rent and food money on them -- meaning that the taxpayers are buying their lottery tickets.

Not only does the multiple-winner situation have to be taken into account, but also the taxes, which are going to hit you between 40% and 50%, depending on state tax rates. I think the lump sum for PowerBall is 60%, so your actual "profit" is somewhere around 1/4 to 1/3 of the jackpot amount. So at a cost of nearly \$600 million to guarantee a win, the jaclpot would need to be between \$1.8 billion and \$2.4 billion to break even -- and that's IF you are the sole winner.

Apr 16, 2010
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14. ### naickej4 Member

Jul 12, 2015
199
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Hi Sir, you are very wise.
Thank God I don't play lottery.
Good article and I am going to share this will my friends.
But I still want to find some way of beating those casino games, I started to count cards but If I am found counting cards I will be banned from the casinos.
thanks.

15. ### jpanhalt AAC Fanatic!

Jan 18, 2008
5,699
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Poker is considered a game of skill by many. Of course you do not beat the casino per se when you play it; it charges for providing the venue. You cannot beat the casino over any significant period.

John

16. ### naickej4 Member

Jul 12, 2015
199
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Hi Sir,
I want and will one day beat the casino because where I come from the numerous casinos have caused people to loose everything, and I am not talking about upper class people, I am talking about the poor people. well you can blame them too for their foolishness. But once I complete my engineering degree I am going to study statistics and probability and I want to win at poker and other card games. Be the robin hood of the casinos

17. ### jpanhalt AAC Fanatic!

Jan 18, 2008
5,699
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Every loser at the casino thinks he can beat the system and win. What evidence can you provide that is any different from that? How will your anticipated superior level of education help you?

As I said, poker is one game where skill enters, but you do not beat the casino. Typically, the casino takes a percentage of the pot ("rake") or charges an hourly rate to play.

John

18. ### naickej4 Member

Jul 12, 2015
199
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Hi Sir, I was just making a joke. Truly impossible to fully beat the system (only the dudes from Oceans 11/12/13 can). I guess I watch too much of movies and have a wild imagination. So the only thing I can do is dream

19. ### WBahn Thread Starter Moderator

Mar 31, 2012
18,087
4,917
If you study statistics and probability you will discover that thinking that you can beat the casino will only lead you to being one of those poor people whom the casinos have taken everything from. The people that design casino games are fully aware of both statistics and human nature -- they have studied both to a far greater degree than you or I ever will.

20. ### naickej4 Member

Jul 12, 2015
199
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TRUE Sir. I just made the comment since i know poor people that lost their money at the casino.