Is the Powerball a good play?

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Leeraar
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Is the Powerball a good play?

Post by Leeraar » Wed Jan 13, 2016 7:54 pm

Let me try to define a game we can play.

Let's take a single dice (die). You give me a dollar, and call a number. Then, you roll the die. If you roll your called number, I give you five dollars and your original dollar. Seems like a fair game to me. (I may be wrong.)

So, let's look at the Powerball. It costs $2 to play, the odds are 292 million. Does that not say if the jackpot is more than about 600 million, it's a good bet?

L.
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TorturedRegret
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Re: Is the Powerball a good play?

Post by TorturedRegret » Wed Jan 13, 2016 7:57 pm

Expected value is now positive. But only if there can only be one winner.
When you factor in the odds of sharing the pot, all bets are off.

jjface
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Re: Is the Powerball a good play?

Post by jjface » Wed Jan 13, 2016 7:58 pm

jackpots are not the lump sum value of receiving it all today. Plus a huge chunk goes to taxes. The current jackpot is probably about fair for a $2 stake.

Dick D
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Re: Is the Powerball a good play?

Post by Dick D » Wed Jan 13, 2016 7:58 pm

Spend $2 and have a fantasy. Who cares if it is a good play.

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ERMD
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Re: Is the Powerball a good play?

Post by ERMD » Wed Jan 13, 2016 7:59 pm

You are referring to, what would be called in Texas Hold'em, pot odds versus drawing odds. I believe you're right in many respects, save for the fact that with a jackpot this large (and publicity to match), the odds of a single winner now are quite small, so the winners will be splitting the pot. Then, you have to factor in taxes. I've seen someone else do the math elsewhere, and the anticipated return on 2 dollars was something like 1.50.
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Bustoff
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Re: Is the Powerball a good play?

Post by Bustoff » Wed Jan 13, 2016 8:17 pm

It is if you don' t want to feel left out.

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Re: Is the Powerball a good play?

Post by joebh » Wed Jan 13, 2016 8:26 pm

Leeraar wrote:Let's take a single dice (die). You give me a dollar, and call a number. Then, you roll the die. If you roll your called number, I give you five dollars and your original dollar. Seems like a fair game to me. (I may be wrong.)

So, let's look at the Powerball. It costs $2 to play, the odds are 292 million. Does that not say if the jackpot is more than about 600 million, it's a good bet?
Let's play a different game.

I'm thinking of a number between 1 and 292 million. If you guess right, I'll give you lots of money, although you may have to split it with an unknown number of people, and I'll give you a lot less than you might think, since I'll need to withold taxes.

Will you give me $2 now?

dl42
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Re: Is the Powerball a good play?

Post by dl42 » Wed Jan 13, 2016 8:33 pm

In the dice example, if you pay $1 for a chance to win $6 the expected value is $1. You don't get the ticket price back in the lottery so if you pay $1 for a chance to win $5 instead the expected value drops to $0.83.

For the current powerball odds you need to win about $785,000,000 for a $1 return, so depending on the taxes owed a $1.5 billion payout is around the break-even point; and that's assuming it's not shared because of the number of people playing.

I was curious enough about the odds to calculate the benefits of buying $2 lottery tickets vs buying $2 of a low-cost Schwab total stock index fund (SWPPX) instead. To get a 10% chance of winning the lower $50,000 prize over an 18-year period (I simulated 1899 drawings), you'd have to buy 100 tickets a week ($200). On the 10% chance that you won in that 18-year period, you would have lost $123,000 even despite the $50,000 win and the various $4, $7 and $100 wins. That amount of money in the index found over that same time period would have resulted in $381,000 (with dividends re-invested) and a final quarterly dividend payment of $11,000.

The numbers above are just from some sample runs in a simulation but it's not a good play by any definition. What I did learn about myself from this lottery is that I will get out of bed for $1.5 billion ;)

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Kenkat
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Re: Is the Powerball a good play?

Post by Kenkat » Wed Jan 13, 2016 8:35 pm

Bustoff wrote:It is if you don' t want to feel left out.
This is the real answer!

Cost of a Powerball ticket: $2
Cost of a Powerball ticket if the office pool hits and you're not in it: priceless

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Re: Is the Powerball a good play?

Post by bhsince87 » Wed Jan 13, 2016 8:53 pm

Dick D wrote:Spend $2 and have a fantasy. Who cares if it is a good play.
Yes, this!

A few days of dreaming about what kind of life you would lead, where you'd live, who you'd share the wealth with, and on and on.

And then the excitement as the numbers are drawn and you check your ticket.

As entertainment, it's a good play. Just don't get carried away.
"If ye love wealth better than liberty, the tranquility of servitude better than the animating contest of freedom, go home from us in peace." Samuel Adams

Day9
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Re: Is the Powerball a good play?

Post by Day9 » Wed Jan 13, 2016 8:58 pm

Just buy deep out of the money short term options.

Go ahead and join the office lotto pool if it increases coworker morale but there are better options out there if you want a low chance for a huge payout.
I'm just a fan of the person I got my user name from

lack_ey
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Re: Is the Powerball a good play?

Post by lack_ey » Wed Jan 13, 2016 9:00 pm

The Federalist has a piece about odds and expected value of a ticket now, if you want to see a bit more details.

They calculated $1.32 expected value per ticket ($2), taking the immediate payout, after tax (but assuming no state tax), after considering pot splits, including prizes that aren't the jackpot. But the figure depends on the number of tickets purchased, assumed to be 500 million. How many are actually playing? 538 estimated that.

I will now smugly tie this in to investing by pointing out (groan, again) that investor preference for lotterylike return distributions with high positive skew pushes down the expected value of such securities.

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dm200
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Re: Is the Powerball a good play?

Post by dm200 » Wed Jan 13, 2016 9:07 pm

One of the internet "teasers" is about strategy to increase your odds of being a sole winner and not having to share the pot. I think is is correct.

While the odds of any series of numbers is the same of being picked, and has no relationship to the numbers being purchased - the numbers being purchased are not random (overall). So many people pick their numbers and tend ot pick lower numbers because of birth dates, anniversary dates, divorce dates, and so on.

When I win, I will still have the same opinions, postings, frugality - even as a "billionaire" as I have had in the past. I have three "numbers" on one ticket and it cost $6.

I am old enough to remember the TV series "The Millionaire" - and what (then) was a huge amount of money did to the recipients.

rkhusky
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Re: Is the Powerball a good play?

Post by rkhusky » Wed Jan 13, 2016 9:14 pm

If you got a check for $1B, what would you do with it? Hope someone doesn't mug you on the way home? Take a picture with your cell phone and deposit it at your Internet bank?

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Re: Is the Powerball a good play?

Post by slickwillbo » Wed Jan 13, 2016 9:17 pm

dl42 wrote:In the dice example, if you pay $1 for a chance to win $6 the expected value is $1. You don't get the ticket price back in the lottery so if you pay $1 for a chance to win $5 instead the expected value drops to $0.83.
Perhaps nitpicking here, but wouldn't the EV be -$0.17, not (+)$0.83?

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dm200
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Re: Is the Powerball a good play?

Post by dm200 » Wed Jan 13, 2016 9:21 pm

rkhusky wrote:If you got a check for $1B, what would you do with it? Hope someone doesn't mug you on the way home? Take a picture with your cell phone and deposit it at your Internet bank?
Nice problem to have!

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Re: Is the Powerball a good play?

Post by lack_ey » Wed Jan 13, 2016 9:22 pm

slickwillbo wrote:
dl42 wrote:In the dice example, if you pay $1 for a chance to win $6 the expected value is $1. You don't get the ticket price back in the lottery so if you pay $1 for a chance to win $5 instead the expected value drops to $0.83.
Perhaps nitpicking here, but wouldn't the EV be -$0.17, not (+)$0.83?
Expected value of what?

EV of how much money you have in the example (starting from $1, to play once): $0.83
EV of the outcome (change in your wealth after playing once): -$0.17

Angst
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Re: Is the Powerball a good play?

Post by Angst » Wed Jan 13, 2016 9:28 pm

The dry math is too public for me to care too much about figuring out, but there's no denying that I've reaped more than $2 worth of enjoyment out of the ticket I purchased yesterday. The drawing's yet to come and I continue to book dividends of amusement and fun out of it all. I can't lose!

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Re: Is the Powerball a good play?

Post by jstat » Wed Jan 13, 2016 9:38 pm

My calculation:

Marginal utility of $2.00 is approximately equal to 0

Probability of winning is > 0

Marginal utility of more than 400 million dollars is at some sort of maximum for money, essentially infinite

Conclusion: Buy a ticket a enjoy the fantasy

dl42
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Re: Is the Powerball a good play?

Post by dl42 » Wed Jan 13, 2016 9:49 pm

lack_ey wrote:
slickwillbo wrote:
dl42 wrote:In the dice example, if you pay $1 for a chance to win $6 the expected value is $1. You don't get the ticket price back in the lottery so if you pay $1 for a chance to win $5 instead the expected value drops to $0.83.
Perhaps nitpicking here, but wouldn't the EV be -$0.17, not (+)$0.83?
Expected value of what?

EV of how much money you have in the example (starting from $1, to play once): $0.83
EV of the outcome (change in your wealth after playing once): -$0.17
Yes the outcome is negative as you mention. I was calculating the expected value of $1 i.e. (1/6 x $5) + (5/6 x $0) = $0.83.
So each $1 is worth $0.83 or a loss of $0.17 per dollar.

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stratton
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Re: Is the Powerball a good play?

Post by stratton » Wed Jan 13, 2016 9:50 pm

Bustoff wrote:It is if you don' t want to feel left out.
That, and a bottle of Two-Buck Chuck.

Gotta enhance that dreaming!

Paul

PS 2bc isn't all that good. Spend the same amount and buy a good bottle of beer or hard cider. :P
...and then Buffy staked Edward. The end.

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Re: Is the Powerball a good play?

Post by DonCamillo » Wed Jan 13, 2016 9:59 pm

stratton wrote:
Bustoff wrote:It is if you don' t want to feel left out.
That, and a bottle of Two-Buck Chuck.

Gotta enhance that dreaming!

Paul

PS 2bc isn't all that good. Spend the same amount and buy a good bottle of beer or hard cider. :P
Plus, 2bc now cost $3! http://www.today.com/id/3076201/ns/toda ... pcOXfFBewk :beer

But $2 or $3 is relatively cheap entertaining. It costs me that much to make a couple of latte's at home with my Nespresso machine, and I don't have any fun conversations about disguises to wear when the Lottery takes your picture.
Les vieillards aiment à donner de bons préceptes, pour se consoler de n'être plus en état de donner de mauvais exemples. | (François, duc de La Rochefoucauld, maxim 93)

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wander
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Re: Is the Powerball a good play?

Post by wander » Wed Jan 13, 2016 10:01 pm

Don't know if it is a good play or not, but spending $2 for a billionaire's dream is worth it. :sharebeer

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TimeRunner
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Re: Is the Powerball a good play?

Post by TimeRunner » Wed Jan 13, 2016 10:38 pm

So did any Boglehead win tonight? I go by the wisdom of the late Herb Caen, famous San Francisco Chronicle columnist, who said "The odds of winning the lottery are the same whether you play or not." :wink:
One cannot enlighten the unconscious.

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Re: Is the Powerball a good play?

Post by Sconie » Wed Jan 13, 2016 10:47 pm

As an economics professor of mine once said, "Lotteries are a tax on the mathematically challenged."
I know you think you understand what you thought I said but I'm not sure you realize that what you heard is not what I meant. - Alan Greenspan

quantAndHold
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Re: Is the Powerball a good play?

Post by quantAndHold » Wed Jan 13, 2016 10:47 pm

rkhusky wrote:If you got a check for $1B, what would you do with it? Hope someone doesn't mug you on the way home? Take a picture with your cell phone and deposit it at your Internet bank?
It'll be one of those giant checks, so you'd just send the picture of the lottery people handing it to you, and send that to the bank.

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Re: Is the Powerball a good play?

Post by Jerry55 » Wed Jan 13, 2016 10:52 pm

Dick D wrote:Spend $2 and have a fantasy. Who cares if it is a good play.
Yep ! Had 3 full days of dreaming....best $2.00 I've ever spent. :happy
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Re: Is the Powerball a good play?

Post by Epsilon Delta » Wed Jan 13, 2016 11:00 pm

Dick D wrote:Spend $2 and have a fantasy. Who cares if it is a good play.
Or don't spend $2 and still have a fantasy.

Let me tell you it's a doozy, you can't imagine what happens when they award me the sesquigigabuck and I don't even have a ticket.

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Re: Is the Powerball a good play?

Post by catdude » Wed Jan 13, 2016 11:47 pm

TimeRunner wrote:So did any Boglehead win tonight? I go by the wisdom of the late Herb Caen, famous San Francisco Chronicle columnist, who said "The odds of winning the lottery are the same whether you play or not." :wink:
No, I didn't win, but I did manage to break even, lucky me. I bought two tickets for 4 bucks this afternoon, and one of the tickets had the powerball (10), which gets me my 4 bucks back.

It was nice to daydream about what I'd do with all that money. Now it's back to bitter reality. :( Oh well...
catdude | | "As much as cats fight, there always seems to be plenty of kittens." (Abraham Lincoln)

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Re: Is the Powerball a good play?

Post by Doom&Gloom » Thu Jan 14, 2016 12:06 am

TorturedRegret wrote:Expected value is now positive. But only if there can only be one winner.
When you factor in the odds of sharing the pot, all bets are off.
Not exactly. With the tax bite, the increased number of tickets being sold, and the increased probability of multiple winners, it never becomes positive.

http://wizardofodds.com/games/lottery/powerball/

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Re: Is the Powerball a good play?

Post by technovelist » Thu Jan 14, 2016 12:21 am

It depends on the number of tickets sold for the current drawing compared with the prize money left over from previous drawings.

For example, if the cash prize is $1 billion and they sell the same number of tickets in this drawing as they did in the first drawing, the chance of a multiple winner is no higher than in the first drawing, but the prize is much higher.
In theory, theory and practice are identical. In practice, they often differ.

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Leeraar
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Re: Is the Powerball a good play?

Post by Leeraar » Thu Jan 14, 2016 12:47 am

jstat wrote:My calculation:

Marginal utility of $2.00 is approximately equal to 0

Probability of winning is > 0

Marginal utility of more than 400 million dollars is at some sort of maximum for money, essentially infinite

Conclusion: Buy a ticket a enjoy the fantasy
:D

L.
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Re: Is the Powerball a good play?

Post by Bfwolf » Thu Jan 14, 2016 1:28 am

What's amusing to me is that there is this Powerball fever at $1.5B that wasn't there when it was at $100M at some point. The marginal utility on the extra $1.4B is so low, but it's what has driven this craze.

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JoMoney
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Re: Is the Powerball a good play?

Post by JoMoney » Thu Jan 14, 2016 3:09 am

The odds of winning the Powerball jackpot from buying a ticket are 1 in 292million.
When I put 1 / 292,000,000 in my calculator it's indistinguishable from zero... My calculator won't even display it, if I go out 8 decimal places it still rounds to something like 0.00000000 ...as far as I can tell the chance of me winning is the same even if I don't buy a ticket.

Answers to the St. Petersburg paradox explain some of the problem with only looking at expected value in a wager. Even if the odds being offered on some bet are favorable, the chance of it occurring can make the utility of it so unfavorable as to be not worthwhile for someone with finite resources of time, money, and opportunities to repeat the bet.

This old news article has a University professor quote saying:
http://www.kcci.com/news/central-iowa/a ... s/20207210
"If you've been buying 100 tickets a week, ever since the time of Jesus, there's a better than even chance you wouldn't have won," said Kenneth Alexander, a math professor.
...and that was back before the rules changed and the chance was still 1 in 175,000,000.
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Leeraar
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Re: Is the Powerball a good play?

Post by Leeraar » Thu Jan 14, 2016 5:31 am

OP here. Let's get back to the original point.

You give me $1, select an number between 1 and 6, and roll a die. If your number is rolled, I give you $6 (maybe it is $5, I don't know.) That is a fair bet.

Now, let's say I will take your dollar, but will pay you 20 dollars if your number (1 to 6) comes up. In other words, the reward is more than three times your bet and odds of winning. Would you not play that game?

Multiply that by 50 million or so, you have the Powerball Lottery of yesterday. That the odds of winning are very small, but the reward is very large, do not to me change the basic calculus: The reward is larger than your bet and your odds of winning. Go for it!

(And yes, I understand the multiple winner issue.)

L.
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Re: Is the Powerball a good play?

Post by dkturner » Thu Jan 14, 2016 5:57 am

I approach the lottery ticket issue differently. Approximately 50% of ticket sale proceeds are essentially charitable contributions to a collection of state governments. The remaining 50% is paid out to the holders of winning tickets, but, in the case of large jackpots like Powerball, probably 40% of the winner's share goes to pay federal and state income taxes - more charitable contributions. I did buy a Powerball ticket yesterday and rationalized my purchase as a $1.40 voluntary charitable contribution to a variety of government entities that need the money. That leaves me with spending 60 cents for a 1 in 292million chance of winning $1.5Billion.

As an aside, a creative tax accountant could probably figure out a way to reduce my taxes by the 60 cents I squandered on my lottery ticket.
Last edited by dkturner on Thu Jan 14, 2016 6:00 am, edited 1 time in total.

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Re: Is the Powerball a good play?

Post by IowaFarmBoy » Thu Jan 14, 2016 5:59 am

To me, there is a difference because I am relatively certain of winning in the dice game but not the lottery before I hit the limit of my money or at least what I was willing to risk. In the dice example, I would keep playing until you were tired of losing and quit, knowing that I had a 1 in 6 chance of winning on a given roll. I am confident that I would start winning quickly and before I hit the limit of what I was willing to invest. In the lottery example, I likely would run out of money long before it paid off since the odds are something like 1 in 292,000,000. I'd probably play a few time hoping lighting strikes but at some point I would hit the point where I felt I didn't want to lose any more.

It's kind of like the quote, "The market can remain irrational longer than you can remain solvent."

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Re: Is the Powerball a good play?

Post by joebh » Thu Jan 14, 2016 8:11 am

jstat wrote:Marginal utility of $2.00 is approximately equal to 0

Probability of winning is approximately equal to 0

Marginal utility of more than 400 million dollars is at some sort of maximum for money, essentially infinite

Conclusion: Buy a ticket a enjoy the fantasy
Fixed that for you.

If you buy it for enjoyment, it makes sense.
If you buy it because you think it's "a good play", not so much.

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Re: Is the Powerball a good play?

Post by Jack FFR1846 » Thu Jan 14, 2016 8:51 am

Instead of powerball, how about this.

I walk up to you and say "I'll bet $2 that I can tell you where you got your shoes".

You think that there's no way I can know or guess as you're wearing some generic, buy-anywhere shoes. You say "here's my $2, I'll take your bet".

I then say : "You got your shoes on your feet". I snatch the $2 and look for the next sucker.

At least you have an amusing story to tell people and it only cost you $2. With powerball, what story will you tell? That you stood in line with people who could barely afford a twinkie and somehow had $20 to throw away on gambling? Cool story, bro.
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Rodc
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Re: Is the Powerball a good play?

Post by Rodc » Thu Jan 14, 2016 9:12 am

One problem with this as a math problem is the cost of one ticket is essentially zero (say we restrict this to middle income and above) while the payoff is essentially infinity. I would venture a guess that while most us of can do math with amounts like $1B we cannot really grasp that much money in an intuitive concrete way.

So what really is the utility of $2 (I could lose a great deal more than $2 and if did not see it go would never know - no impact on my life whatsoever)?

And what really is the utility of $1B?

So who knows what the expected cost-benefit is of the "utility cost" of $2 vs the "utility" of winning, each probability weighted?

This is basically what is known as the "zero times infinity" problem: I can get any number I want by how I choose the (near) zero cost and the (near) infinity payoff. That is to say this is a problem that is numerically unstable.

Really the payoff in play is the entertainment value: if that is worth $2 you should play. If not then don't.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.

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Re: Is the Powerball a good play?

Post by wolf359 » Thu Jan 14, 2016 12:03 pm

Leeraar wrote:OP here. Let's get back to the original point.

You give me $1, select an number between 1 and 6, and roll a die. If your number is rolled, I give you $6 (maybe it is $5, I don't know.) That is a fair bet.

Now, let's say I will take your dollar, but will pay you 20 dollars if your number (1 to 6) comes up. In other words, the reward is more than three times your bet and odds of winning. Would you not play that game?

Multiply that by 50 million or so, you have the Powerball Lottery of yesterday. That the odds of winning are very small, but the reward is very large, do not to me change the basic calculus: The reward is larger than your bet and your odds of winning. Go for it!

(And yes, I understand the multiple winner issue.)

L.
Your underlying premise is incorrect. Your example is a fair bet. Six people throw $1 into the pot, one number wins, the winner takes the pot.

In the lottery example, for every $1 in the pot, only 60 cents is paid out. For the amount paid out, you get hit with windfall taxes, so it will be further reduced. The dollar amount being bandied about is the annuity value, not the cash value, which is about half. Powerball is NOT A FAIR BET.

The math does not support playing this type of lottery. You play for other reasons, like entertainment, or social inclusion. You can also console yourself that about 17 cents of the money goes to education. Typically, it's not for the education of the kids of the Powerball players.

I'm not sure it's a good play for society, either.

I'd rather the states let lotteries be used to fund retirement accounts. (For every lottery retirement account opened, a tiny percentage (maybe .01%) is pulled off the top. Once a month, that amount is awarded to the retirement account of one lucky investor. You can otherwise invest the account in the market in the usual fashion. Think people would be more likely to open retirement accounts?)

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Epsilon Delta
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Re: Is the Powerball a good play?

Post by Epsilon Delta » Thu Jan 14, 2016 1:13 pm

635,103,137

This is the number of tickets sold for Wednesdays draw. Fewer than I expected, perhaps powerball need to invest more in terminals. It is now certain that the expected dollar value was negative.

You don't need to calculate the number of duplicate winners, just the total amount spent, the total of present value of prizes, including minor prizes (which is a fixed percentage) and the chances of zero jackpot winners.

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Re: Is the Powerball a good play?

Post by joebh » Thu Jan 14, 2016 1:14 pm

Rodc wrote:Really the payoff in play is the entertainment value: if that is worth $2 you should play. If not then don't.
This is exactly the right way to look at it.

If you enjoy spending $2 to dream of being a millionaire, then spend it. Don't expect to win, just enjoy the dream.
If you enjoy spending $2 to dream of being a billionaire, then spend it. Don't expect to win, just enjoy the dream.
And don't worry if it is mathematically a good play or not.

Nobody worries if purchasing a movie ticket is a good play or not. Nobody worries if attending a ballgame is a good play or not.

Lottery tickets aren't an investment. They are an entertainment expense.

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Re: Is the Powerball a good play?

Post by chatbotte » Fri Jan 15, 2016 3:17 am

Epsilon Delta wrote:635,103,137

(...)

You don't need to calculate the number of duplicate winners,
I just did. :) The probability of at least two tickets out of the 635,103,137 sold winning is about 64 percent. The probability of no ticket winning is about 11 percent and the probability of exactly one ticket winning is about 24 percent.

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JoMoney
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Re: Is the Powerball a good play?

Post by JoMoney » Fri Jan 15, 2016 5:18 am

I just ran across this tag line on a CA Lottery website, and found it both laughably absurd and yet seemingly fitting of the explanation people give for playing:
"... grab a ticket and believe in something beyond belief! "
It seems like a Moore's paradox or a form of Doublethink propaganda
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Re: Is the Powerball a good play?

Post by Dulocracy » Fri Jan 15, 2016 10:53 am

I won the PowerBall!!! How? I did not play. Instead, I went online and put $2 towards my mortgage principal. Yes, I am THAT guy.
I'm not a financial professional. Post is info only & not legal advice. No attorney-client relationship exists with reader. Scrutinize my ideas as if you spoke with a guy at a bar. I may be wrong.

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Re: Is the Powerball a good play?

Post by BogleBoogie » Fri Jan 15, 2016 8:34 pm

I read somewhere in an article that buying $300 million in powerball tickets would give you about a 50% shot at winning. If that were true, wouldn't that be a good bet to make if the win is $1.5 billion!?! Just something to think about...

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Epsilon Delta
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Re: Is the Powerball a good play?

Post by Epsilon Delta » Fri Jan 15, 2016 8:56 pm

BogleBoogie wrote:I read somewhere in an article that buying $300 million in powerball tickets would give you about a 50% shot at winning. If that were true, wouldn't that be a good bet to make if the win is $1.5 billion!?! Just something to think about...
First of all the prize has a cash value of just under $1 billion. The extra $500 million is marketing.

Second If you bought $300 million in tickets and nobody else bought any you would have a good bet. Unfortunately, everybody else bought 635,103,137 tickets. With that many tickets you end up sharing the jackpot with two or more others most of the time. Overall the shared jackpots make it a bad bet.

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Re: Is the Powerball a good play?

Post by LadyGeek » Fri Jan 15, 2016 8:57 pm

This thread has run its course and is locked (not investing related, going nowhere). See: Unacceptable Topics
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