## When to buy a lottery ticket

by Ari Siletz
31-Mar-2012

For the past ten years or so someone I know has been dutifully buying lottery tickets. His return on investment so far has been at most 25 cents to the Dollar. This is how I tried to explain to him that lotteries are a sucker's bet. "Look," I said, "I'll give you a much better deal than any lottery. Just give me \$10 every week and I will return \$5 of it to you." But he remains unconvinced, and it's not because he's math challenged. He points out correctly that in some cases a \$1 lottery ticket is worth more than \$1. How does this come about? It happens when there are more Dollars in the pot than there are players. So if 1000 players each buy a one Dollar lottery ticket and the jackpot is,say, \$2,000 then that \$1 lottery ticket is worth \$2.  But how can 1000 players putting in a Dollar each make a \$2000 jackpot? It can't, but if there's money left over in the pot from previous no-winner lottery purchases the money piles up. In fact it happened in yesterday's \$640 million drawing in the U.S. "Mega Million" lottery.

There are quite a few flaws in this argument. The most fundamental one being that the expected return is more than the lottery ticket price only if you haven't been buying lottery tickets in the no-winner rounds. In the simple example above, if there were, say, 3 previous no-winner rounds then a consistent player has already paid \$3 into the pot--his lottery ticket price is effectively \$4 (\$3 losing tickets + \$1 for the latest round).  One other flaw is specific to the rules of each lottery. For example, if the prize is to be split between 3 winners then the jackpot is effectively cut to 1/3 as far as each individual player is concerned (quiz: where is the weakness in my own logic on this point?). The rest of the flaws have to do with taxes and such. Bottom line, economics 101 tells you not to get into the lottery game.

But life isn't all about basic economics.  For many, a Dollar is a smal price to pay for the thrill of hope and the incentive to daydream about a life of luxury. Consider it part of your entertainment budget. Also lotteries are a way of  raising funds for big projects. A million Dollars in one pile can do a million times more than a million separate Dollars buying random things (taking some artistic licence here). As I said, economics 101 tells you not to buy lottery tickets,  however advanced economics may have a different answer. If the lottery authorities use the money for worthwhile projects that wouldn't be possible otherwise then there are benefits to the public and therefore ultimately to the individual. For example, the tomb of Ferdowsi in Toos was built with funds from a national lottery held in Iran in 1934. Above photo is of one of these historic lottery tickets discovered in the Golestan Palace archives. It may even be the winning ticket--not sure.

Have a lucky sizdeh bedar.

چرا مصدق آسوده نمی خوابد.
8
Aug 17, 2012
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2
Aug 16, 2012
Double standards outside the boxing ring
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Aug 12, 2012
more from Ari Siletz

### Poor and ugly people

by Farfromheaven2002 on

Lottery and gambling are for poor and ugly people.  It's a rare exception for a handsome long-hair man to purchase a lottery ticket.

### some replies

by Ari Siletz on

جناب آل ایرانینز:

از توجه شما به این بلاگ سپاسگزارم. مقاله شما
در مورد "چکنم الملک" از یک سری بسیار خواندنیست. تصویر این بلاگ را هم
می‌توان یک ضمیمه آن مقاله پنداشت.

جناب دیوانه:
دست بر اصل مطلب
گذاشتی. ضریب احتمال را نیز باید در نظر گرفت. اگر جایزه را بین سه برنده
تقسیم کنیم، درست است که جایزه یک سوم میشود ولی‌ در عوض احتمال بردن سه
برابر شده است. به این ترتیب ارزش اقتصادی بلیت تغییر نمیکند.

جناب
شراب سرخ.
خاطرات شما یکی‌ از آن یکی‌ شیرین تر است. اینطور که بنظر میاید
خوش شانسی‌ در میان خانواده و دوستان خانواده شما ارثی است، و همچنین
سخاوت.

### ...

by Red Wine on

خداوند حکیم الملک را رحمت کند.

پدر بزرگم در نواحی جعفر آباد شمیران ملکی‌ کوچک اما پر درخت و پر نشاط داشت که یکی‌ از دوستانش که از شازدگان قزلباش بود  به چند برگه‌ از همین اوراق ملک را فروخت و اندی بر این تصور بودند که حضرت والا سخت در اشتباه بوده و چنین و چنان اما چندی بعد معلوم شد دو برگ از آن چند برگ برنده اعلام شده و تا چند صد تومان به حاملِ آن اوراق برنده پول می‌‌دادند .

ما هیچگاه به این چیز‌ها اعتقاد نداشتیم،خیلی‌ سال بعد که چند ماهی‌ را در ژاپن زندگی‌ می‌‌کردیم،دوستی‌ به ما یک برگه‌ از بخت آزمایی آنجا به ما هدیه داد و چند ده هزار ین برنده شدیم... تا آخرین پولِ بخت آزمایی را خرج دوستان نکردیم ..به خانه باز نگشتیم :) .

جشن طبیعت بر شما و دیگر دوستان فرخنده باد.

### Dear Ari

by divaneh on

I think the biggest flaw in the argument about the real value of the ticket is ignoring the probability. If 1000 people bought ticket last week and if 1000 people buys ticket this week, then there is no difference in the probability of 1/1000 that you may win. If the fund rose to \$6000 next week and 2000 people bought tickets, then it may be argued that each ticket now worth \$3 whilst in reality the probability of winning has been halved.

### Jenab Ari

by All-Iranians on

Thank you for your great blog and fantastic observations. The historical photo you posted reminded us what we wrote in one of our articles

در سال ١٣١٣ شمسی رضا شاه به منظور تجلیل از شاعر بلندنام‏ ایران فردوسی طوسی به تجدید بنای آرامگاه این گویندهء بزرگ اشارت فرمود. برای اینکه همهء مردم امکان شرکت در این کار نیک را داشته باشند به پیشنهاد محمد علی فروغی ذکاء الملک و تصویب شاه قرار شد هزینهء تجدید بنا از محل فروش بلیت های بخت‏آزمایی تأمین شود و حکیم الملک به ریاست هیئت‏ مدیرهء بخت ‏آزمایی انتخاب شد.
//iranian.com/main/blog/all-iranians-70