Massachusetts Positive EV Lottery Game
This is a simple pick 6 out of 46 game. Here is my table showing the EV for the 7/18/11 game. The cost per ticket is $2, so the return column is the win*probability/price.
| Catch | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 6 | 2392699.1 | 1 | 0.00000011 | 0.12772207 |
| 5 | 19507 | 240 | 0.00002562 | 0.24990768 |
| 4 | 802 | 11700 | 0.00124909 | 0.50088509 |
| 3 | 26 | 197600 | 0.02109574 | 0.27424465 |
| 2 | 0.24 | 1370850 | 0.14635171 | 0.01756221 |
| 1 | 0 | 3948048 | 0.42149293 | 0.00000000 |
| 0 | 0 | 3838380 | 0.40978479 | 0.00000000 |
| Total | 9366819 | 1.00000000 | 1.17032170 |
The prize for catching two numbers is a free game. I get a value of 24 cents for that, assuming the prizes seen for the following 7/21/11 game.
Anyone see any flaw in my math? I would keep an eye on this for my readers in the north-east. However, the publicity the 7/18 drew may induce more sharp players, depressing prize values. Evidently they pay out whatever was in the jackpot pool or 2x sales, whichever is less. In the 7/18 lottery the pool value was less, so they lowered the prizes to the uneven amounts you see in the table.
I welcome all comments, corrections, and questions.
Does the top prize pay out in a full lump sum or over time? Edit: The game website specifies a lump sum payout for all cash prizes.
Quote: AyecarumbaAn important note is that you will not get into the 100%+ range unless you are willing to put in $500,000+.
Where do you get that from?
Quote: WizardWhere do you get that from?
Quote: Boston.com Article page 4
Mark Kon, a professor of math and statistics at Boston University, calculated that a bettor buying even $10,000 worth of tickets would run a significant risk of losing more than they won during the July rolldown week. But someone who invested $100,000 in Cash WinFall tickets had a 72 percent chance of winning. Bettors like the Selbees, who spent at least $500,000 on the game, had almost no risk of losing money, Kon said.
Quote: Wizard
This is a simple pick 6 out of 46 game. Here is my table showing the EV for the 7/18/11 game. The cost per ticket is $2, so the return column is the win*probability/price.
From the website you linked to, it looks like 7/14 game, not 7/18 ... Or am I reading it wrong?
The reason I am asking is ... I am in the North East so I am going to need the exact methodology here :)
The real question is how to find out a future game is going to be +EV. Is it explained somewhere how exactly the amount of next jackpot is calculated, and how it gets rolled down to the lower levels? Or is it common knowledge? :)
Quote: AyecarumbaAn important note is that you will not get into the 100%+ range unless you are willing to put in $500,000+. This makes it a risky venture for smaller plays, even $100k will only have a 72% chance of breaking even or coming out ahead.
100% + return is not the same as 100% chance of winning. I'll take a 72% any day :) Don't even mind a 51% chance :)
Quote: boston.comBettors like the Selbees, who spent at least $500,000 on the game, had almost no risk of losing money, Kon said.
That does not mean the same thing as needing $500,000 to have a positive EV. The writer is trying to say how much you would need to have "almost no risk" of losing. Buying just one ticket would have a positive EV. Consider a bet with a 1 in a million chance of winning that pays 2 million. Just one ticket would have a positive EV, but you would need to buy 693,147 tickets to have a greater than 50% chance of winning.
Quote: weaselmanFrom the website you linked to, it looks like 7/14 game, not 7/18 ... Or am I reading it wrong?
I think you're reading it wrong. The odds I came up with agree with the Mass Lottery web site.
Quote: WizardThat does mean the same thing as needing $500,000 to have a positive EV.
You mean does not mean ... right?
Quote: Wizard
Consider a bet with a 1 in a million chance of winning that pays 2 million. Just one ticket would have a positive EV, but you would need to buy 693,147 tickets to have a greater than 50% chance of winning.
It must be my stupid day or something ... Why wouldn't buying 500,000 tickets give you a 50% chance?
Quote: WizardI think you're reading it wrong. The odds I came up with agree with the Mass Lottery web site.
Could you link to the page you are comparing the odds to?
So, are you saying they are publishing future prizes on the site?
Quote: MassLottery
718 07/28/11 5-6-11-19-20-23 $556,581.00 None $4000 $150 $5
717 07/25/11 3-6-8-17-30-44 $533,614.00 None $4000 $150 $5
716 07/21/11 10-13-15-18-19-29 $500,000.00 None $4000 $150 $5
715 07/18/11 1-25-30-36-38-39 $500,000.00 None $4000 $150 $5
714 07/14/11 3-13-18-22-28-38 $2,392,699.00 None $19507 $802 $26
Does this mean that the August 1st jackpot is $556,581.00, not July 28?
I don't think that is the case, because currently on that page, there is a new line added for August 1st:
719 08/01/11 11-17-28-33-34-41 $621,090.00 None $4000 $150 $5
And, $621,090.00 does seem to be August 1st jackpot, because the line on top of the page says "Current jackpot: $700,000"
That was me, when I posted the link on Sunday. By Syndicate, I meant nothing nefarious or illegal, just an Investment Group. The article references several Investment Groups that exploit the game. Kudos to them for determining the advantage play.
http://www.boston.com/news/local/massachusetts/articles/2011/08/02/lottery_restricts_high_level_players/
State now restricting the number of sales that can be made per store. Still possible to gain advantage it seems, but now requires a bit more logistical planning.
Quote: Wizard
I welcome all comments, corrections, and questions.
Comment- excellent analysis
Correction- none
Question- Wiz- if this were in Nevada, how many $2 would you have bought? Assuming a store could print them out fast enough, would you take $100k to a store for a positive EV of 17k?
Quote: weaselmanYou mean does not mean ... right?
You're right. I just fixed that typo in my own post.
Quote: weaselmanIt must be my stupid day or something ... Why wouldn't buying 500,000 tickets give you a 50% chance?
It would it was a lottery and each ticket was different. I didn't specify the kind of game, but for purposes of a lottery, think of a quick-pick, in which case you might win more than once.
Quote: SOOPOOWiz- if this were in Nevada, how many $2 would you have bought? Assuming a store could print them out fast enough, would you take $100k to a store for a positive EV of 17k?
As many as possible. I might not take 100K all at one time to the store, but buy about 20K worth at a time.
A bit off topic, but if someone needs a bodyguard for just a day, how would one go about finding one?
Quote: WizardAs many as possible. I might not take 100K all at one time to the store, but buy about 20K worth at a time.
A bit off topic, but if someone needs a bodyguard for just a day, how would one go about finding one?
Someone in general? Call a security service, verify their bonding, and contract with them.
You? Call Jim Morrison, ask him if he knows a bouncer who has the day off and wants to make $250...
Quote: WizardAs many as possible. I might not take 100K all at one time to the store, but buy about 20K worth at a time.
A bit off topic, but if someone needs a bodyguard for just a day, how would one go about finding one?
I'm not good at finding them, but there was an entire thread talking about this a few months back.
Quote: WizardThat does not mean the same thing as needing $500,000 to have a positive EV. The writer is trying to say how much you would need to have "almost no risk" of losing. Buying just one ticket would have a positive EV. Consider a bet with a 1 in a million chance of winning that pays 2 million. Just one ticket would have a positive EV, but you would need to buy 693,147 tickets to have a greater than 50% chance of winning.
Thanks for the clarification Wizard! I learn something new from your sites everyday.
Quote: WizardA bit off topic, but if someone needs a bodyguard for just a day, how would one go about finding one?
I would suggest speaking to the head of security at one of the major strip hotels. They must have a list of referrals for their VIP's, or they may be able to provide the service from their own staff for one of their guests.
Even if that isn't the case this would come into effect:
"8.) If the total prizes won for any drawing, exceed 200% of the net sales for that drawing the prize amounts will be based upon a formula detailed in the Rules and Regulations or Administrative Bulletins issued thereunder. "
Guessing around one million tickets were sold for the rollover drawing.
If you do receive the payouts from the normal pay schedule its still profitable, but the variance goes through the roof. With even the largest ticket buyers getting pummeled ~12% of the time from my estimate.
Quote: MATT1983How do you get the 24 cents for the free game? Is a free game the same thing as another $2 ticket? If so, it seems to me that the value would be much higher than 24 cents even if it couldn't be used in a roll down week. Is the game THAT bad normally?
I assumed it had to be used the following week, with a $500,000 jackpot, and more free tickets for getting 2 numbers right. The game IS that bad after a rollover.
Quote: lucky13Fun while it lasted....
http://www.boston.com/news/local/massachusetts/articles/2011/08/02/lottery_restricts_high_level_players/
State now restricting the number of sales that can be made per store. Still possible to gain advantage it seems, but now requires a bit more logistical planning.
Yes, the cat is out of the bag.
State Treasurer Steven Grossman said stores are restricted to a maximum of $5000 worth of Cash WinFall ticket sales per day. He also said the game, which has seen declining sales since it was introduced in 2004, will be phased out next spring.
