Massachusetts Positive EV Lottery Game

I'm posting this after reading the following article, A game with a windfall for a knowing few, from the boston.com web site. Briefly, the Mass lottery has a game called Ca$h Winfall. Unlike most lottery games, when the jackpot gets over a certain amount they bump up the lower prizes. How they do it is confusing, but on the July 18, 2011 drawing the game had a return of 117%. Unlike most positive EV lottery situations, this one did not have most of the value in a gigantic top prize, making a winner vulnerable to the annuity, taxes, and decreasing utility of money as the jackpot gets bigger.

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.

was this the same game someone cited and claimed it was a "syndicate" making the betting? [made it sound like mobsters to me]

An 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.

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: Ayecarumba

An 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: Wizard

Where 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: Ayecarumba

An 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.com

Bettors 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: weaselman

From 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: Wizard

That 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: Wizard

I 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"

"was this the same game someone cited and claimed it was a "syndicate" making the betting? [made it sound like mobsters to me]"

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.

Fun 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.