Ben Mezrich’s New Gig
I know that yesterday, I proclaimed that the greatest gift you could give this holiday season is your time, attention, and love, and I still stand by that post. However, I wouldn’t be a good American if I didn’t claim (tongue firmly placed in cheek) that the second greatest gift you can give is money! 
Since this is the season of giving, I’m going to give you the gift of (virtually, or at least statistically speaking) free money. Which brings us to Ben Mezrich.
In case you missed the movie “21” or his book “Bringing Down the House,” Ben Mezrich led wrote about a team of professional card players from MIT and successfully (and legally) beat casinos at the game of black jack.
Beat the casinos? Yes, it is possible. The trick is to deploy a team-based strategy where one player bets the minimum and keeps track of the high value cards in the dealer’s card shoe. As the cards are dealt, the shoe can get hot if a larger proportion of small cards have been dealt. At this point, the card counter calls in a teammate to make large bets and take advantage of this situation. Once the ratio of high to low cards balances out or the shoe is emptied, the window of advantage to the large better is closed and he leaves the table with his winnings.
Despite the legality of this approach, the casinos finally caught on and politely ‘requested’ that the players never return. As I was reading the book, I was trying to think of other games that could be similarly taken advantage of.
It took a while, but I finally found a winner in the lottery.
Yes, the lottery!
I know, most people call the lottery a tax on the stupid. And, for the most part, they are right. However, there is at least one game that provides the player with a similar scenario that Ben took advantage of when he beat the casinos playing black jack.
The Massachusetts Lottery offers a $2 game called Cash Winfall and it resembles most other lottery games except in one very important aspect. Similar to most lottery games, the player must pick 6 numbers out of a total of 46. Match all 6 and you win the jackpot. If nobody matches all 6, the jackpot increases in value for the next draw.
Where the game diverges from most draw-type lottery games is when the jackpot reaches $2 million. Once that threshold is crossed and there is no jackpot winner, the prizes for all of the players that matched 3, 4, or 5 balls are increased up to 10 times their normal value. In essence, your winnings are subsidized by all of the losers who played the game prior to this draw. This subsidization is so strong that even though the lottery skims off a sizeable percentage to cover their expenses and send money to the towns of the Commonwealth, the result is a positive expected value (as long as you place enough bets).
Stated more simply, if you place enough bets on a draw when the jackpot reaches $2m, you are statistically guaranteed to make money.
For example, the odds of matching 2, 3, 4, and 5 balls are 1 in 6.83, 47.4, 800.58, and 39028.41 respectively. In the March 13, 2008 draw, the jackpot was not won and the amounts of the other prizes increased: matching 2 earned a free $2 bet on a future Cash Winfall draw, 3 earned $30, 4 earned $943, and 5 earned $29,367.
If you had bought 100 tickets ($200 total cost) for this draw, you could expect that 14 bets match two (100 bets / 6.83) and 2 match three (100 bets / 47.4) for a total return of $88 ((14 * $2) + (2 * $30)). You would also have a 12.5% chance to match 4 (100 bets / 800.58) and a .25% chance (100 bets / 39028.41) to match 5. If you apply an expected value calculation (that is, if you could repeat this experiment a large number of times and average the results), the value for your 12.5% chance to match 4 would be $117 (.125 * $943) and $75 (.0025 * $29,367) for your .25% chance at matching 5. All totaled, the expected value of your $200 in bets is $285.
Of course, this assumes that you could repeat this experiment multiple times and average the results. As I mentioned above, the roll down scenario only occurs a few (8 to 10) times per year. So, the best option to take advantage of this ‘stupid man’s tax’, is to place a large number of bets each time the jackpot rolls over.
Let’s return to the March 13, 2008 example. But this time, lets ramp up the number of bets to 5000, for a $10,000 investment. (I use the term ‘investment’ somewhat in jest as this is still gambling.) In this scenario, you could expect 732 tickets to match 2, 105 to match 3, 6 to match 4, and a 12.8% chance to match 5. The expected value in this scenario is $14,280.
If you are observant, you will note that for this payout structure, the ratio of investment to winnings is a constant 42.8% return. That is, for every dollar invested, you can expect $1.428 in return over the long term.
That’s not too shabby for simply matching numbers. However, all is not well in the land of free money.
A number of things could go wrong:
1. Someone could match 6 and win the jackpot.
If someone does win the jackpot, all of the other prizes return to their normal values of $2, $5, $150, and $4000. If this occurs, your rate of return plummets to a -65.5%. At the current average number of bets placed for a roll down draw, this doesn’t occur frequently. However, it did occur on July 10, 2008.
2. The jackpot might not reach $2m
Each draw, the Mass Lottery estimates the amount of the upcoming draw based on historical ticket sales. It is possible that they can make a mistake, project a $2m jackpot, and then have the total fall short of the $2m threshold. If this occurs, the prizes remain at their normal values and your expected rate of return is -65.5%. Again, this is not a frequent occurrence, but it did occur on July 11, 2005.
3. You might pick bad numbers
The calculations I describe above are based on the theory of expected value. That is, they assume that you have the means to make a large number of bets and, thus, average out your winners and losers. Based on that assumption, your winnings will tend to the statistical averages in the long run. However, it does not guarantee that any particular draw would yield a positive winning result.
4. Too many people try to take advantage of this scenario
If too many people follow in your footsteps and try to game the system, the amount won for matching 3, 4, and 5 balls will decline as the lottery will have to spread the total jackpot across more winners. Worse yet, the chance that someone could match all 6 increases and would ruin the return for everyone else.
5. You might run out of money before matching 5 balls on a ticket
This crux of this strategy is based on buying tickets that match 4 and 5 balls. It is only then that the expected value calculations bring up your winnings to the expected rate of return. If your bankroll isn’t large enough to carry you through until you match 5, you won’t realize a positive return and your dreams of living easy would end quickly.
So, am I quitting my day job and becoming a professional lottery player? No.
But, I could see groups of enterprising college students pooling their beer money to earn a positive rate of return on their investments and possibly even pay their way through college.
In any case, this (literally) Million Dollar Idea is not quite free money. However, it is the closest legal option that I can think of.
By the way, based on the current jackpot amount as of 12/23/2008, the next roll down draw will probably occur on 12/29. Good luck!
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January 27th, 2009 at 12:08 pm
Hi, like this post but one thing that bothered me was that you mis-attribute Ben Mezrich as being a member of the MIT Blackjack Team. He was the author of the books only, and participated only with one of the former members while writing.
Very good analysis of the lottery.
January 27th, 2009 at 1:12 pm
Way to get mentioned on the Freakonomics blog. My question for this get rich quick scheme though is what about all the taxes you have to pay on the winnings? Those taxes aren’t taken out before the payoffs, and you have to cover them yourself, last I checked. So even though you would be “winning” money, most of that would just go into the government’s coffers anyway, no?
January 28th, 2009 at 9:46 pm
James,
Thank you for the correction. I did, indeed, incorrectly state his relationship to the team.
- Mark
Mark Muir, Million Dollar Idea Guy
January 28th, 2009 at 9:51 pm
Wykell,
You are correct about the taxes. In Massachusetts, the Lottery takes out 5% in state taxes for prizes above $600 and 25% in federal taxes for prizes above $5000. Winners will need to make up the difference if their tax bracket is higher.
However, on your federal taxes, you will be able to deduct the cost of all of your non-winning tickets against your winnings. This should wipe out a sizeable portion of your tax.
- Mark
Mark Muir, Million Dollar Idea Guy
February 21st, 2009 at 3:02 am
the $2 tickets aren’t worth $2 though, since you have to put them through the lottery again to cash them. unless you can hold them for the next >$2 million scenario — can you?
so assuming you can’t, it takes your ROI down a bit. not that much through since it is the high value tickets that give you the most return.
nice idea, but I agree the taxes kill it if you are in the higher brackets. unless you want to have your broke relative cash the tickets..
February 21st, 2009 at 7:33 pm
Cash Winfall has been paying out about 6 times higher when there are roll downs, it hasn’t been paying 10 times, so it is not profitable unless if you have better than average luck, or unless if you are extremely lucky by getting a 5 when there’s a roll down. Cash winfall has had 6 roll downs a year for the last 2 years. I wish Cash winfall was profitable but it is not.
You’re very right about the taxes Steveo. The IRS and most states are very unfair when it comes to gambling winnings. With the IRS to deduct your gambling losses you have to itemize your deductions and miss out on your standard deduction of $5,700 for individuals for 2009, and you can’t deduct your losses from your adjusted gross income with the IRS, so if you have very much gambling winnings that will cause you to miss out on exemptions and credits even if you lose more than you win on gambling for the year. With massachusetts state taxes you can’t deduct losses. Also, if you don’t live in Massachusetts, in many states you will have to pay state taxes on all your winnings to the state you live in in addition to having to pay state taxes to Massachusetts on all your winnings.
February 21st, 2009 at 10:58 pm
MarkMuir, are you saying that in Massachusetts people only have to pay state taxes on prizes over $600, and people only have to pay federal income tax on prizes over $5,000. If a person validates a winning ticket for $800 at a lottery office the lottery won’t take federal taxes out of that, but the lottery will report that $800 to the IRS and the person will have to report those winnings when they file their tax return. All gambling winnings, even $2 winners are suppose to be reported on your returns. Most people don’t report lottery winnigs that they can cash in at stores, but they are suppose to report them. If a person claims lots of winners over $600 at lottery offices, and deducts losses, but doesn’t report any of his winnings under $600, likely that person would be audited and be in a lot of trouble.
February 23rd, 2009 at 5:12 pm
I just wanted to clarify what I said in my previous 2 posts. Obviously Cash Winfall is a great opportunity when it’s expected to roll down because the prizes will probably be about 6 times higher than usual. But MarkMuir says that if you place enough bets you are statistically guaranteed to make money, that definitely is not true because of the things that could go wrong which MarkMuir lists. If a person bets a lot on Cash Winfall they could lose a lot long term because sometimes the jackpot might not roll down because of a jackpot winner or because the jackpot doesn’t reach 2 million, and a person could lose a lot long term because of having less than average luck. Even if a person puts down $10,000 when the jackpot rolls down,they will lose money unless if they have better than average luck when you take taxes into consideration.
If a person only has 1 or 2 winners above $600 in a year that they claim at a lottery office, if they don’t report their winners that are under $600, I don’t think there’s any chance they’ll be audited for that. But if a person bets about $10,000 every time there’s expected to be a roll down and that person has a lot of winners above $600 that he claims at a lottery office, if that person doesn’t report his winnings under $600 I think there is a high likelihood of him being audited by the Massachussets government and the IRS.
I don’t even know if anyone will read anything of what I’ve said, and if some one reads it they might disagree with what I’ve said, but I just gave my opinions.
February 23rd, 2009 at 10:13 pm
AlanBC,
Thank you for your input on this thread. You are correct that if someone were to utilize this strategy, taxes would take a bite out of their earnings and I should have put more analysis into this issue in the original post. Since you brought up this great issue, I ran the numbers through TurboTax to see what the real impact would be.
First, let me state that I made a number of assumptions with this analysis. Everyone’s tax situation is different, so the ultimate impact on any individual tax return may differ. Caveat emptor.
Ok, here are my assumptions:
- The bettor is single, has no dependents, no other income, and no other deductions (and probably lives in the basement of their parents’ home as they have no life!).
- The CashWinfall rolls down 8 times this year.
- The payout for each roll down matches the payout from the March 13, 2008 drawing (note: the actual payouts are different each draw).
- 5000 tickets ($10,000) are purchased each roll down for a total investment of $80,000.
- None of the things that I highlighted as possible issues occur; there is always a roll down and nobody wins the jackpot.
- The bettor matches 4 balls 50 times (the expected number of matches is 40000/800.58) and matches 5 balls 1 time (40000/39028.41).
- The bettor lives in MA and the Lottery collects $3825.85 in MA taxes on winnings of $76,517 (50 matches of 4 balls = $943*50 + 1 match of 5 balls = $29,367). The Lottery collects $7,341.75 in federal taxes on the 1 match of five balls (25% * $29,367).
- The total estimated value of winnings is $114,243.40, calculated by dividing the 40,000 tickets purchased by the odds per each matching scenario times the winning value of each.
According to TurboTax, the bettor would be eligible for a federal refund of $3,703 and owe the state of MA $1,280. Thus, the total taxes due would equal $8,743 ($7,341 - $3,703 + $3,825 + $1,280). As the player grossed $34,243 ($114,243 - $80,000), the total winnings net of taxes would be $25,500. This equals a 31.9% return. While this amount is less than the 42.8% I mentioned in the original post, it is still impressive.
Thank you again for helping me to think through this idea in more depth.
- Mark Muir, the Million Dollar Idea Guy
By the way, the next reported roll down is tonight (2/23/2009), so go buy your tickets and good luck!