Monday, January 26, 2009

Off Topic: Just Because I Hate Stupidity -- How To Win At The Lottery-- NOT!

I know this is off-topic for this blog, but I couldn't pass up the opportunity to comment on this. Today's New York Daily News has an article called "Playing to win: Insider tips on winning the lottery." The article discusses some of the lottery games that are available in New York and gives tips on picking the right numbers to win.

I won't comment on the fact that the lottery is often correctly called a tax on those that are poor at math. I won't go on about how the odds of winning the lottery are so remote as to be practically nil. I just want to discuss the "tips" that the author provides and point out how stupid and illogical they are. The article gives nine tips and, sadly, of the nine, only one actually makes any sense. That one is the first one:


There are three lottery games in New York (aside from scratch-offs and the daily numbers games). Those are Mega Millions (with the highest odds and usually the highest payoff), Lotto and Take 5 (with a top pot of about $100,000 and much better odds of winning). The article notes that it's much easier to win $100K with Take 5 than to win millions of dollars with Mega Millions. This tip actually makes sense -- sometimes. If the Lotto or Mega Millions pot is large enough, it's possible that the expected value for those games could be greater than the Take 5. You have to do the math to find out which game will give you the best odds and the best return.

The rest of the tips, however, are worthless. As you read them, I want you to keep two principles in the back of your mind:

1. Assuming the game is not rigged, any set of numbers has exactly the same probability of coming up as any other set. 18-19-20-21-22 is just as likely as 2-8-11-23-38.

2. As the old investment adage goes, past performance is not an indicator of future results. Let's say you flip a coin (again, assuming the contest isn't rigged in some way) 100 times and, against all odds it comes up heads 100 times in a row. What are the odds of it coming up heads on the 101st throw? The correct answer is 1 out of 2. This is because the coin doesn't have a "memory" of previous flips. Each flip is independent of every other flip and the effects of one flip have no effect on any future flips.

So, keeping these two points in mind, let's look at the remaining eight tips offered by the article:


Quoth the article:
When it comes to picking numbers, you want as balanced a playing card as possible. Never play all one-number groups, like all 20s (21-23-25), nor all single-digit numbers, like 1-5-9. "If you play it that way, squishing all your numbers together, you're not playing a balanced game," Howard says. "You should give a relatively even mix between high numbers and low numbers, because the numbers are drawn across the number field."

The truth: It doesn't matter. All combinations have an equal chance of coming up on any one draw. The odds of getting any set of five numbers all in the 20s are exactly the same as getting any other specific set of five numbers.


Similar to the last tip, the article suggests not playing only even numbers or only odd numbers. Again, keep my first principle in mind.

DON'T COUNT ON 1-2-3-4-5

Quoth the article:
It's the absolute worst number combination to play in any lottery drawing. "It's guaranteed not to win," says Howard. Not only are these digits all at the tail end of the number spectrum, but the odds that consecutive numbers will ever be drawn are slim to none. Yet, it's the most popularly played number set. "Even after my 25 years of preaching against it, they (lottery retailers) still must sell 20,000 tickets every drawing with that combination," she says.

Again, see my first principle. 1-2-3-4-5 has just a good a chance of winning as any other combination.

It should be pointed out that, assuming the article is correct (that a lot of people play 1-2-3-4-5), then you may be at a disadvantage if you are playing a game where winners split the pot (such as Mega Millions or Lotto). But in Take 5, that is not the case. In addition, of course, if 1-2-3-4-5 are going to win, then it doesn't really matter how many people pick that combination... if you don't pick it, you're not going to win anything.


Again, from the article:
Don't play patterns (picking numbers that make a line straight across or down, that make diagonals, or that make an initial) because, believe it or not, everyone else has the same idea. "There have been 150,000 tickets in just one drawing of people playing patterns," Howard says.

See my point on the last tip. The same thing applies.


The article contends that becuase people tend to play birthdays and anniversaries, they often don't use numbers past 31. If you do this, the article contends, you are not playing a "balanced game."

Once again, let's repeat the mantra: Any single combination of numbers has the same odds as any other set.


From the article:

When playing Quick Pick, a computer generates the number combinations on your playing card — and it doesn't have your best interest in mind.

"Don't play them!" she says. "What the computer generated for me were the most awful combinations — all these things that I told you not to do. The computer would generate all lower numbers, or all higher numbers." Pick your own.

Again, it doesn't matter. The numbers the computer picks have the *exact* same odds as any other set of numbers. Your "best interests" are meaningless in a situation like this.


This tip says that you shouldn't play numbers that have been drawn recently. The article even states that if you play numbers that have recently won, you will only make it more difficult for yourself to win.

To counter this bit of stupidity, I urge you to go to the second principle I stated above. It doesn't matter what happened in the past. Assuming the game isn't rigged, what happened in past drawings has absolutely no effect on future drawings. You have just as good a chance of winning by playing the numbers that won the last jackpot as by playing numbers that haven't won in three years.


Howard has, however, used winning numbers to come up with a mathematical formula to predict future winners.

"Were you to add up the five winning numbers for the last drawing, and do that for each of the drawings going back to the beginning of the game, you'll find that 70% of all the winning Take 5 numbers have a sum between 75 and 125," she says. "So when playing Take 5, the sum of the five numbers you pick should add up to between 75 and 125."

This is one of the stupidest pieces of advice I've seen. This would only matter if you were gambling on the sum of the numbers (as you might do in a game of dice). But you're not gambling on the sum of the sum of the numbers, you're gambling on the combination of numbers.

I'm sorry to take you all off-topic, but I can't help but try to fight stupidity whenever I see it, and this ranks right up there.

The Wolf


Rich Perkins said...

you are right about all the stupid suggestions that can help one win the lottery. however, where else can you invest only a buck, with minimal effort, and have the chance to get back so much? so while the odds suck, it is real easy to get in on the game.

btw, i think the best way to explain the horrific odds of winning to non-mathematical people is as follows:
If you give me a dollar, i will give you a chance to get 10 million dollars from my friend.
Now that you have paid your dollar, go take a train to New York City.
Now, get on any subway and take it to one of the 5 boroughs.
At any point, get off at a stop of your choosing.
Look & walk around and pick a building/house.
Knock on a door in the building.
If you find my friend you can get the money.

Your odds of finding my friend are better than winning the lotto jackpot.

of course, like i said before, playing the lotto for a buck is easy and my scenario is a pain in the ass.

Ezzie said...

Freakonomics has interesting pieces noting that the euphoria created when someone buys a ticket and anticipates winning is quite high, which might make it a good cheap thrill. Doesn't make it less stupid as a way to make money, but it might make it more worthwhile than going to a concert.

I wonder if 70% of the combinations total between 75 and 125, too. :P

FWIW, advice such as the 1-2-3-4-5 one are not wrong, while neither are you: True, it has no less odds than any other combination, but simply because there are more non-consecutive combinations, you are more likely to win by not picking consecutive numbers than if you do. It's picking what the other numbers should be that is the issue.

The splitting of pots is the best reason to take a computer-generated pick. Actually, one Freakonomics piece had a commenter who noted to pick more numbers above 31 in Powerball lottos so as to be less likely to split the pot; many people use birthdays.

BrooklynWolf said...


It can't be that we're both right. :)

If you're betting on a consecutive vs. non-consecutive number sequence, then you might have a point. But you're not betting on something that general -- you're betting on *your specific* five (or six, depending on the game) numbers. And for that, the odds are the same no matter what set of numbers you pick.

The Wolf

tesyaa said...

The only tip I can think of is not to pick combinations that others are likely to pick, so if you win you won't have to share the jackpot.

I can only envision what would ensue if someone were to post the original article on the YWN Coffee Room. I'm not a member there so I can't, but if someone does, I'll enjoy the entertainment.

Larry Lennhoff said...

My wife gets literally hours of fun planning what she would do if she won the lottery. I don't understand why she can't have the same fun without wasting the dollar buying the ticket, but it is much cheaper than going to a movie and occupiers her for more time.

She buys quick picks, despite acknowledging she would be better off (in Mega Millions) picking only numbers above 31. And we have an ironclad rule of only buying one ticket per lottery - if Hashem wants us to win one is sufficient, and if Hashem doesn't than it doesn't matter how many we buy.

Ahavah Gayle said...

They way most people think about it is that they have a 50/50 chance:

1. God wants them to win some money.

2. God doesn't want them to win some money.

You can't really argue with that.

Child Ish Behavior said...

Ok, I'm a contrarian so I'm going to try to defend the article even though I understand what you are saying.

If the goal is to not only be the winner but also be the only winner then it makes sense what the guy was saying. You don't want to pick the same numbers as someone else if you cared about being the only winner of the game. If a lot of people pick the numbers and the prize gets spit up then you actually get less. If you pick numbers that no one else picked, and these happen to be the winning numbers, then you win and you are the only winner of that game.( Assuming the prize gets split up with multiple winners.)

Personally, I don't usually play lotto. It really doesn't seem like an actuarialy fair return no matter how you slice it.

Mikeinmidwood said...

If you have bitachon in Hashem no matter what number you pick will allow you to win. Thats why I dont play lotto.

Leon Basin said...

This was a great post! Thank you for sharing.

Michael Koplow said...

Yes, it is all pretty stupid. According to the article, the highest Take 5 number is 39. So the average Take 5 number is 20; the average total in a given Take 5 ticket is 100. So what does it mean that winning tickets have a total between 75 and 125? It could mean that the drawings of winning numbers are random.

Ahavah Gayle writes that most people think they have a 50/50 chance--God either wants them to win or doesn't want them to win--and that "you can't really argue with that." Actually, I can. The two probabilities have to add up to 100%--they don't need to be 50% each.

BrooklynWolf said...

And we have an ironclad rule of only buying one ticket per lottery - if Hashem wants us to win one is sufficient, and if Hashem doesn't than it doesn't matter how many we buy.

Ha! That's *exactly* my approach too!

When I play (usually only when the pot is really big) I only buy one. Not that I really think I have a chance of winning, but at least it gives me the right to fantasize for a few days. :)

The Wolf

Dave said...

For most people of moderate means, a single lottery ticket when the jackpot is large is perfectly reasonable. More than one is foolishness.

There is an enormous difference between no chance in 50 million, and 1 chance in 50 million. There is, however, little difference between 1 chance in 50 million, and 20 chances in 50 million.