Lotto Probability

[BillyJoe]

Well, other combinations aren't counter-intuitive. That's my whole point. Many people do not think 1-2-3-4-5-6 has the same odds as 7-12-24-28-36-39 because six numbers in sequential order have not yet come up, let alone the first six numbers in the Western number system.

You and I know that 7-12-24-28-36-39 probably hasn't either, but lots of combinations like that have, so they aren't counter-intuitive to most folk.

1-2-3-4-5-6 looks unique, and it is.
7-12-24-28-36-39 looks like any other collection of 6 random numbers that come up every week but it is as unique as 1-2-3-4-5-6.

I know we are repeating ourselves, but some people will never understand this.

BJ

 

[Rasmus]

Why does anyone play lotto?

Selecting 1,2,3,4,5,6 has the same chance of winning as selecting
3,8,13,34,41,49. After ten years, my brother-in-law still doesn't believe
this.

That is sad. Still, it is smarter to play random numbers because the quaotas are usually better.

On the other hand, if you want to know just how unlikely your
numbers have of coming up, just think of how unlikely the numbers
1,2,3,4,5,6 have of coming up. It's exactly the same.

Yep.

Playing lotto is like throwing your money away.

If I throw my money away, I have a zero chance of getting back several million bucks. With the lottery, that chance is small, but it's there.

So I gamble a bit of money sometimes for the sheer excitement and the few moments of hope. That is sometimes better than having a pint in the local pub. If not, I'll have the pint instead.

 

[nimzov]

Hi.

I think this "system" is the only one that may be good in theory and in practice. Here it is:

Choose your numbers from the list of numbers that came out the most often ("hot list").

Now the justification:

Lets take for a fact that we don't know if the numbers come out perfectly randomly or if some small anomaly or bias in the drawing mechanism that may affect the draw; or that some unknown variables are in cause.

1) If there is a bias in the drawing mechanism (geometry of the balls, initial position, mixing of the balls, etc.) that favours these numbers that come out more often. The best strategy is to choose from this "hot list" hoping that the mechanism is still in operation.

2) If the difference in frequency favorizing these numbers of the "hot list" is totaly random, there is nothing to loose in playing numbers choosen from the hot list, as the probability that they are draw again is the same as any other combination.

As we do not know if 1) or 2) is true, we maximize our chance of winning by choosing our numbers in the "hot list".

In the case the drawing mechanism has no bias, this system is the same as any other. But in the case where there is a bias in the drawing mechanism this method will get better as the bias gets larger.

(Of course the best method is to not play lotto at all)

nimzo

 

[macgyver]

nimzov,

Why that's almost a "Pascal's Wager" of gambling!

But I think you make a good point....so where's the hot list for my BC Lottery games?

 

[Skeptic Ginger]

nimzov,

Why that's almost a "Pascal's Wager" of gambling!

But I think you make a good point....so where's the hot list for my BC Lottery games?

Sheesh, where've you been?

http://www.bclc.com/app/DidYouWin/WinningNumbers/Lotto649.asp

zip file, winning numbers from day 1

The rest are there too, go back to the homepage. And most US lotteries have similar info available on their web pages as well.

I usually take quick pick because it's faster but when I'm up for it I go for a random mix of the top picks to avoid sharing a pot should the numbers actually get drawn. Depends on if you think the ping pong balls fall a certain way in the WA state drawing. I dunno how BC does it.

As far as wasting money, I'd rather pay my taxes with a chance of winning than pay them with no chance. The winning pots come out of money played so I suppose there is some wasted spending there but I enjoy the fantasy of winning. I certainly don't make a special trip to get tickets. I buy them if I'm in the store and feel like it. They really get you here. When you buy groceries, all you have to do is push a few buttons on the machine in front of you at the checkout counter. It's even easier access than the tabloids and the candy bars that are lined up on the way through the checkout.

 

[Rasmus]

Hi.

I think this "system" is the only one that may be good in theory and in practice. Here it is:

Choose your numbers from the list of numbers that came out the most often ("hot list").

Now the justification:

Nice one.

Of course, if many people follow that strategy, and I think they might, then your increased odds might be counter balanced by lower prices.

 

[tsg]

Here ya go:

    #               count                1 in
------------------------------------------------------
   31                 379                43.2
   43                 375                43.6
   47                 372                44.0
   34                 372                44.0
   27                 365                44.8
   45                 353                46.4
   46                 351                46.6
   30                 348                47.0
   40                 347                47.2
   42                 347                47.2
   36                 347                47.2
    7                 346                47.3
   20                 346                47.3
   21                 344                47.6
   32                 343                47.7
   41                 343                47.7
    1                 341                48.0
   26                 338                48.4
   38                 337                48.6
    5                 337                48.6
   12                 336                48.7
   18                 335                48.9
   23                 335                48.9
   16                 333                49.1
   49                 333                49.1
    3                 333                49.1
   39                 332                49.3
   44                 330                49.6
   25                 330                49.6
    8                 329                49.7
   19                 329                49.7
   17                 328                49.9
    9                 327                50.0
    4                 327                50.0
   37                 327                50.0
   33                 326                50.2
   11                 326                50.2
   35                 323                50.7
   10                 318                51.5
   29                 318                51.5
   14                 316                51.8
   13                 315                52.0
   22                 310                52.8
   24                 309                53.0
    2                 307                53.3
   48                 306                53.5
   28                 305                53.7
    6                 303                54.0
   15                 289                56.6

 

[tsg]

Now the fun part. If we take the top 6 numbers from the hot list, and play them every week for the drawings we calculated the hot list from, here's what we end up with:

   0/6      1071
   1/6       955
   2/6       285
   3/6        26
   4/6         1
   5/6         0
   6/6         0

I didn't see that 2/6 only wins something if the bonus number matches as well until after I ran it. So what number do we want to use for the bonus number? The next most common? Or should I figure out what the most common bonus number is?

 

[tsg]

Okay, so it turns out 11 is the most common bonus number. That gives us another 11 wins. Our total so far is:

$75 (rough guess) for 4/6, $10 * 26 = $260 for 3/6, and $5 * 11 = $55 for 2/6+bonus for a grand total of $390 - $2338 for the tickets = a net loss of $1948.

 

[Mason]

A few years back, I worked in a tobacco shop that sold lottery tickets. Lemme just say that when I become facist dictator of planet America, we'll not be starting with the lawyers, but with the lotto players. Starting with the oldest.

Anyway, the machine cuts out about ten minutes prior to the drawing. Right before that, one dark and rainy night, one of the Macy's perfume girls dashes in to make it under the cut. She plays her numbers, the machine cuts out, and we start talking about the lottery and old people and stuff. People think that the guy in the tobacco shop has all the keys to life's mysteries. I don't see it, myself.

Meanwhile, we start on probability and the lottery. I give her a quick rundown on probability and how anything with odds will follow a wavy curve instead of a strait line... That is, flipping 50 pennies won't produce h-t-h-t-h-t-h-t-h-t-h-t-h-t in perfect order like that. So, if she really wants to win the lottery, she needs to follow the numbers and follow the trends. Hey, it was off the cuff, but she was cute and thought I was cute AND smart. She smelled nice, too, but I guess that goes with the job.

So, I show her some of the trends on the record boards for the past few months, and tell her she should pick two single-digit numbers, but not 7 or 5. Then, the fifth digit is almost always in the thirties, with the sixth digit being half in the forties and half in the thirties (the game was the pick-6). The remaining two numbers simply tended to be above 20 but below 40, with the occasional number in the teens. So, while doing this, I picked six numbers as examples.

Then, we watched the drawing on the little TV kept in the back of the shop for just that purpose (she was on break so she still had a few minutes to kill). Not surprisingly, of the six numbers I'd written down, five came out. She looks at me in utter awe as the numbers roll out one at a time. Of course, I'm all like "Yeah, I make it look easy". Then, when the last one was drawn, I said to her "Man, I can't believe I wasted that amazing line of ******** on the Macy's perfume girl! I could have been chatting up the Strawbridges jewelry-counter chick!" Sometimes, to my dismay, my fun sarcasm sounds almost exactly like my not-so-fun sarcasm.

So, two days later, the rest of the Macy's perfume flock came in to play their numbers, and asked me if I was that jerk who can pick the numbers. That's why I shop at Strawbridges...Because I can afford Strawbridges prices with my non-lotto-winning paycheck and the jewelry counter chick doesn't know I'm a jerk yet. .

 

[nimzov]

Okay, so it turns out 11 is the most common bonus number. That gives us another 11 wins. Our total so far is:

$75 (rough guess) for 4/6, $10 * 26 = $260 for 3/6, and $5 * 11 = $55 for 2/6+bonus for a grand total of $390 - $2338 for the tickets = a net loss of $1948.

Hi.

If you make simulations and your software permits. I would think more in terms of

1) choosing 6 random numbers from the top 15 of the hot list.

and

2) 6 random numbers from bottom 15 of the cold list (the numbers with smallest frequencies).

Making maybe 1000+ runs with 1) and 2) and comparing the results.

Not that I think it would show any significant gains.

What software are you using for your simulations ?

nimzo

 

[BPScooter]

I wondered about the reason that people don't seem to get the randomness in a lotto where every number could be in every position. Why not 1-1-1-1-1 or any other lucky number? Maybe it's our brains, we look at extreme values as "outliers" and given any range (say 1-50) and any set of intervals (say big/small or quarters, quintiles, deciles...) so we might notice a 1-4-3 as being noteworthy but not a 22-27-26? Maybe we import a bell curve onto this kind of thing. So to play the "curve" it feels better to have a bunch in the middle of the range.

This might be an example of a cognitive bias, an evolutionary adaptation sort of thing. Has anybody researched this? Not the math of the actual numbers, but the likelihood that individuals would predict random numbers in various ways?

(Edited to clarify what I was wondering about)

 

[BillyJoe]

If I throw my money away, I have a zero chance of getting back several million bucks. With the lottery, that chance is small, but it's there.

You missed the point.

I said that spending your money on the lotto is like throwing your money away. In other words, instead of spending your money on lotto (which is like throwing your money away), you'd be better off saving it for some other useful purpose - like buying a pint at the pub

BJ

 

[BillyJoe]

With the lottery, that chance is small, but it's there.

My most recent discussion with my brother-in-law went something like this...

me: Do you think 1,2,3,4,5,6 will ever come up?

him: No.

me: Then why do you spend your money on the lotto?

him: I don't pick those numbers.


regards,
BillyJoe

 

[tkingdoll]

Now the fun part. If we take the top 6 numbers from the hot list, and play them every week for the drawings we calculated the hot list from, here's what we end up with:

   0/6      1071
   1/6       955
   2/6       285
   3/6        26
   4/6         1
   5/6         0
   6/6         0

I didn't see that 2/6 only wins something if the bonus number matches as well until after I ran it. So what number do we want to use for the bonus number? The next most common? Or should I figure out what the most common bonus number is?

Of course, you never want to use the top 6 numbers from the hot list, because if they do come up, you'll have to share the prize with the hundreds of other folk who picked their numbers that way

 

[tsg]

Hi.

If you make simulations and your software permits. I would think more in terms of

1) choosing 6 random numbers from the top 15 of the hot list.

and

2) 6 random numbers from bottom 15 of the cold list (the numbers with smallest frequencies).

Making maybe 1000+ runs with 1) and 2) and comparing the results.

Not that I think it would show any significant gains.

It wasn't really a simulation. All I did was find the most common numbers drawn by counting their occurrances in the winning numbers list, and then ran those numbers back through the winning numbers list to see how often they would have won anything. If there was any advantage in a hot list strategy it should have shown up there.

Computer simulated drawings aren't really meaningful since the principle behind a hot list is that there is something in the drawing process itself which is favoring some numbers over others.

There are a couple of problems with this. The first is that, with under 2500 drawings, the sample size is just too small to be meaningful. The second is that most lottery commissions usually go to great lengths to prevent some numbers being favored over others, including multiple sets of balls and machines chosen at random. The third is that the lottery commissions usually make the same analysis of the winning numbers to detect and correct any conditions which may lead to some numbers being drawn more often than others. Even with the small sample size, from the numbers posted before you can see that the most common number has only come up in 90 more drawings than the least common number for a total difference of under 4%.

The cold list strategy has the same flaws with the addition that the idea of a number being more likely to come up because it's "due" is a fallacy.

In the end, my numbers only really show what would have happened if you had played these numbers in this particular lottery since it started. Another lottery may yield very different results.

What software are you using for your simulations ?

I wrote a script in PERL.

 

[tsg]

Of course, you never want to use the top 6 numbers from the hot list, because if they do come up, you'll have to share the prize with the hundreds of other folk who picked their numbers that way

And therein lies the lottery paradox. Anyone with a system that would truly give them an advantage is best served by not sharing it since others using that same system will split the prize. Anyone willing to share their system is likely not making any money from it (except by selling it to others).

Just as a matter of curiosity, I'd like to see if there is a single number combination that would have won more money than any other. Whether there would have been a way to know beforehand what that combination was is another matter.

 

[This Guy]

Okay, so it turns out 11 is the most common bonus number. That gives us another 11 wins. Our total so far is:

$75 (rough guess) for 4/6, $10 * 26 = $260 for 3/6, and $5 * 11 = $55 for 2/6+bonus for a grand total of $390 - $2338 for the tickets = a net loss of $1948.

Maybe I missed this point, forgive me for repeating it, if so.

Since you picked your Hot list from winning numbers, taking the numbers that showed up most, then went back over the same list of winning numbers that the Hot list was drawn from (that is correct?), you sorta forced your winnings higher than would be likely I think.

In other words, you took the numbers listed most, and went back and looked for how many times those numbers showed up, in effect.

My only point is that I think if you used those same numbers going forward, your winnings would be less (or your losses would be higher, in your example).

That make sense?

ETA: Maybe you could take your Hot list from the first half of your winning numbers list, then see how well you do on the second half of the list? Would be interesting to see the outcome

 

[69dodge]

While it is a fallacy about playing the same numbers, I don't think it is so obvious.

It is hard to reconcile A) the idea that with all numbers having an equal chance, multiple draws should eventually result in all combinations being drawn once with B) the idea that the number you play over and over has the same odds as any number for that drawing.

You can stay awake a very long time thinking about that one.

I'm not sure I understand. Can you elaborate?

I think I might know what you mean, and the short answer is: conditional probability.

 

[macgyver]

I remember reading a Sci-Fi novel when I was a kid (Larry Niven I think) where an alien race had run a lottery to allow another race to procreate. The purpose was to breed "luck" into the race, because after several generations of lottery draws only the "most lucky" families would still exist....

Seemed appropriate to our pondering probability on this thread...