# Beating the system Probabilities

1. May 6, 2006

### denski

There is a gambling game here in my country Philippines (I hope this discussion's allowed in this section - if not then I truly apologize).

Its based on the last two digits of the daily lottery from 00 to 99. So there is a chance of a number comming out 1/100 in a year 365/100...

But since these last two digits are drawn randomly, then its a game of probability. Some two digit numbers come out more than the others.. then again some come out succeddingly... then some numbers dont come out at all.

I'm not a gambling man (nor am I a math whiz) but when I heard about this betting game it sparked my interest to beat the system... for fun and as a hobby.

This formula was given to me in another math forum:

(1/100)^(N) * 1/365 = probability

I think its flawed.

How can you correctly predict a double digit number (from 00 to 99)coming out on a specific date with the use of mathematics (math formula)? Is a year's data sufficient or is it needed at all?

-the game runs daily 365 days
-based on the last two digits of the daily lottery
-winning bets are multiplied to 70 (if you bet 20 then you win 1,400)
-drawn numbers are random

2. May 6, 2006

### HallsofIvy

Staff Emeritus
The people who set up this system are "math whizzes" (or at least consulted some) and they set it up so that it can't be beat. Most publicly run lotteries (here in the U.S. they are becoming more popular) are designed to fund schools, hospitals, etc. and are designed to make money for the lottery, not the people playing the lottery.

Since you area asking about the probability of a specific number coming up on a specific day, the answer is very simple- there is no "N" and the fact that there are 365 days in a year is irrelevant. The probability of a specific two digit number coming up is 1/100. There, that wasn't so hard, was it? Do you notice that 1/100 is less than 1/70? Let's say you decide you simply must win to day so bet the same amount (the 20 you mentioned, say) on every possible combination. Then you definitely win and get back 1400! But, of course, to win you had to wager 100*20= 2000. You have lost 600= 20*30. The "20" in that product is the 20 you originally wagered and the "30" is 100- 70, the difference between the denominator in your chance of winning (100) and the "multiplier" used in determining winnings (70).

3. May 7, 2006

### denski

So in other words, its impossible to predict... even with math equations?

There is a 70/30 chance though you could break even and 69/31 chance you could win.

If you bet 20 dollars on 70 numbers, you have invested 1,400. If one of the 70 numbers you've bet on wins, then you break even.

Odds are high since its above 50/50.

There has got to be a way.

4. May 8, 2006

### ksinclair13

The only way you could "beat the system" is if it wasn't random.

5. May 8, 2006

### Nimz

You could consider the expected value of picking N numbers. The expected value is how much you can win on average. Mathematically, it can be found as the probability of winning times how much you win minus the probability of losing times how much you lose.
N=1 --> Expected value = -6 (13.8 - 19.8)
N=2 --> Expected value = -12 (27.2 - 39.2)
and so on. Do you see the pattern? Expected value = -6N. No matter how many numbers you chose, the lottery makes money on average, not you.

6. May 9, 2006

### Tide

You should have just convinced yourself that it's impossible. In the scenario you describe the BEST you can do is break even - but you lose 30% of the time. Zero plus a negative number cannot be positive. And you did it mathematically! :)

7. May 12, 2006

### denski

Problem is its not the lottery. Its just a game brought about by financers that sponsors the game based on the last two digits of the daily lottery that came out. In other words, this game gambles on what another gambling game puts out.

Three divisions that run the game: Financers, Organizers and ushers.

Organizers and ushers get 20% of the total collection of a sponsored game. Capitalization depends on the financer. It only grosses thirty percent of what ever is put out by the financer.

Lets say a financer puts out 50 thousand on one pad (500 hundred max bet taken per number)... it will gross at an average of 15 thousand in collection... less 20% for the usher's and organizer's share. Win or lose the usher and the organizer gets their share. The real winners are these two. Financers also gamble their money here but they have better odds than the gamblers.

If a gambler bets and closes one number at its maximum bet and then it hits, he will recieve around 35 thousand.

Financer pays the 35 thousand. He surrenders what ever is left of his gross (15 thousand less usher's and organizer's share) then puts up the money for the remaining balance.

If nobody bets on the winning number, then the financer earns. If somebody bets 150 then financer breaks even... less than that then financer earns a little.

Its not government sponsored and there are no contributions to any help funds, schools, etc... its not legal... its not also illegal.

Amature CPA's just brought up this game. These are not professional mathematicians (Well actually they are, but... they're no Einstien).

I've read in an article someone in the states figured out a way to beat the lottery. This isnt a lottery. Its much more simpler than the lottery... less numbers to compute.

Its a problem on percentage and probability where there is a statistical data on which numbers come out more than the others.

Nothing is imposssible. There has got to be a way. It all just numbers.

EDIT:

I've seen gamblers hit more than 80% of the time and I dont believe in luck. They have this computation they do. Thats what I'm trying to figure out. Magicians dont give out their secrets thats why I'm turning to math whizzes outside my country.

Last edited: May 12, 2006
8. May 13, 2006

### Tide

You said the numbers were drawn randomly. Now you say "there has got to be a way." You cannot have it both ways. If it is random it cannot be predicted. If it is predictable then it is not random.

I would double check your assertion that anyone has a consistent and persistent 80% hit rate. I believe your "data" is woefully flawed. Selective memory is likely the culprit.

9. May 13, 2006

### denski

It is "drawn" randomly (numbered balls taken out are random) but there is a pattern and consistency on which numbers go out. That is what I'd like to know... how to compute the probability. I just learned the number 59 came out 20 times more than the others this year. Thats a 20/100 ratio. 15 more numbers have high hit rates.

Culprit is miscommunication.

I guess I've explained and given facts as much as I can. I'll just check this thread once in awhile just incase someone figures it out.

10. May 14, 2006

### Tide

That is entirely consistent with random drawings. The probability of a particular number coming up r times in 1 year is

$$ncr(365, r) \left( \frac {1}{100} \right)^r \left( \frac {99}{100} \right)^{365-r}$$

The picture shows a simulation and depicts all the features you described - and it's a random process!

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11. May 14, 2006

### HallsofIvy

Staff Emeritus
Why do you post a question here and then pay no attention to the replies? "Random" means there are no patterns. At any time any number is equally likely to come up.

Yes, that is quite possible. And says nothing about whether those number are more or less likely to come up than other numbers this year.

12. May 14, 2006

### denski

Hallsofivy: Alright alright I'm not arguing with you... I just would like to hear other opinions. I've listened to yours (your answer is "there is no way") , now let me hear from the others.

Tide: could you further explain that formula to me?

13. May 15, 2006

### lalbatros

denski,

Maths is about using the available information in a rational, precise and optimal way. The Mathematics cannot create information.

The only information you have here is the chance of 1/100 to choose the winning number. With this information maths is of no help. It can only tell you what is your chance to win under various scenarios, the average win, the variance of the win ... But all such calculations will always tell you the same story: gambling is gambling.

The possibilities offered to you here by mathematics might look very deceptive.
However, mathematics have helped humanity and made fortunes much more than gambling games.
Simply because it is the discipline to analyse our world in a rational way.

I suggest you to discover how math can help life.

Michel

14. May 15, 2006

### matt grime

Denski, you cannot beat the odds by definition: in a truly random game with your expected winnings negative you will lose in the long run.

As it stands the only information we have makes the assertion that each number is equally likely to occur the correct one, and, no, a small sample of the draws this year does not contradict that belief.

If you wish to perform an analysis on the hypothesis that 'the draw is uniformly distributed' versus 'the draw is biased to some numbers' then feel free to do so, though I doubt that you have enough samples to do a statistically valid hypothesis test.

Maths just models the draw, and on the information we have the model to use is the 'all equally likely' model.

I can assure you those running the game will analyse the outcomes, and will have performed trials that make sure that this model is reasonably accurate. If they had any reason to suspect otherwise they would have changed the odds they offered.

Go to a race track; do the bookkeepers or the gamblers drive the expensive cars? But for heavens sake don't bet when you're there.

As for the article you read about the Lottery. Lotteries do not offer reward purely based upon the odds of the numbers coming out, they offer a proportion of the money paid into the fund by the ticket buyers (which demonstrates on its own that in the long run you must lose sine half the money is always lost to worthy causes (in the UK)). There is however one exception to this: sometimes they offer guaranteed jackpots, or the fund is stupendously large from a rollover. In this case if you buy one of each combination you're guaranteed to win. If that expected earnings is more than the purchase price of all the tickets you make a gain. Of course you have to allow for having to share the money with other potential winners so it's a gamble in another way.

Last edited: May 15, 2006
15. May 15, 2006

### Tide

Regarding your comment to Halls (and others), you can be argumentative if you wish but understand that you are dealing with some very knowledgable, high-powered and respected mathematicians none of whom casually offer opinions on technical matters. You can bet that their statements are solidly reasoned and based on considerable experience. You can learn a great deal from them and I would avoid being dismissive.

Regarding the formula I wrote, it's based on the following: If a particular number will show up r times in n = 365 trials then that number could occur on any of r days each with a probability of 1/100. Since they are independent events, the probability that a particular set of days would yield that particular number is the product $(1/100)^{r}$.

Of course, on the remaining days, that number will not occur and on each of those days the probability is 99/100 that some other number comes up. Again, they are independent events so we use the product $(99/100)^{365 - r}$.

That is all for one particular realization of that particular number having occured on r days. But there are ncr(365, r) ways those days could have occured over the course of a year. Therefore, the total probability of a particular number occuring r times in a year is the product of those terms which I displayed in my previous message.

Finally, r can be any number from 0 to 365. Note that if you add up ALL the probabilities from r = 0 to r = 365 you will get 1.

16. May 17, 2006

### Staff: Mentor

Late reply, but you want more opinions...
On what basis do you think this? Do you know what the definition of "random" is?
Nope. Flip it over: if nothing is imposible, then should't it be possible to create a game that can't be won?

"Nothing is impossible" is nonsensical.
There are games that can be beaten, but only games that aren't completely random - such as card games with a limited number of decks.

If you see someone winning at a game that is completely random, it is because of probability. Probability dictates that every now and then, someone will win a lot and every now and then, someone will lose a lot. Whether you choose to call that "luck" or not is up to you (I don't - belief in luck can be dangerous), but those people do not have a "system" that causes them to win and they will not win more than average over a long period of time.

Last edited: May 17, 2006
17. May 17, 2006

### shmoe

Given that the numbers are uniformly chosen from 00 to 99, your best strategy is to guarantee breaking even by not playing.

Alternatively, you can win by being one of the people running the game. Even a very slight edge (which isn't how I'd describe this one) makes a game worth it for the side with the edge if you can convince people to play it enough times.

Over 365 draws, if they are in fact uniformly distributed it would be extremely unlikely to see any number appear 20 or more times more than any other. The probability that no number appears more than 12 times (over 365 draws) is something like .98982.. So even having a number turn up 20 or more times is extremely unlikely, let alone 20 times more than any other number.

Where did you get this information about 59 appearing so much more frequently? What are the full results for a years worth of draws? I would be suprised if the state run lottery has anything non-random about it, so precise information about the observed distribution is in order.

Of course it's also impossible to be certain it's not random, even if it drew 45 on every day for a year (but you might get suspicious).

18. May 21, 2006

### denski

I guess you guys have mistaken me for a gambler. Actually I'm not. I'm a 31 year old businessman (industrial bakery operator) who was just offered to finance this game. I have never gambled in my entire life thats why I'm researching for math equations since this deals with numbers.

As I said in my beggining post. I am no math whiz... thats why I'm here. I am the best in my feild locally and so are you guys on yours. There is mutual respect here... I'm just allegic to the word "NO," so pardon my assertiveness.

Since the time I posted this thread I have learned a lot about the game. The possibility of succeeding in this business is 70:30. 30 is a risk I'm not willing to take... all in all... this project is scratched and I have dabbled in the distributorship line (sideline business/gas money) supplying medical transcription pedals for MT schools and agencies. Mark up is at 26% with return on investment as soon as its delivered to clients and paid for.

Thanks for the information supplied. Its still a learning experience gained.

No hard feelings aight?

So is it safe to presume, since you guys know numbers and probabilites, that you guys arent gamblers?

19. May 21, 2006

### matt grime

oh no, I certainly gamble, but I just make sure that I'm playing against people who don't know what they're doing.