Lotto Probability

Calculation explained in choosing 6 from 49

In a typical 6/49 game, six numbers are drawn from a range of 49 and if the six numbers on a ticket match the numbers drawn, the ticket holder is a jackpot winner—this is true no matter the order in which the numbers appear. The probability of this happening is 1 in 13,983,816.

Starting with a bag of 49 differently-numbered lottery balls, there is clearly a 1 in 49 chance of predicting the number of the first ball selected from the bag. Accordingly, there are 49 different ways of choosing that first number. When the draw comes to the second number, there are now only 48 balls left in the bag (because the balls already drawn are not returned to the bag), so there is now a 1 in 48 chance of predicting this number.
Thus, each of the 49 ways of choosing the first number has 48 different ways of choosing the second. This means that the odds of correctly predicting 2 numbers drawn from 49 is calculated as 49 × 48. On drawing the third number there are only 47 ways of choosing the number; but of course someone picking numbers would have gotten to this point in any of 49 × 48 ways, so the chances of correctly predicting 3 numbers drawn from 49 is calculated as 49 × 48 × 47. This continues until the sixth number has been drawn, giving the final calculation, 49 × 48 × 47 × 46 × 45 × 44, which can also be written as . This works out to a very large number, 10,068,347,520, which is however much bigger than the 14 million stated above.
The last step is to understand that the order of the 6 numbers is not significant. That is, if a ticket has the numbers 1, 2, 3, 4, 5, and 6, it wins as long as all the numbers 1 through 6 are drawn, no matter what order they come out in. Accordingly, given any set of 6 numbers, there are 6 × 5 × 4 × 3 × 2 × 1 = 6! or 720 ways they could be drawn. Dividing 10,068,347,520 by 720 gives 13,983,816, also written as 49! / (6! × (49 - 6)!).

This may seem like gobbledygook to most,but the bottom line is you have a 1 in nearly 14 million chance of choosing 6 numbers out of 49 correctly.

However,look at these winners.In draw 56 for example,the dividend is R511 550 and the number of winners is 6 as indicated by the number furtherest on your right:

Draw No Draw Date Ball 1 Ball 2 Ball 3 Ball 4 Ball 5 Ball 6 Bonus Ball Div1 Div2 Div3 Div4 Div5 Div6 Div7 Div1 No Win


56 11/03/2000 48 21 38 29 3 12 11 511550 199646 2730 1594 148 118 23 6(winners)
67 27/05/2000 27 34 38 19 16 12 8 586375 17279 1901 315 107 48 20 7(winners)
78 12/08/2000 16 37 14 48 34 27 8 1666666 54620 3677 709 183 69 24 6(winners)
85 30/09/2000 21 19 4 33 29 11 2 1878737 45236 1912 674 105 67 16 14(winners)
123 23/06/2001 4 12 24 31 40 42 28 269046 44776 2345 916 151 88 24 17(winners)
137 29/09/2001 7 4 11 33 19 39 32 3333333 59343 1654 699 84 79 15 6(winners)
146 31/10/2001 7 5 3 14 11 4 37 191900 63410 304 1151 57 91 11 19(winners)
149 10/11/2001 14 10 18 4 34 26 45 730694 79026 2624 1254 135 102 20 6(winners)
181 02/03/2002 7 16 40 19 4 5 39 6000000 83024 3930 1294 135 97 17 5(winners)
288 15/03/2003 25 33 31 23 29 27 20 111901 47739 2354 1144 218 123 27 33(winners)

I could go on.This is in a population where large numbers of people are uneducated and very few have access to computers.The witch doctors must be very good to help them pick numbers,or maybe fafi numbers do actually work.The numbers of multiple winners have admittedly tapered off a bit since 2003(I think there has been a change of operator),although there were 18 multiple winners on a day in 2009.These dividends are declared after a takeout that I worked out to be about 60%,although that figure may be slightly incorrect.

Admittedly I am a bit of a conspiracy theorist,but do the multiple winners look odd to anyone else?I'll stick to racing thanks!

Dave,

just turned to page 3 of my morning paper and on it is an article about the National Lotteries Board being taken to court by two organizations who help poor township children.They allege that the Lotteries Board is sitting on R6 billion earmarked for worthy causes,so to answer your question from the other thread I would say it is probably immaterial as to where the money is supposed to go,it's not going there anyway.

Ever wonder why Scorpians were disbanded. This is but one, of the many ,fraudulent government schemes,they would have exposed.

Another way to redistribute / misdirect public funds, with the uneducated, and unquestioning masses, been none the wiser.

When the lotto machines shut down half a hour before draw, this in itself should trigger the alarm warning bells.

Easy to pull wool over the publics eye, when the large majority follow like sheep.

Thanks Jap have had threads along the above lines before and to the punters with a bit maths easy to understand 49x48 etc divided by 1x2 etc gives you odds of the 14 Million to one, same as working out doubles, trebles, foursomes etc, just on a bigger scale

You are right, how comes so many can hit the combination?

I have seen me saying to Mrs S, will take 1-2-3-4-5-6 and her reaction is thats impossible and me trying to explain that any combination of 6 numbers out of 49 has the same odds chance, or when she checks the result will say they are "funny" or "stupid" numbers.

lol

The bottom line or only slight explaination why some times we "could" have a few winners is based on numbers such as 7/17/27 as "7" is a "lucky" number and possibly "29" (just for scotia) also the fafi dream guide could have something to do with many following the dream guide and having a large part of the population playing certain numbers.....................

However, I will also stick to the nags..........X(

I wish I had a bank of R6 billion,it would be fun to bid for a billion of a horse on IB just to see how much I could get matched.

Love reading threads like these,but with my scrambled brain i just don`t understand them..(

The simple conclusion is that playing the Lotto is for mugs. Unless you win, of course.

magiclips Wrote:

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> The simple conclusion is that playing the Lotto is
> for mugs. Unless you win, of course.


try telling the bloke that just won 84 million pounds last friday that he is a mug

Justanotherpunter Wrote:

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> I wish I had a bank of R6 billion,it would be fun
> to bid for a billion of a horse on IB just to see
> how much I could get matched.


Jap - In the days when I regularly backed horses I sometimes asked Interbet ( for a laugh ) for a big bet ( say R10,000 of a horse ) on UK racing where, admittedly, the market is even thinner than the threadbare RSA market. The response was always the same :

ALL offers were instantaneously removed. Then there was the usual delay whilst the 'offerers' rushed off to Betfair to check the odds. Shortly thereafter they would offer about R200 of the horse at a rate usually about three points below Betfair.

Where these rocket scientists imagined my inspired form was coming from beats me. But they certainly treated my guesses with a great deal more respect than they deserved and in doing so missed out ( in most instances ) on getting the money.

The part I never really understood was : Why remove ALL offers and even 'the price'. I fully understand that everybody has their limit but then surely you lay up to what you are comfortable in laying and ignore the remainder or tempt the backer into taking a progressively shorter price? Small wonder most bookmakers never make money.

Like I said, you're not a mug if you win.

true magiclips. I had 6 numbers twice but only in the daily play lotto where it pays a fixed amount of 300 pounds. I celebrated well into the night. Imagine winning a real amount of money. In all probability I would get so excited that I would either have a heart attack or die from a panic attack.

It's fun to dream...and for a very tiny handful the dream comes true. All well and good as long as the other 99.999% don't forget where the winner's winnings come from.