National Lottery Losing Line Odds

[johne1892]

I'll try and word this as best as I can.....

What is the probability of you playing the SAME 6 numbers since the lottery first started and never have won anything?

e.g. if you played 1,2,3,4,5,6 every draw (including Wednesdays) but a combination of 3 of those numbers have never been drawn to win at least £10.

If there has been such a combination can anyone work out what the numbers would be?

[vascop]

The probability of winning is the same every time regardless of what's happened previosly, whether you use the same numbers each week or different ones.

[Calibax]

Probability is almost zero.
Probability of winning any prize in anyone draw (at least £10) is about 54-1 or roughly 2% so the probability of not winning is 98% (0.98). Lottery has been going over ten years so assume 100 draws. Probability of not winning anything in 100 draws is 0.98^1000 = 0.00000000168 or about 600 million to one

[Calibax]

*assume 1000 draws

[Calibax]

*Probability of not winning anything in 1000 draws
sorry - getting late

[mike11111]

As Vascop has pointed out the probability of winning each draw is the same every time. Each draw is independent of the last one so you cannot mathematically combine two or more draws to calculate the odds. If you toss a coin the odds of it being heads is 50%. Even if 99 times out of 100 it lands tails, the odds of it being heads on the 100th toss are still 50%. I agree that the likelihood of this is very small, but that is not the same thing as mathematical probability.

[Calibax]

Hi Mike, Even though they are independent events you can still calculate the odds of a coin not coming up heads 10 times in a row (0.5^10) or in this case the odds of not winning the lottery 1000 times in a row (0.98^1000)

[mike11111]

Many people have thought that hey have found a sure fire way to break the bank at roulette. Wait till the same colour comes up 3 times running then bet on the opposite colour, doubling your stake on each subsequent loss. Because of the exponential nature of this system you do not need a very long losing streak to bankrupt yourself.

[Calibax]

I agree that even having lost 1000 times in a row the odds of winning the next draw are still 54-1

[ABerrant]

There have been 1615 draws thus the odds are approaching a quadrillion (10^15) to one.

[Calibax]

I didn't realise there'd been quite that many draws ABerrant. that does indeed reduce the odds even further to something approximating zero.

[R1Geezer]

vascop is correct but if the calculation is done from the outset then it's n/14m ish where N = the number of lotteries there has been (for the jackpot). So from day 1 the chance of winning the jackpot in the next 1000 draws is about 14000 to 1.

[R1Geezer]

dunno what planet aberrant is on!

[R1Geezer]

sorry my answer relates to the jackpot only. Assuming it is 1/54 to win any prize then to not win aything at all for 1615 draws is 1615/54 ie approximately 1 in 30 so that's a 28 to one shot john.

[Ellipsis]

> So from day 1 the chance of winning the jackpot in the next 1000 draws is about 14000 to 1.

That's not right R1, as it implies that if you enter the next 14 million draws you have a 100% chance of winning.

> Assuming it is 1/54 to win any prize then to not win aything at all for 1615 draws is 1615/54

That's not right either. Calibax and ABerrant have given the correct answers. The chances of winning nothing at all 1615 times in a row are very small indeed. Much lower than 28 to one!

Chances of winning something on first lottery ~= 0.02
Therefore chances of winning nothing on first lottery ~= 0.98
Chances of winning nothing on first two lotteries ~= 0.98*.98 = 0.98^2
Chances of winning nothing on first n lotteries ~= 0.98*.98 = 0.98^n

If n=1615 ...
Chances of winning nothing on first n lotteries ~= 0.98^1615 = 7.75E-14 - a very small number

And it makes no difference whether you play the same 6 numbers every time, or use a lucky dip every time ...

[secsee1]

I saw a TV programme quite recently about lotteries and the subject about the numbers 1-2-3-4-5-6 was raised and they said as far as they knew that combination has NEVER been drawn anywhere in the world.

[R1Geezer]

sorry you are correct on the second point elipsis. But the first party about the jackpot is right.

[R1Geezer]

I will qualify the bit about the jackpot. if I have the same set of numbers for 10 draws from the outset then the probability is 10 times the single draw probability, as long as the selections each week are different. To take ellipsis point if I do the same numbers for 14 million weeks and each week they are different then I will win at some point but in reality after a few thousand weeks the selections will start to repeat so the coverage of all the combinations will tend to infinity. Sorry for any confusion. Anyone know if during the 1615 draws there has been a repeat set yet?

[johne1892]

Thanks very much for your answers....

I found a website with every winning combination on. I took those numbers and popped them into excel. With a bit of tweaking I was able to enter 6 numbers and it would check how often that combination matched 0 balls, 1 ball, 2 balls etc... of every draw.

In a totally random set of chosen numbers it always appeared that they matched 3, 4, 5 or 6 numbers between 30-35 times.

I know this is the totally un-scientific way of doing it but I couldn't check the 13 million or so different combinations.

I'll see if I can find a matchng set R1 but I can't ever remember hearing of it.

Would also be interesting to see at which draw every possible combination of numbers could have matched at least 3 numbers......might be beyond my Excel skills with that though!

[Ellipsis]

> if I have the same set of numbers for 10 draws from the outset then the probability is 10 times the single draw probability, as long as the selections each week are different.

No it isn't. You seem to be assuming that the jackpot numbers remain the same each week, and the selections change. That's analagous to making multiple selections in one week, which DOES multiply your odds ... i.e. if you make ~14 million DIFFERENT selections in one week then one of them is bound to win the jackpot. But if you make one selection each week for 14 million weeks, with the jackpot numbers changing each week, then you are never guaranteed to win the jackpot - whether your selection changes each week or remains the same. In fact,your chances of not winning the jackpot if you bought a ticket each week for 14 million weeks are about 37%, i.e. you'd only have about a 2 in 3 chance of winning!

> To take ellipsis point if I do the same numbers for 14 million weeks and each week they are different then I will win at some point

No, you may not. See above.

[R1Geezer]

sorry ellipsis if I have 9,8,7,6,5,4 for example then do 14 million draws that produce different combinations then I will win as every possibility is covered.

We seem to be at cross purposes here. The whole thing is "from the outset" not as you go. the questioner asked about the SAME 6 numbers.

If every draw produces a set of numbers that has not been out before then eventually all combinations will arise, eg 1,2,3,4,5,6 for example will occur. However as already stated above for all the combinations to get drawn out could take forever.