Lottery is a bit crap

[TwigtheWonderkid]

loafer123 said:

I am flabbergasted that you don't understand how ludicrous your reasoning is.

If you buy one ticket and I buy one ticket you are saying that between the two of us, the chances of winning have gone from 1 in 45m to 1 in 22.5m?!

Would you like to buy some magic beans?

Errr...yes, that's right. The chances of me winning are 1 in 45m. The chance of you winning are 1 in 45m. The chances of either of us winning are 2 in 45m, or 1 in 22.5m.

How would you calculate the odds of either one of us winning?

[TwigtheWonderkid]

DoubleByte said:

TwigtheWonderkid said:

loafer123 said:

Perhaps it is easier to try this from a different angle;

If you buy one ticket, you have one chance of winning and 45,057,473 chances of not winning.

If you buy two tickets, you have two chances of winning and 45,057,472 chances of not winning.

If I have to roll a 6 with a dice (or is that die) to win a prize, and have a 5 in 6 chance of not winning. On average I will win once every 6 rolls.

If I have to roll a 5 or a 6 to win a prize, I have a 4 in 6 chance of not winning. But on average, I will win once every 3 rolls. By doubling my chances of winning, I have halved my odds.

Bookies chances and odds are slightly different, because you are not dealing with fixed maths, but more of a feeling. A non league team might be 1000/1 to win the FA Cup, but that's just a feeling. No one knows if on average it happens once every 1000 years, or every 500 years, or never. Same as horse racing.

But when talking about chance of winning and odds in something with fixed maths, like roulette, the roll of dice, the lotto, marbles in a pool, then the 2 are the same. Double your chances, halve your odds.

But if the odds are very very remote, then doubling them makes little difference in reality. If you do the lotto once a week you might win on average once every 500K years (or whatever the maths dictate). By doing 2 lines, you reduce that to once every 250K years. Either way, you are highly unlikely to win.

Edited by TwigtheWonderkid on Wednesday 30th December 09:30

Edited by TwigtheWonderkid on Wednesday 30th December 09:35

Quite. And if I run a book on whether you'll win anything in any kind of event, the odds I offer wouldn't bear much resemblance to the actual chances or I wouldn't make any money

Precisely. If a bookie was giving odds on flicking a coin, he wouldn't give evens, or there's no profit margin. Like casinos and roulette, the odds they give ignore the green 00. That's their profit margin.

[feef]

If the basics of the lottery can't be grasped, then I'd love to see how folk deal with the Monty Hall problem

[TwigtheWonderkid]

feef said:

If the basics of the lottery can't be grasped, then I'd love to see how folk deal with the Monty Hall problem

Switch.

They key to it is to imagine there's 100 doors. You pick No 71. Monty opens all the others apart from 17 and then asks if you'd like to swap. Of course you'd swap. The chance of you being right at the outset was 1 in 100, and the chance of him being right was 99 in 100. That's still the case with 2 doors left.

So with 3 doors, he is right 2 in 3 times, and you're right 1 in 3 times. So swap doors.

[loafer123]

TwigtheWonderkid said:

loafer123 said:

I am flabbergasted that you don't understand how ludicrous your reasoning is.

If you buy one ticket and I buy one ticket you are saying that between the two of us, the chances of winning have gone from 1 in 45m to 1 in 22.5m?!

Would you like to buy some magic beans?

Errr...yes, that's right. The chances of me winning are 1 in 45m. The chance of you winning are 1 in 45m. The chances of either of us winning are 2 in 45m, or 1 in 22.5m.

How would you calculate the odds of either one of us winning?

The probability of me having the winning ticket is 1 in 45m. The probability of you having the winning ticket is also 1 in 45m. If, after the draw has taken place you know that a) someone has won the jackpot and b) it isn't me, your chances of holding the winning ticket are now 1 in (45m less 1).

[V8LM]

It's worse than that, you could have chosen the same numbers.

[Condi]

TTmonkey said:

TwigtheWonderkid said:

loafer123 said:

Perhaps it is easier to try this from a different angle;

If you buy one ticket, you have one chance of winning and 45,057,473 chances of not winning.

Yes, on average you will win once every 45,057,473 draws.

loafer123 said:

If you buy two tickets, you have two chances of winning and 45,057,472 chances of not winning.

Yes, on average you will win once every 22,528,736.5 draws. You have doubled your chance of winning, and halved the odds.

The lottery draws every week are completely independent of all other draws past present and future. You are no more likely to win the lottery after having played it 500k times in a row than you are having played it 50000k times in a row. It has no 'memory' and what happened before or in the future plays no part in what happens today. None. It is an independent occurrence at a fixed time and nothing changes this. If you play one ticket per draw you could play it forever and not affect your odds of winning it an any time in the future. The odds would remain the same (or until Camelott change the rules).

Of course, but we're not talking about different draws, were on about buying more than 1 ticket for the same draw. As such, you change your odds by buying more than 1 ticket...

[Condi]

loafer123 said:

TwigtheWonderkid said:

loafer123 said:

I am flabbergasted that you don't understand how ludicrous your reasoning is.

If you buy one ticket and I buy one ticket you are saying that between the two of us, the chances of winning have gone from 1 in 45m to 1 in 22.5m?!

Would you like to buy some magic beans?

Errr...yes, that's right. The chances of me winning are 1 in 45m. The chance of you winning are 1 in 45m. The chances of either of us winning are 2 in 45m, or 1 in 22.5m.

How would you calculate the odds of either one of us winning?

The probability of me having the winning ticket is 1 in 45m. The probability of you having the winning ticket is also 1 in 45m. If, after the draw has taken place you know that a) someone has won the jackpot and b) it isn't me, your chances of holding the winning ticket are now 1 in (45m less 1).

Yes.... but before the draw you have 2 chances in 45m, which is the same as 1 in 22.5m. Once you know the outcome (ie someone has won, its not you), the odds have changed because you can discount one possibility of a result.

[loafer123]

Condi said:

loafer123 said:

TwigtheWonderkid said:

loafer123 said:

I am flabbergasted that you don't understand how ludicrous your reasoning is.

If you buy one ticket and I buy one ticket you are saying that between the two of us, the chances of winning have gone from 1 in 45m to 1 in 22.5m?!

Would you like to buy some magic beans?

Errr...yes, that's right. The chances of me winning are 1 in 45m. The chance of you winning are 1 in 45m. The chances of either of us winning are 2 in 45m, or 1 in 22.5m.

How would you calculate the odds of either one of us winning?

The probability of me having the winning ticket is 1 in 45m. The probability of you having the winning ticket is also 1 in 45m. If, after the draw has taken place you know that a) someone has won the jackpot and b) it isn't me, your chances of holding the winning ticket are now 1 in (45m less 1).

Yes.... but before the draw you have 2 chances in 45m, which is the same as 1 in 22.5m. Once you know the outcome (ie someone has won, its not you), the odds have changed because you can discount one possibility of a result.

You have two tickets. There are 45m possible combinations. Each ticket has a 1 in 45m chance. Each ticket doesn't have half of the 45m allocated to it in probability terms, they both have the same pool of potential outcomes.

[V8LM]

Before the draw, with two tickets (of different numbers) there are 45m possible outcomes and you have chosen two. The chance of one winning is

2/45057474

After the draw, if one ticket hasn't won, then the chance that the other has is

1/45057473

[Condi]

loafer123 said:

You have two tickets. There are 45m possible combinations. Each ticket has a 1 in 45m chance. Each ticket doesn't have half of the 45m allocated to it in probability terms, they both have the same pool of potential outcomes.

But you have, before the draw starts, TWO tickets, each with an IDENTICAL chance of winning (assuming different numbers on each ticket) therefore you have, between both tickets, 2 in 45m chance of winning. 2 in 45 is the SAME as 1 in 22.5 in probability/mathematical terms.


Which bit of that are you arguing with? And why are you arguing with it, because all the statements above are 100% mathematically, statistically, empirically correct!

Not sure how I can explain it any simpler. Please return to school and complete year 7 maths again.

EDIT;

See this BBC maths website for 7-11 year olds if you want help.. http://www.bbc.co.uk/bitesize/ks2/maths/number/equ...



NB, may not be empirically correct, Im not buying 45m tickets to be sure.

Edited by Condi on Wednesday 30th December 17:57

[SpeckledJim]

Pwig said:

On the other hand I like the big jackpot.

I couldn't retire at 30 on 2m I would need 10-15m to make it semi comfortable.

Some basic maths.

3m jackpot.

Interest at say 5% £150,000

Take off inflation at say 2.5% £75k

Less tax £40k pa.

But that's assuming you didn't buy anything and you could get 5% interest.

Hardly massively life changing.

What's the point of winning the lottery if you can't spunk a cheeky million on a nice gaff and a few choice cars and sort out the family with some.

Why are you charging yourself £75k a year in inflation? That doesn't make sense.

£3m in the bank gives you a very healthy (if not mindblowing) risk-free income for life.

Managed carefully, you'll be in a nearly new Ferrari forever, if you so wish.

[SpeckledJim]

The first ticket is 1 in 45m. The second ticket takes you to 1 in 22.5m.

The 22.5 millionth ticket gets you to 1 in 2. 50/50. 0.5. Half.

1 in 2 doesn't mean you're 1 ticket away from 1 in 1. It means you're halfway there.

To be sure of winning, you still have to buy another 22.5m tickets.

The appearance of the fractions is deceiving.

[22]

Wow! Bookmarked (and buying 45 tickets for a 1/1000000 chance)

[SpeckledJim]

The second ticket can be drawn as 1 in 22.5m.

I think where people are confused is thinking that each extra ticket halves the odds again.

It doesn't.

Where people think the third ticket would then mean 1 in 11.75m, it actually means 3 in 45m.

Which is 1 in 15m.

Then the 4th ticket which people think will be 1 in 5.875m is actually 4 in 45m.

Which is 1 in 11.25m. Nearly half the perceived chance.

This divergence between intuition and reality gets wider and wider with each extra ticket. Only the second ticket halves the odds. Because only the second tiket represents a doubling of your risk. The rest change the odds by smaller and smaller fractions, because they are smaller and smaller parts of your investment (or risk).

In probability terms, the first ticket is the most important, as it represents the difference between some chance and no chance. Each ticket remaining equally likely to win - but that's different to the impression made by misunderstanding the fractions.

Edited by SpeckledJim on Wednesday 30th December 18:32

[SpeckledJim]

Thought of a more concise way to put it:

If you want to double your chances you have to double your risk.


At the £2 level, going to £4 gets you a doubling from 1 in 45m to 22.5m.


At the 22.m ticket level, going from 1 in 2 to 1 in 1 requires you to buy another 22.5m tickets.


And that's true of all odds inbetween.

[V8LM]

And which is why you are better off spunking all your lottery money on one draw using different numbers than you are spreading the betting over different games.

[TTmonkey]

If you had access to a lottery terminal, and spent 12 hours printing out sheet after sheet of lucky dips, 5 per sheet, you wouldn't dramatically increase the likelihood of winning the draw.

This was tried once by some thieves. They took a shop keeper 'hostage' and ran lucky dips all day. The idea was to secure the waning ticket and then pay for the tickets printed out. It didn't work. They didn't win any decent prizes.

[SpeckledJim]

V8LM said:

And which is why you are better off spunking all your lottery money on one draw using different numbers than you are spreading the betting over different games.

Not true at all. Thats exactly the misunderstanding I'm on about.

1 go at 10 draws is exactly the same as 10 goes at one draw.

1 in 45m ten times is the same as 10 in 45m.

[22]

If 1 ticket gives me 1 in 45 million, there are 44,999,999 possible outcomes that don't make me a winner. 2 tickets gives me 44,999,998 outcomes that mean I don't win.

The way you play the same game with 2 tickets there's only 22,499,999 bad outcomes, millions of outcomes disregarded.

The /45mil is a constant, what you stick in front of it doesn't matter.