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Ologhai Jones

Fancy A Flutter

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More or less all of my savings are squirrelled away in one way or another, and they're growing steadily (maybe even in real terms -- slightly), but, at present, there's no chance of winning an unexpectedly large amount of money. I guess this is okay, but it would be nice to feel as if there's more than no chance at all that a nice surprise might come my way one day.

I've been pondering the best way to add this small chance of coming into a largish amount of undeserved cash into my 'portfolio', and it's come down to Premium Bonds or The Lottery... but which one offers the best chance of winning?

In order to compare the two on some kind of equal footing, imagine I have £5k to use in this cause. I could either buy £5k's worth of Premium Bonds, or put £5k into a savings account and use the interest gained to buy Lottery tickets (which would allow me to play roughly twice a week by my arithmetic). Both of these approaches would leave me with £5k at the end of a year plus whatever 'winnings' I may or may not receive...

But which one would produce the best chances of winning, or, to put it another way, on average produce the most winnings?

Does anyone feel they have the mathematical skill to work this out? I've kind of had a go, but it'd be interesting to see an independent attempt to make the same judgement highlights any problem with my thinking.

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More or less all of my savings are squirrelled away in one way or another, and they're growing steadily (maybe even in real terms -- slightly), but, at present, there's no chance of winning an unexpectedly large amount of money. I guess this is okay, but it would be nice to feel as if there's more than no chance at all that a nice surprise might come my way one day.

I've been pondering the best way to add this small chance of coming into a largish amount of undeserved cash into my 'portfolio', and it's come down to Premium Bonds or The Lottery... but which one offers the best chance of winning?

In order to compare the two on some kind of equal footing, imagine I have £5k to use in this cause. I could either buy £5k's worth of Premium Bonds, or put £5k into a savings account and use the interest gained to buy Lottery tickets (which would allow me to play roughly twice a week by my arithmetic). Both of these approaches would leave me with £5k at the end of a year plus whatever 'winnings' I may or may not receive...

But which one would produce the best chances of winning, or, to put it another way, on average produce the most winnings?

Does anyone feel they have the mathematical skill to work this out? I've kind of had a go, but it'd be interesting to see an independent attempt to make the same judgement highlights any problem with my thinking.

Some other people have already had a crack t it (there are loads of sites like this, I was looking at it a few weeks ago).

http://www.thisismoney.co.uk/premium-bonds-guide

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As I read it, you win 'on average' 1.5% of premium bond holdings, which sounds poor, but is an average of course. You could win £1 million.

Personally, I won nought in 2008, 2.5% in 2009 and just last week 5% in 2010 so far. I think they're OK, but I'm sure there are those out there with tales of poor returns.

I only play the lottery, same numbers every draw by d/d, because I've used them since it started. Wish I hadn't started really but if they come up?! I doubt the return is more than negligible, less than 1%. Using just the interest to play the lottery is an interesting plan.

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I think the national lottery prize fund is about 50%.

Premium bonds return 1.5% tax free. So if you are earning more than 3% (1.5%/50%) tax free on your savings the lottery is the better bet, if less than 3% the premium bonds are the better bet.

I don't think you're comparing like with like there:

The 50% winnings on the lottery is 50% of £104 (in my example where I'd use the interest on £5k), whereas the PB %age is 1.5% of the £5k, no?

(A million doesn't get you much these days. I can't believe I wrote that.)

£1m is still more than enough money for me to buy the rest of my life off -- and that feels priceless to me! :)

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Played 150 times in a year = 1 in ~100,000 (using very rough rounding).

This can't be correct,

Every time you play the lottery you have the same chance of winning it, you don't increase the odd's of winning the draw each time you play it.

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Every time you play the lottery you have the same chance of winning it, you don't increase the odd's of winning the draw each time you play it.

So, someone who plays 150 times has as much chance of winning the jackpot as a person who plays just once?

Are you sure? :)

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Here's another idea. Most rollovers have a prize fund value greater than the one pound ticket stake. So invest your money in a tax free ISA, and only bet the interest on intermittent rollover days, and mathematically (in terms of maximising your expected return), you are on to a sure-fire winner.

Whilst I don't do it on the basis of earned interest, I otherwise, only play on rollovers. As you say above, (a million is not enough) a share in a normal jackpot, £2.5M midweek, just would not be worth it.

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So, someone who plays 150 times has as much chance of winning the jackpot as a person who plays just once?

Are you sure? :)

Well each draw is completely independent of the other. So your chances of winning any of them is technically the same. Whether you have played it 100 times before or it is your first time.

Think about a roulette wheel. Someone has spun it 20 times and has not ended up on Zero yet. You then wander up and decide to spin the wheel instead of them. Are you LESS likely to end up with a zero because this is your first go ? If they had spun it instead - would they have been MORE likely to end up on ZERO because they hadn't in the previous 20 attempts ?

No. They are completely unrelated and independent. Tricky subject to get your head around though !! I studied a bit of this at Uni so I have a basic understanding. Sort of.

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Well each draw is completely independent of the other. So your chances of winning any of them is technically the same. Whether you have played it 100 times before or it is your first time.

The key word here is 'before'.

However, a person who is going to play 150 times has a greater chance of winning during those 150 plays than someone who is going to play just once.

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Premium bonds return 1.5% tax free.

Erm, no...you might get 1.5% tax free, or you might get nothing (as I did with the full allowance of bonds over 12 months, never again).

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That was unlucky! With the full £30k worth allowed, you can expect an 'average' of 15 wins a year.

The longer you hold bonds, the more likely you are to win, because only the bonds that are in existence are in the draw.

Each national lottery draw is independent of all the others, or is supposed to be, despite loonies who probably insist 'Guinevere' gives lower numbers than 'Merlin' or somesuch. The odds reset at each draw.

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The key word here is 'before'.

However, a person who is going to play 150 times has a greater chance of winning during those 150 plays than someone who is going to play just once.

I am not sure the above is correct. I am sure someone else will be along to dive in and confirm !!

I think each attempt is completely Independent. You are trying to win using random numbers with a random draw each and every time. How many times you do this has no bearing on each individual result.

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That was unlucky!

Yeah, that's what I thought, and it's why I mention it to anyone thinking of buying Premium Bonds.

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The odds reset at each draw.

Yes that is exactly what I think. Whether you have tried it 150 times before means sweet FA on the upcoming draw. Most people however think it does. Probably not advertised for a good reason !!

"I have played it non stop for 3 years so surely I am due a win - I must keep on playing until my win comes in !!!"

Eh...no.

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Yes that is exactly what I think. Whether you have tried it 150 times before means sweet FA on the upcoming draw. Most people however think it does. Probably not advertised for a good reason !!

"I have played it non stop for 3 years so surely I am due a win - I must keep on playing until my win comes in !!!"

Eh...no.

If you play 150 times your odds change depending upon how many lottery draws you enter. If you enter a total of 150 tickets in one lottery draw (assuming you don't use the same number combination on all 150 tickets) your odds of winning are better than if you enter 150 total tickets playing once per lottery draw.

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Well each draw is completely independent of the other. So your chances of winning any of them is technically the same. Whether you have played it 100 times before or it is your first time.

Think about a roulette wheel. Someone has spun it 20 times and has not ended up on Zero yet. You then wander up and decide to spin the wheel instead of them. Are you LESS likely to end up with a zero because this is your first go ? If they had spun it instead - would they have been MORE likely to end up on ZERO because they hadn't in the previous 20 attempts ?

No. They are completely unrelated and independent. Tricky subject to get your head around though !! I studied a bit of this at Uni so I have a basic understanding. Sort of.

You are correct that the probability on one event is not changed by previous results, but the probability of winning with multiple tries is greater than with just one try.

Consider guessing the rolled number on a dice.

If you guess once on one roll your odds are 1 in 6, i.e. ~0.17.

If you have 3 (different) guesses on one roll your odds of being correct are 3 in 6 i.e. 0.5

If you guess once on 3 different rolls your odds of being wrong are 5/6*5/6*5/6 = ~0.58, so odds of being right at least once are ~0.42.

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I think each attempt is completely Independent. You are trying to win using random numbers with a random draw each and every time. How many times you do this has no bearing on each individual result.

Each attempt is completely independent. However, collectively (and in advance) the chances of winning by playing the Lottery 150 times is greater than playing it once.

Where's that bashing-your-face-against-a-wall emoticon when you need it?! :D

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In reality yes, but I am talking mathemamatically, which assumes the long game over infinite plays. (Same with the lottery - you're not really going to get 50% of your money back - some other sods are going to win the lion's share in jackpots. But theoretically you would get 50% back if you could play all the games forever - were it to run forever.)

Ok, I just wanted to highlight the reasonably high chances of getting feck all.

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If you play 150 times your odds change depending upon how many lottery draws you enter. If you enter a total of 150 tickets in one lottery draw (assuming you don't use the same number combination on all 150 tickets) your odds of winning are better than if you enter 150 total tickets playing once per lottery draw.

Would agree with that. However the subject of this thread was about playing it a certain number of times per week and not all in the same draw.

You are correct that the probability on one event is not changed by previous results, but the probability of winning with multiple tries is greater than with just one try.

Consider guessing the rolled number on a dice.

If you guess once on one roll your odds are 1 in 6, i.e. ~0.17.

If you have 3 (different) guesses on one roll your odds of being correct are 3 in 6 i.e. 0.5

If you guess once on 3 different rolls your odds of being wrong are 5/6*5/6*5/6 = ~0.58, so odds of being right at least once are ~0.42.

I don't think that is true. The odds of each roll are completely unrelated. Times them by each other means nothing. As far as I remember anyway. Your odds of being wrong are 5/6 on each roll. That is it.

Each attempt is completely independent. However, collectively (and in advance) the chances of winning by playing the Lottery 150 times is greater than playing it once.

Where's that bashing-your-face-against-a-wall emoticon when you need it?! :D

Mmm. I did a bit of googling. But my head hurts. :lol:

If anyone wants to have a gander through all this let us know the result.

Conditional Probability

Likelihood function

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I don't think that is true.

It is - it is very basic probability theory.

The odds of each roll are completely unrelated.

Correct - if you mean that each roll has no effect on the others.

Times them by each other means nothing. As far as I remember anyway.

You remember incorrectly. Multiplying probablilities gives you the probability of all the independent events happening.

Your odds of being wrong are 5/6 on each roll.

Yes.

That is it.

No!!!!

Mmm. I did a bit of googling. But my head hurts. :lol:

If anyone wants to have a gander through all this let us know the result.

Conditional Probability

Likelihood function

You are overcomplicating things. Whether you win the lottery has nothing to do with conditional probability (which is the probability of something happening if another condition is true). As you correctly say, each draw is an independent test.

Forget the maths and use common sense. Do you really think you could flip a coin every day of the year and it never lands tails once? We'd both agree that on each individual flip the probability of it landing tails is 0.5. I'll happily give you 200 to 1 that you can't do this without cheating.

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  • 145 Brexit, House prices and Summer 2020

    1. 1. Including the effects Brexit, where do you think average UK house prices will be relative to now in June 2020?


      • down 5% +
      • down 2.5%
      • Even
      • up 2.5%
      • up 5%



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