If I win £1000, should I spent the lot on lottery tickets?

[HardMaths]

Hi,

I just had a really dumb idea and I wondered if I could ask what you think?

I'm not actually proposing to do it.

Getting to the point though:

I just filled in a survey with George at ASDA and it gives the possibility of winning £1000.

If I won the money, would I get even more money if I spent the lot on lottery tickets or lottery scratchcards?

I know the answer is that I shouldn't. However, I also know that there is a probability calculation that I need to do to work that out, and I wondered if any of the wise MNers know how to do that calculation?

I have relatives like that too. They much prefer to buy equities. I just do what they tell me and it works well. Melts my head though.

Each ticket has exactly the same chance of winning as any other, does it not? The odds don't accumulate in some way the more tickets you buy. So you could buy a million lucky dips and not win anything.

How about matched betting?

DS was telling me recently if a YouTuber he follows who did a scratch card experiment. He bought £1000 of scratchers and won £300.

That's very encouraging. Seems like the settled order of nature.

Isn’t it all too easy to miss a winner on a scratchcard? Maybe that’s the idea?

How is it encouraging to lose £700?!

If £1000 spent on the lottery was likely to result in a greater than £1000 payout, then the lottery wouldn't be profitable and so wouldn't exist. This principle is often referred to as "the house always wins".

As each ticket purchased is an individual miniscule gamble on the same event (eg you don't get a bigger prize for gambling more) you can't even do any kind of matched betting or doubling bets method to try to increase the likelihood of a positive return.

You could get lucky but the probability is you would come away with significantly less than £1000. You don't need to run any statistics. It is self evident.

You could spend a pound and win millions, you could spend thousands and win nothing but over all the punters don't beat the house. Some individuals will win more than they spend but many more will spend more than they win.

I've had 5k in premium bonds for around 2 years and won about £350. Not loads. So 1k is likely to win a tiny amount

But you also still have your 5k. If you spend it on lottery tickets you don't still have the stake money.

I can’t remember how many balls are there but assume 49 (I think may be 59 now???)

And six numbers???

Then ball one you have a 6 in 49 chance of winning 6/49

Next ball there’s 48 balls and then 5 possible balls you need in 48 so 5/48

4/47
3/46
2/45
1/44

So the calculation is:

6/49 5/48 4/47 3/46 2/45 * 1/44 = a very small number don’t have my calculator to hand

I don’t play the lottery so no idea how many balls or how many numbers you need but that’s the calculation.

edited to add this is for the jackpot. If you want to calculate the other prizes too then you need to breakdown the probability of each “winning” combination and add the probabilities together. You’ll be able to do it using the Bernoulli trial “6 choose 3” - think that’s what it’s called? To work out how many combinations fall under each probability.

True. That's why I buy premium bonds and not lottery tickets

The house always wins.

Fantastic! Thanks, this is what I was looking for.

I can hear DM’s voice in my head saying “ But you haven’t even won the money yet”!

The best way to ensure you don't lose is the put it in premium bonds. You might win something but you don't lose your stake. Anything else is unlikely to be profitable. Casinos don't go bankrupt (unless it is a trump operation 🤪).

The important thing to remember with gambling is "the house always wins" - in bulk, the player will always end up poorer and the organiser will always end up richer. You cannot generally rely on getting rich by gambling - although it is possible, for every one person who got rich there are huge numbers who just got poor.

However the numbers aren't quite as dire assome above posters make out because you don't need to hit the jackpot to make some money. You can win something with 3 matches, and the chances of getting at least 3 matches are better than 1% - still a low probability but not impossible.

I bought 10 tickets once in a week where I felt I really ought to win, and from that £20 outlay I got £228 back - but the chances of that happening again would be very low.

Taking into account all the potential wins from all possible prizes if you spend £1000 on lottery tickets you'll probably win about £500 ish - so a net loss of £500 ish - but it's entirely possible that you could beat the odds and end up with a net positive. You'd effectively be rolling a 100-sided dice 500 times and you only need to roll a "100" outcome about 17 times in that 500 (with some extra-lucky rolls meaning it might only need to be as few as 7 or 12 times) to be in net-positive. Obviously statistically you are more likely to only get "100" a maximim of 5 times so in the vast majority of attempts you would lose money but the chances of making a profit aren't ridiculous.

You are still better off with premium bonds though.