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This is one about lottery tickets, sorry.
I do know the odds are terrible so a rubbish concept as investment but this is just for a bit of fun with max 5 quid a week spend.
I would like to think I have a generally good maths understanding/knowledge but one shocking blind spot I have always had is in relation to probabilities. I have a very poor natural 'instinct' on probability concepts..
anyway I got to thinking about 3 of the main games on UK lottery and looking at relative odds (rough figures)
Euromillions jackpot is often well into the tens of millions or more but odds of winning are 1 in 140,000,000. cost of a ticket £2.50
lotto jackpot is 2M rolling over to max of about 12M. odds of winning circa 1 in 45,000,000
cost of a ticket £2
Set for Life is jackpot of £10k/month for 30 years (i.e. total 3.6M, which after 30 years is obviously a lot less than todays money) odds of 1 in 15,000,000 cost per ticket is £1.50
so, I got thinking about relative value against odds and cost of ticket against the variable jackpots.
Now the more tickets one buys for any particular draw (assuming random ticket numbers every time) the odds go down proportionately.
I imagined a 30 quid spend every few weeks, so that would get you either
12x euromillion tickets so odds of jackpot down to 1 in 11.7million for 30£ spend
15x lotto tickets, so odds of jackpot down to 1 in 3million for 30£ spend
20x set for life tickets so odds of jackpot down to 1 in 750,000 for 30£ spend
that looks to me like although set for life is a 'smaller' win, odds are more in favour when the other jackpots are at their minimum.
Now I got confused as to how to compare relative odds if the jackpots start rolling over.
Set for life never gets any bigger but in any week Lotto could be 6M or 8M or even £12m.
Euromillions could start at £17m but go up to £60m or even £170m jackpot.
how to I do the comparison as to which is a better bet, and at what point it's better odds to go for euromillions rather than set for life for example....(if that becomes the case)?
(I'm excluding all sub-prizes at the moment as they are relatively small and I can't get my head around the main concept yet)..
Any thoughts/wisdom appreciated thanks. I may well be thinking about this a completely duff way.
Before you can get into the maths, you need to decide whether there's a size of win that's 'enough'. Would you need more than £1M, £2M, or £5M? In other words, is an £8M win worth twice as much to you as a £4M win, or would you prefer, instead of £8M, twice the probably of £4M?
TLDR, formatting etc. make it unreadable.
There are lots of analyses of every lottery on earth.
The basic strategy is that you save your money for when there are jackpots. You have to calculate the odds based on the expected payout if you bought every possible combination of numbers. It's not just about winning the big prize, it's how much you pick up on all the smaller prizes.
Unless you have a large syndicate that can pour millions into a long-term program, it's not a great business model.
Also. Gambling has never been a good business model unless it's actually a game of skill and you are highly skilled, or you own the casino and the game is rigged in your favour.
OK good point. I forgot to mention that. I was kind of thinking compare to the max set for life win, so for the purposes of this exercise, lets say the win needs to be £2M lump sum, which I would lock away and pay myself 10K per month and invest the rest
Buying 12 tickets doesn't reduce your odds to one in 12 million. If you want to improve your odds by a factor of 10 (or so) then you'll need to buy 14 million tickets. I think 🙂
Having taken greybeard's point on board, with the 'target' win £2M, another way I've been thinking about it is if one game has odds 4x 'worse' than another game then the prize needs to be 4x bigger.
so if game A has odds of 1/X to win £2m
and game B has odds of 1/4X to win, jackpot of game B needs to be 4 times bigger, i.e. £8M to be equivalent?
@woody are you sure?
1 in 140,000,000 for one ticket.
12 in 140,000,000 for 12 tickets in same draw?
It's not just you. Humans in general are bad at probability.
1 in 140,000,000 for one ticket.
1 in 140,000,000/12 = 1 in 11,666,666 for 12 tickets.
1 in 140,000,000/140,000,000 = certainty for 140,000,000 tickets.
The prize is independent of the odds of winning it. As more people play (for example in a rollover) there is a higher chance a win might be shared. Is set for life guaranteed £10k/month for the prizewinner, even if more than 1 person wins? If so that's quite appealing at the improved odds 1:15m compared with the other 2.
Exactly, you don't want win on the week that loads of others win. From memory, many years ago I think the prize was shared between 120 people (presumably all numbers under 30 and covered birthdays, anniversaries etc,.)
There's a chapter in the book Humble Pi by Matt Parker (one of those "make maths accessible" books) that deals with lottery probabilities and has some funny stories from various worldwide lottery draws.
Most people choose numbers based on birthdays - it means that there's a big peak for 1-12 and a lesser peak for 1-31 so, on the assumption that all combinations/permutations of numbers are equally likely, if you want to increase your chances of winning a big prize, choose higher numbers.
Your overall odds of winning remain the same but the odds of sharing the jackpot are much lower.
@TomB yes, I'm pretty sure the set for life 10k/month for 30 years is always never split, i.e. multiple people could win it.
and yes, I hadn't even factored in the point that jackpot might be shared.
and going back to Greybeard's original point, (and still ignoring the other sub-prizes because these can vary considerably, particularly if multiple winners),
I think I'm wrong to be reducing the 'effective' odds for winning say a target of £2m because the jackpot is say £100m in a particular week.
There would still only be one way of winning that jackpot even though it looks like 50x more 'chance' of getting £2m. you'd just be 50x more chuffed I guess.
Most people choose numbers based on birthdays – it means that there’s a big peak for 1-12 and a lesser peak for 1-31 so, on the assumption that all combinations/permutations of numbers are equally likely, if you want to increase your chances of winning a big prize, choose higher numbers.
Just before Christmas South Africa’s national lottery had the winning numbers of 5,6,7,8,9,10. 20 people shared the jackpot.