I was thinking do all the results have the same odds in say a standard 8 ball lottery, it feels like to me you’re less likely to get a sequential set (eg. 1, 2, 3, 4, 5, 6, 7, 8, not necessarily drawn in that order) than get a heap of balls at random, it just makes me wonder if the odds are the same or if I’m over thinking.
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Assuming all balls are numbered 0-9 then you have a 1 in 100,000,000 of getting any single outcome. From 00000000 to 99999999 it seems unlikely that 00000001 would be a result, but it’s just as likely as 12674562. The odds are never in your favor.
No, all of them have the same odds. However the estimated yield scales with how often saif combination is chosen by others since the reward is shared. The easiest example is picking a common combination, winning the jackpot and getting very little money for it because a lot of people chose the same combination.
Disclainer. Lotteries are a scam and the only thing you are buying is hope and dreams. Not chances. Anyone arguing that doesnt know or chooses to ignore how miniscule those probabilities are.
The odds are exactly the same as any other combination of numbers.
Part of the reason why we tend to feel it’s less likely is in your post.
You’re comparing “a sequential set” – and you give a specific example – to “a heap of balls at random”. So you’re comparing something quite specific and small to something quite vague and large.
We do the same when we’re looking at past results. If you see a result like ’48, 7, 41, 13, 39, 1′ this goes in your mental “heap of balls at random” category. If you see a result like ‘1, 2, 3, 4, 5, 6’ that’s your “some kind of logic” category.
Now of course, there’s a lot less in the “logic” category than the “random” category, so it rarely comes up (probably you’ve never seen a result like that). Your brain is right to think the odds of a number from the “logic” category coming up are lower. Unfortunately it will tend to go a step further and go “this category comes up less often, so individual members of it must come up less often”.
TL;DR human brains take a lot of shortcuts, and are generally rubbish at probability.
The odds of getting any specific set are the same, there are just a lot more sets that aren’t sequential, so when the numbers are drawn it’s usually a set that’s not sequential.
Take this classic for example :
You flip a coin (heads /tails) and you bet with your friend that each time it is heads you get paid 1 dollar and if it is tails you pay him one dollar.
It goes extremely bad and you flip 50 times tails (i know, much wow).
Fed up with your losses you say to him : “double down : 100 dollars for me if next one is heads, tails means I pay you 100 dollars”. To your delight he accepts. What a dummy, since it has been tails 50 times in a row, what are the odds it is tails again, right? RIGHT?
Guess what :
1) all though unlikely it is entirely possible for the first 50 times to have flipped heads AND
2) guess what? The 51th flip ended up tails again.
That’s because the odds of each consequential flip is exactly the same : 50 percent. Believe it or not.
The coin does not have a “memory” : it does not take the previous results into account when flipping.
The same with your example, it is not because the first number is 1 that the lottery machine will say : “wait, drawing a 2 would be silly, let’s not do that”
This is called the Gamblers Fallacy.
The odds of a particular set don’t depend on the numbers. However, your average outcome will be better playing randomly selected number instead of a nice pattern.
The reason is that lots of people will intentionally pick 1-2-3-4-5-6-7-8. But very few people will intentionally pick 5-6-14-23-27-32-47. So if you pick the first set and win, you’re more likely to have to split the winnings with other people.
My wife picks my kids birthdays. But that’s restricting yourself to numbers between 1 and 12 plus numbers between 1 and 31. Those are going to be popular so it’s a bad choice. I dont particularly care, though, because while I think she’s basically feeding dollar bills into a paper shredder for fantasy thrills, there are a lot worse ways to get your kicks.
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