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Stats - Help with an argument I am having with myself

cullennz

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cullennz
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Sep 21, 2006
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Long story short

Lotto power ball built over several weeks to 38 mill

They said the chances of winning were 36 mill to one

Two people got it.

Are the chances of a person getting the right numbers 36m-1 at the same time as another person gets them 36m-1, higher than 36m-1, or still just 36m-1?

Swaying to the later but was never good at stats

I wasn't one of the people btw
 
caveat: I think this is right, but tell me if I'm wrong:


If people picked their numbers randomly the chances of more than one person hitting a 36*10^6 to one would be (36*10^6)^n, with n being the number of people picking the same numbers.

However, we know that people pick predictable numbers with certain patterns or significance. Therefore, in practice, the chance of more than one persons winning is pretty high.
 
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cullennz said:
I wasn't one of the people btw
Click to expand...

Bugger!

(nor was I)

As Zaganza noted the odds remain the same - just as when you throw 8 sixes in a row on a die, the odds of throwing another one are still 1 in 6.

Interesting side point on Lotto - it's struck far more often than maths says it will be. Right from the start, it was set up the way it is because jackpots were expected to be very frequent.

Except that didn't happen.

It's why statistics can be tricky - people don't pick 1, 2, 3, 4, 5 & 6 as their six numbers, so the odds aren't entirely random.
 
The Atheist said:
Bugger!

(nor was I)

As Zaganza noted the odds remain the same - just as when you throw 8 sixes in a row on a die, the odds of throwing another one are still 1 in 6.

Interesting side point on Lotto - it's struck far more often than maths says it will be. Right from the start, it was set up the way it is because jackpots were expected to be very frequent.

Except that didn't happen.

It's why statistics can be tricky - people don't pick 1, 2, 3, 4, 5 & 6 as their six numbers, so the odds aren't entirely random.
Click to expand...

True

The 1,2,3,4,5 and 6 just as likely thing still seems a bit illogical, but quite a cool thing.

I seem to remember once when they were all under 10, which was quite close to it.
 
No math, but do we know how many tickets were sold?

The likelyhood that the winning number will have been chosen by 2 or more people increases with the number of tickets sold.
 
Puppycow said:
No math, but do we know how many tickets were sold?

The likelyhood that the winning number will have been chosen by 2 or more people increases with the number of tickets sold.
Click to expand...

Only got this

"More than 1.7 million tickets were expected to be sold for a chance to claim Wednesday night's draw, Lotto NZ said."

They needed to get 6 right to win a mill normally and then a one extra power ball to hit the accumulated bigger prize.

All the ball are 1 to 40 I think
 
cullennz said:
Only got this

"More than 1.7 million tickets were expected to be sold for a chance to claim Wednesday night's draw, Lotto NZ said."
Click to expand...

Slightly misleading, because each ticket has multiple entries.

I'd expect the average ticket to be a $20 multi shot, which has 15 lines of Lotto?

That gives 25.5 million individual entries.
 
I don't think the question is well posed:

When we say the odds of winning are 36 million to one we are referring to a single individual's chance of winning. Comparing this to two people winning (under whatever given conditions you wish to include) is a completely different question: For example, if only one person plays, the chances of two people winning are obviously zero. On the other hand, if 72 million people strategically select two of every ticket, the chances of two people winning are obviously 100%.

Asking if individual A will win is not the same question as asking if some individual (or some pair of individuals will win.
 
Remember the birthday problem. How many people must be in a room before it is more likely than not that two have the same birthday?

The counter intuitive answer is 23.

IXP
 
Puppycow said:
No math, but do we know how many tickets were sold?

The likelyhood that the winning number will have been chosen by 2 or more people increases with the number of tickets sold.
Click to expand...

True, and generally speaking, when the jackpot gets big, a lot more tickets get sold. Another consideration is that, with most lotteries, $38 million is not really $38 million. Usually that is the total payout of an annutity (20 years for the Colorado Lottery, I'm not sure about others). This translates to a cash value considerably lower than the advertised prize.
 
The Atheist said:
As Zaganza noted the odds remain the same - just as when you throw 8 sixes in a row on a die, the odds of throwing another one are still 1 in 6.
Click to expand...
Unless your plan is to throw the die eight times in a row. Then your odds of rolling the same number are (1/6)8
Stats are funny like that.
 
DuvalHMFIC said:
Unless your plan is to throw the die eight times in a row. Then your odds of rolling the same number are (1/6)8
Stats are funny like that.
Click to expand...

Actually, if you roll a fair die eight times in a row, the probability of rolling the same number every time is (1/6)7, not (1/6)8.
 
The Atheist said:
Bugger!

(nor was I)

As Zaganza noted the odds remain the same - just as when you throw 8 sixes in a row on a die, the odds of throwing another one are still 1 in 6.

Interesting side point on Lotto - it's struck far more often than maths says it will be.
Click to expand...

I am very skeptical of this. Do you have a cite?

Right from the start, it was set up the way it is because jackpots were expected to be very frequent.

Except that didn't happen.

It's why statistics can be tricky - people don't pick 1, 2, 3, 4, 5 & 6 as their six numbers, so the odds aren't entirely random.
Click to expand...

Actually, I am under the impression that lots of people pick 1, 2, 3, 4, 5 & 6 as their six numbers:

https://www.dailymail.co.uk/news/ar...id-Going-1-2-3-4-5-6-bring-tiny-windfall.html
 
The Atheist said:
Bugger!

(nor was I)

As Zaganza noted the odds remain the same - just as when you throw 8 sixes in a row on a die, the odds of throwing another one are still 1 in 6.

Interesting side point on Lotto - it's struck far more often than maths says it will be. Right from the start, it was set up the way it is because jackpots were expected to be very frequent.

Except that didn't happen.

It's why statistics can be tricky - people don't pick 1, 2, 3, 4, 5 & 6 as their six numbers, so the odds aren't entirely random.
Click to expand...
Fun fact from Norway: A lot of people actually pick the numbers 1, 2, 3, 4, 5, 6, 7 every week, because they think they are smart. I used to to this myself, until I found out that this is the far most common number combination. The day I win, I want to be the only winner.
 
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