Assuming a fair coin, a coin toss is always a 1/2 chance of either heads or tails. The result of a flip is always independent of any previous flip. 20 heads in a row is always just as probable as not flipping 20 in a row. That is, any given arrangement of heads/tails flips is equally unique and has an equal chance of occurring because past flips have no actual influence on future flips.

For more information: https://en.wikipedia.org/wiki/Gambler%27s_fallacy\

Edit: my point being that winning the lotto actually has far worse chances, the chance of any given result of coin tosses at 20 tosses is something like 1 in 2 million.

Furs wrote:

Actually the lotto is different, since there's always one winner. Yeah, the chances for one individual to win it are very slim, but you can say for sure there will be one winner, exact. You can't say the same about throwing 20 heads.

Not all lotteries work the same way. Some countries use pick-6-of-46 (or some similar values) and sometimes there are no winners for that week, and sometimes there are multiple winners for that week. The best time to buy tickets in those is when the carry over jackpot ensures a payout of >100%.

ford wrote:

... the chance of any given result of coin tosses at 20 tosses is something like 1 in 2 million.

1 in 2^20, ~= 1 in a million.

revolution wrote:

The best time to buy tickets in those is when the carry over jackpot ensures a payout of >100%.

> 100%? Is that possible?

I am not sure about the legal practices in other countries. Here in HK, a certain % of the pot (15% or so) is mandatorily taken for charitable purposes. The payout can never be greater than (100% - that %), let alone 100%.

YONG wrote:

> 100%? Is that possible? I am not sure about the legal practices in other countries. Here in HK, a certain % of the pot (15% or so) is mandatorily taken for charitable purposes. The payout can never be greater than (100% - that %), let alone 100%.

Yes, both possible and common.

In a week with no winners the jackpot is carried over to the next draw. Sometimes there are multiple weeks with no winners and the jackpot value becomes very large.

revolution wrote:

ford wrote: ... the chance of any given result of coin tosses at 20 tosses is something like 1 in 2 million. 1 in 2^20, ~= 1 in a million.

so... yeah, you're right:

binomial(20 + 0, 20) 2^(-(20 + 0)) = ((20 + 0)!)/(20! 0! 2^(20 + 0)) = 1/1048576 ≈ 9.537×10^-7 ≈ 1/(1.049 million)

EDIT:

Also, I just noticed your posted location... awesome

revolution wrote:

In a week with no winners the jackpot is carried over to the next draw

In the week where there are no winners, a certain % of the pot is still mandatorily taken. The jackpot carried forward is less than 100%.

i think it is kinda weird, why it is so rare to toss 20 heads,

if i get 20 person, and toss at the same time, would heads and tails always reach balance? like 50/50,

or the coins just knew and balance themselves like water?

YONG: Yes, but you have to look at each week independently of the others.

Some bogus figures

Week1: 1 million tickets sold at $1, no one wins the $300k first prize
Week2: 2 million tickets sold at $1, no one wins the $600k+$300k first prize
Week3: 3 million tickets sold at $1, someone wins the $900k+$900k first prize.

So for week1 the payout is 85%-30% = 55% only
For week2 the payout is 85%-30% = 55% again
For week3 the payout is 85%+900k(30%) = 115%

So you can buy your tickets in week3 and have an expected return of 115%. But don't buy in week1 or week2, let everyone else make up the jackpot for you.

Naturally ticket sales increase as people get excited about the jackpot being carried over, so on week4 it is back to 1 million tickets as before.

I just assumed 30% for the top prize. It could be something else of course, it depends upon the actual lottery.

sleepsleep wrote:

if i get 20 person, and toss at the same time, would heads and tails always reach balance? like 50/50,

No. It doesn't work that way. And gamblers often fall for this misnomer. The law of large numbers says that (paraphrasing) the deviation from the norm (i.e 50%) is expected to get smaller. It doesn't mean that you can guarantee to always get 50% eventually.

sleepsleep wrote:

or the coins just knew and balance themselves like water?

Coins don't have a memory. But if your tossing technique is always the same, and the surrounding air is still and of constant density, and 100's other factors that affect the outcome are all constant; then you would always get the same, heads or tails. But there is almost no chance that you can control all those factors so precisely, so essentially it is considered random.

revolution wrote:

So you can buy your tickets in week3 and have an expected return of 115%. But don't buy in week1 or week2, let everyone else make up the jackpot for you.

So, your strategy is "never buy a ticket unless there is a jackpot".

Think about it. If everyone sticks to your strategy, no-one will buy any ticket in the first week. So, there will be no jackpot to carry forward to the second week. And no-one will buy any ticket in the second week because there is no jackpot then. As such, there will never be any jackpot.

At the end of the day, it just appears to have a > 100% payout in the jackpot-bearing week. If you look at the big picture, a certain % of the pot is always taken from the pot.

YONG wrote:

So, your strategy is "never buy a ticket unless there is a jackpot".

I don't buy tickets anyway, but if I was to then, yes, that would be my strategy.

YONG wrote:

Think about it. If everyone sticks to your strategy, no-one will buy any ticket in the first week. So, there will be no jackpot to carry forward to the second week. And no-one will buy any ticket in the second week because there is no jackpot then. As such, there will never be any jackpot.

You are right. But in practice that has never happened. Probably because no one follows my advice.

YONG wrote:

At the end of the day, it just appears to have a > 100% payout in the jackpot-bearing week. If you look at the big picture, a certain % of the pot is always taken from the pot.

Sure, if you are the person running the lottery then you always get your 15% cut. But for the people actually buying tickets they can improve their odds to >100% expected return.

No One Has Ever Left Earth On A Rocket Don Pettit NASA
https://www.youtube.com/watch?v=XG75PWvnNPU

sleepsleep wrote:

No One Has Ever Left Earth On A Rocket Don Pettit NASA https://www.youtube.com/watch?v=XG75PWvnNPU

As long as we can find one YouTube video that says so, the conspiracy must be true.

Perhaps all those detailed analyses of moon rocks were just made-up:

Moon rock
https://en.wikipedia.org/wiki/Moon_rock

'Moon rock' given to Holland by Neil Armstrong and Buzz Aldrin is fake
http://www.telegraph.co.uk/news/science/space/6105902/Moon-rock-given-to-Holland-by-Neil-Armstrong-and-Buzz-Aldrin-is-fake.html

Quote:

Curators at Amsterdam's Rijksmuseum, where the rock has attracted tens of thousands of visitors each year, discovered that the "lunar rock", valued at £308,000, was in fact petrified wood.

sleepsleep wrote:

'Moon rock' given to Holland by Neil Armstrong and Buzz Aldrin is fake http://www.telegraph.co.uk/news/science/space/6105902/Moon-rock-given-to-Holland-by-Neil-Armstrong-and-Buzz-Aldrin-is-fake.html Quote: Curators at Amsterdam's Rijksmuseum, where the rock has attracted tens of thousands of visitors each year, discovered that the "lunar rock", valued at £308,000, was in fact petrified wood.

So because a single rock given to single museum is a fake, all moon rocks must be fake? You do realize how insane that argument is, right?

ford wrote:

So because a single rock given to single museum is a fake, all moon rocks must be fake? You do realize how insane that argument is, right?

i didn't say or claim all moon rocks must be faked

i only posted, 'Moon rock' given to Holland by Neil Armstrong and Buzz Aldrin is fake

maybe there are real moon rocks somewhere on earth, and maybe most of those moon rocks are fake, idk,

in fact, if somebody brought me a rock, i can't verify whether it is earth rock, petrified wood or moon rock,

sleepsleep wrote:

in fact, if somebody brought me a rock, i can't verify whether it is earth rock, petrified wood or moon rock,

Just check if the rock "comes with both a metal and paper color identification card from the world famous Hupe Planetary Collection".

Refer to:
http://www.ebay.com/itm/Legendary-NWA-5000-Lunar-Meteorite-Moon-Rock-2-40-grams-Dual-ID-Cards-/201652161985

revolution wrote:

sleepsleep wrote: why we can't see lots of satellites in front of full bright moon? Just for sleepsleep: https://phys.org/news/2017-01-image-iss-transits-moon.html

Still more people in on the conspiracy. This time from some people from France have been paid by NASA/ESA/etc. to pretend that they viewed the space station.

https://phys.org/news/2017-02-image-iss-transits-moon.html

This conspiracy just gets larger and larger. How long until the whole population is on the payroll to pretend that space travel is real?

revolution wrote:

revolution wrote: sleepsleep wrote: why we can't see lots of satellites in front of full bright moon? Just for sleepsleep: https://phys.org/news/2017-01-image-iss-transits-moon.html Still more people in on the conspiracy. This time from some people from France have been paid by NASA/ESA/etc. to pretend that they viewed the space station. https://phys.org/news/2017-02-image-iss-transits-moon.html This conspiracy just gets larger and larger. How long until the whole population is on the payroll to pretend that space travel is real?

But didn't you know?!?!?! THE RUSSIANS AND THE AMERICANS AND THE EUROPEANS AND THE JAPANESE AND THE IRANIANS AND THE CHINESE ARE ALL IN ON IT!!!! They are all conspiring to fool the entire planet into believing that space travel and the moon landing are real! Oh, and SpaceX and Google and Virgin Galactic and DSI are all in on it too! Oh, and all of the "satellite" TV and internet providers are in on it too!