to ask if you can answer a question re probability (Maths question)

[Fainne]

So, say I have 20 cards in a pack.

I pick one. It's the Ace of Diamonds let's say for argument's sake.

I then pick another one out of the same pack of 20 cards the following day.

Am I correct in saying that the odds of me picking the same card is a multiple of the single odds?

So 1/20 x 1/20 = 1/400

?

Because I've someone telling me the odds are still 1/20 that I'll pull the same card.

mummmy2017

The trick here is that all individual combinations of coin tosses are equally impossible, but the combinations that don't make a pleasing pattern outnumber ones like Heads-Heads-Heads-Heads-Heads-Heads-Heads-Heads-Heads-Heads.

If you throw a coin 10 times, the individual chance of any of these combinations being produced is the same:

HTTTHTHTHT
TTHTHTHTHT
HHTHTTHTHT
TTTTTTTTTTT
HHHHHTHTHT
HTHTHTTHTH

If you toss that coin and you want to get HTHTHTTHTH right now, I bet you won't get that string!

Whether you have to win a game by getting HTHTHTTHTH or TTTTTTTTTT, the odds are rubbish. However, because there are so many more combinations that look rather like HTHTHTTHTH, your odds of getting a combination that contains short strings of both H and T is greater.

This means, that from the point of a gambler, it looks like a set of lucky and unlucky runs. But the odds of H or T never actually change.

Odds of pulling the ace of spades twice are as you describe.
But if you’ve drawn it once, the odds of drawing again are 1/20.
If you’re just asking the odds of drawing the same card twice it’s 1/20 as it only depends on the probability of drawing the card in the second draw.

Because you are playing the game over and over

It doesn't matter.

Seriously.

I get 5 heads in a row. Would you give me £5 if it came up heads again and if it came up tails, I would give you just £1?

If you measure at the start, then the probability of you getting 10 tails in a row is low.

But if you've already had 9 tails, then when you come to flip that coin the 10th time (assuming it's a normal coin) then it is still 50/50.

No the longer you win the more likely it is that the next time you will lose.

Give it up. You don't get it and you never will.

The chances of flipping a coin and getting 10 heads in a row, before you've started, are very small. But having started, and already got 9 heads in a row, the chance of getting heads next time are 50/50.

The coin has no memory

It does go back to the original problem.

The chances of rolling double 6 are low.
But the chances of me rolling a 6, given I've already rolled a 6 are 1 in 6.
Which is exactly the same chance of me rolling a 6 even if I didn't roll a 6 before.

@PotholeParadise
Yes your right by saying you want all T for 10 times, even though your personal odd are 1/2 your next throw will give you another T.
In reality the possibility of 10T is 1/1024 of a chance.
Bookies know this so bet on how hard it is to actually manage to complete the run of T.

"the odds on you winning games in a row is a different thing to just winning a game."

Yes, this is how this thread started. The odds of winning the car twice in a row is 2/3 × 2/3 = 4/9.
But that doesn't change the fact that everytime you play you should pick the most likely outcome. Picking the less likely outcome won't improve your chances. The only way not to lose for sure is... not to play.

I wrote this last night but it apparently didn't post.

It's the AND rule when calculating probability - choosing 'x' card on day 1 is 1/20; choosing '' card on day 2 is 1/20.
The probability of choosing 'x' card on days 1 AND 2 is 1/400 (1/20 x 1/20)

In reality the possibility of 10T is 1/1024 of a chance

But that's completely irrelevant to your question.

Bookies know this so bet on how hard it is to actually manage to complete the run of T

I have never seen bookies bet on a run of Tails.

Bookies win by taking advantage of people who don't bet on the favourite because there are horses with higher odds out there,

They have higher odds for a reason.

Of course, horse racing and other gambling like that is not as reliable as cards or dice. Because the probability is known.

Also

"No the longer you win the more likely it is that the next time you will lose."

And

"You have a chance of winning or losing each time. Yes that stays the same..."

Are contradictory statements

At outset, it's 1/1024
By the time you've completed 9, it's 1/2

But your mixing up a single show and the odds of rows of winning shows.
These are not the same
You have heard of doubles or quits.
All I have to do is never stops you doubling your bet, because sure as eggs is eggs at some point you will throw a T.
So I knew from the first double you would lose a toss at some point and I would never have to pay out.

I'm not mixing up anything.

I love how people don't print the but bit.

So any managed ten T in a row yet .

All I have to do is never stops you doubling your bet, because sure as eggs is eggs at some point you will throw a T.

This is why most casinos have a limit on stakes. And that's why everything is weighted in their favour.

Eventually you'll have a losing streak, and keep doubling to win it back, but you'll reach the house limit, and be unable to.

Notwithstanding the fact that few casino games are 50/50 anyway - even red or black in roulette.

But your mixing up a single show and the odds of rows of winning shows

Let's say you always change.
WWW is 2/3 2/3 2/3 = 8/27

So quite unlikely.
The next one could be L
So we are looking for WWWL or WWWW as our run.

WWWW is 2/3 2/3 2/3 * 2/3 = 16/81
WWWL is 2/3 2/3 2/3*1/3 = 8 /81

Which event is more likely?

Actually, you introduced the rows of winning shows. Your original point was that you wouldn't swap doors on your first attempt, but you would if you played more games.
Which is totally incorrect, you should always swap, the streaks of running shows is irrelevant.

Yes you are mixing things up.
I am taking a out rows of wins.
Not independent wins.

I am taking a out rows of wins

Which event is more likely?
Assuming win is 2/3 and L is 1/3

WWWWWWWWWWWWWWWW
WWWWWWWWWWWWWWWL

Which event is more likely?

HHHHHHHHHHHHH
HHHHHHHHHHHHT

But what specifically about rows of wins? Because you seem to be saying that the number of games you have played changes the probability of winning the next one, which is incorrect. Or are you saying that winning games in a row is less likely than winning one? I don't think anyone is disputing that.

I said on the first time I wouldn't swap as the probability was not that different .
I really do have 50% chance of picking the right door.
With the knowledge my door has a true value of 33% of winning.
So I am only gaining a 16ish % advantage.
So I am going to stick, I feel lucky.
But as the goes increase probability tells me to swap, because the odds on winning by swapping make more sense.
However the k factors starts kicking in , the more times you win the more the odds of another win on the trot sway towards a loss.
I say again anyone got 10 T in a row.?

But you are saying (and have said repeatedly) that you believe that what has happened previously influences your decision making. Or are you now backtracking on that?

I say again anyone got 10 T in a row

Getting 10 T in a row is unlikely.
But given someone has got 9 T in a row, then they have a 50% chance on the next throw of getting another T.

With the knowledge my door has a true value of 33% of winning

And the other door has a 67% chance of winning.

A fool and their money are easily parted..........