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.

I need to win each show to progress

I honestly don't understand what point you are trying to make.

You do not have a 1/1024 chance of winning 10 shows in a row with this game if you always swap.

It's a 2/3 ^ 10 chance of winning 10 shows in a row if you always swap.

Because the odds are always in your favour if you swap.

Casinos and bookies rely on people like you, who think they know better. They don’t care if sometimes your gamble pays off, because the whole system is designed in their favour. Over the course of the millions of bets they take, the statistics guarantee they take in more than they pay out

THIS.
It's different with things like horses and football - but pure games of chance are rigged in the casino's favour.

Back to apples and pears.
Odds on 10 pears in a row. Show wins.
1/1024.
Odds on Apple behind the door. Car win.
1/3 chance on no swap door.
On one show your faced with only two doors. When you open a door you win or lose.

But when my family ask I either win the show or lose the show

Yes - you can say I won or I lost.
And as someone who understands probability, I think you would say that given enough people who think like you, then a third would say they won and 2/3 would say they lost.

If only there was some strategy to double your chances of being in the winning group?

There was a good Louis Theroux doc where he went to Vegas to meet some ‘big rollers’. A common theme was that many of these people thought they were ‘due’ a win after a run of ‘bad luck’. They would stay at one roulette table for hours on end waiting for their win. Once they’d got one, they felt validated, even though they were many thousands of dollars down from where they started.

When your sat in the pub the next day after the show .
You get asked did you win?
Do you talk about thirds or do you say
A. I won.
B. I lost.

On one show your faced with only two doors. When you open a door you win or lose.

You need to look at the bigger picture.

Assume 99 people were faced with the same issue.
So you repeat the experiment with 99 people.
They have NO idea about what just happened
So they pick a door.
Out of those 99 people, how many will pick the winning door?

You get asked did you win

But that has nothing to do with odds.

If 99 people were asked did they win, how many would say yes?

It's like drug trials.
A drug might work or it might not work.
Give it to 1 person and it might not work.

That tells you nothing about the odds of that drug working.
Give it to enough people and then you can see the odds of that drug working.

No one is disagreeing with long term you should swap to get more wins.

No one is disagreeing with long term you should swap to get more wins

But - and I shall say it again - you should ALWAYS swap if you want to win.

Not just the long term. But right at the start. On Day 1.

Do you agree with that?

However in order to have 10 wins in a row there is a 1/1024 chance to win.
Only 1 sequence of 1024 gives you 10 wins in a row.
The door odds do not count.
It is the answer yes you won the prize that allows you to move on to the next show.

No one is disagreeing with long term you should swap to get more wins.

And you’re also more likely to win by swapping even if you only play the game once.

No on a single show you do not always have to swap to win.
The swap offers you a better chance to win a single show, but there is no guarantee the car is 100% behind door 3. You can win with door 1.

However in order to have 10 wins in a row there is a 1/1024 chance to win

No.
If the chance of winning is 2/3 if you swap, then the chances of winning 10 times is 2/3 ^ 10

That is basic probability.

The swap offers you a better chance to win a single show, but there is no guarantee the car is 100% behind door 3. You can win with door 1

No on a single show you do not always have to swap to win

I know. Everyone knows that.

But if you were in a pub and there were 99 people there and they all swapped, then there would be 66 winners and 33 losers.

If you were in a pub and there were 99 people and no one swapped, there would be 66 losers and 33 winners.

Your confusing the odds on a single show with a row of wins.

Imagine you did a large randomised trial.

With lots of people.
Tell half not to swap
Tell half to swap.

Just do 1 round per person.

What do you think would happen?

But she does your logic changed? At what point do you decide to change your strategy from sticking to swapping? Game 2? Or game 10?

our confusing the odds on a single show with a row of wins

Believe me, I am not the person who is confused here.

Ok - let's try a different approach.

We have a bag of 5 balls. 4 red and 1 black.

What do you think the chances are of getting 3 Reds in a row?

Is it 1/8 or 64/125?

Your confusing the odds on a single show with a row of wins.

You're confusing a row of wins with the outcome of several shows

Believe me, I am not the person who is confused here

😂

*when

The swap offers you a better chance to win a single show, but there is no guarantee the car is 100% behind door 3. You can win with door 1
And this logic applies on game 1 and game 2 etc etc all the way through to game 10.

The swap offers you a better chance to win a single show, but there is no guarantee the car is 100% behind door 3.

No-one has ever said you’re guaranteed to win by swapping. Just that you’re more likely to win. Just like you’re more likely to die if you play Russian Roulette with a gun that has 2 bullets than 1 bullet. Both guns can still kill you. Both guns can still leave you alive. But I know which gun I’d pick.