Yes but had you chosen the other card to begin with, those odds would be the same, therefore equal probability
Sorry slackjaw but you are wrong.
Say there were 10 cards and one is an ace.
When you get down to the last two cards there are two possiblities either:
1. the card you chose (when there were 10 to choose from) is the ace
2. the other card is ace
The odds that the card you chose initially was the ace are 1 in 10
The odds you chose a card other than the ace are 9 in 10
So, some may say counter-intuitively, the odds are significantly greater
that you will end up with the ace if you switch.
When you can use that to make money from forecasting visit the casino.
That's crap. Both cards have a 50% chance of being the ace, so it makes no difference whether you change your selection or not (in terms of the long term average).
Your selection only has a 25% chance of being the ace when all four cards are present. The moment one is removed, the probability changes.
I sorta agree pepperoniDeal or no deal makes high or low offers to make the show interesting. No forumula....
IE 2 cases 1c and 200k ... offer 150k ... TAKE IT ...
I think you will find that switching is the way to go!Exactly to all of the above.
If the other person, in charge of the game knows where the ace is,
Looks like a variant of the 3 door gameshow puzzle.
It should be stated that the person turning over the cards knows the location of the Ace of Diamonds and deliberately does not turn it over.
It does not come to 50/50.
If the odds started at 90/10, then that is what they remain, whether you see 'most' of the cards face up or face down makes no difference, the cards as delt are the same.
In the games mentioned, the dealer knows where the ace is, therefore all he is showing face up are the irrelevant cards. He has to have at least 8 irrelevant ones. If he shows them to you face up or face down makes no difference to the odds, he had a 90% probability of having the ace you had a 10% probability of having the ace.
Are you, per chance, interested in a game of cards???
what would u do... take the unfair offer of $80K or take a chance at 50/50... knowing you could go home with 50c...
Pepper,
It does not come to 50/50.
If the odds started at 90/10, then that is what they remain, whether you see 'most' of the cards face up or face down makes no difference, the cards as delt are the same.
In the games mentioned, the dealer knows where the ace is, therefore all he is showing face up are the irrelevant cards. He has to have at least 8 irrelevant ones. If he shows them to you face up or face down makes no difference to the odds, he had a 90% probability of having the ace you had a 10% probability of having the ace.
Are you, per chance, interested in a game of cards???:
brty
Four playing cards are laid face down on a table.
One of them is the Ace of diamonds.
Your job is to nominate the card that you believe is the ace of diamonds.
After you have made your choice the moderator turns one of the three other cards face up.
It is not the Ace of diamonds.
The game continues.
Another card is turned face up
It is not the Ace of diamonds.
The game continues with two card left face down on the table.
One of them is the Ace of diamonds, the other is not.
You are now given an opportunity to change your selection.
A 50/50 choice.
Do you stay with the original selection or do you change cards?.
If the moderator does know where the ace is then you should change because its 75/25 in favour of it being the one the mod has left.
If the moderator doesn't know, and is randomly turning cards over - then if the cards were in his lot there is a 2/3 chance he won't turn it over first go, a 1/2 chance he won't turn it over second go. Therefore if the card is in his lot of three and he hasn't turned it over through random selection then there is only a 1 in 3 chance he wouldn't have turned it over. So that makes me think the odds are in favour of not swapping because if it was the moderators lot of three there's a 2/3 chance he would have turned it over already.
i.e. extrapolate this out to a million - if the ace was in the moderators set of 999,999 cards and he is truning them over randomly, then odds on the moderator turning over 999999 cards without turning over the ace is very slim - thus if he manages to do this its likely to be because the ace is your card and not amongst his cards.
I could probably have explained that better but am feeling too lazy to rewrite it.
i.e. extrapolate this out to a million - if the ace was in the moderators set of 999,999 cards and he is truning them over randomly, then odds on the moderator turning over 999999 cards without turning over the ace is very slim - thus if he manages to do this its likely to be because the ace is your card and not amongst his cards.
I could probably have explained that better but am feeling too lazy to rewrite it.
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