All good.
So to start with, you have three boxes to choose from. This is clearly 1 in 3 chance. The table shows that.
Hoe has mentioned an aspect of the game where the host shows that the box he takes away is empty.
But this doesn't change the odds because you were already a loser. Giving you a chance to change a losing box for another losing box is an invalid play.
The game is just as effective if the host takes away an empty box and doesn't show the contestant.
The point of a second chance is to give you another chance to win assuming you a holding nothing, or trick you into giving up a winner.
The maths pages that describe the problem use 10 boxes. The host takes away 8 leaving you with 1 to swap with.
If you hold the winner, then it can be any box. If you're holding a loser, then the other box is the winner.
So in the 10 box example, you odds dropped from 1 in 10 to 1 in 2. This example exaggerates the reason to change.
Back to the 1 in 2 boxes, it changes the odds, it doesn't ensure a win. Acting on the new better odds is the smart play.
This brings us back to quantum physics. When new information arrives, the future probabilities change.
Last edited by trash; 24-01-19 at 10:31 PM.
Yes I am an agent of Satan, but my duties are largely ceremonial.
Aaah OK. Yeah it was the box being taken away that threw me initially.
The latest that the "random number generator" kicked out:
Winning numbers: 23, 24, 26, 28, 30, 32 Bonus: 50
Very believable.
I'm a bit like Sheldon Cooper, I have to ask if this is sarcasm (just to be sure). I will make the assumption that it is sarcasm.Very believable.
23, 24, 26, 28, 30, 32 sup 50.
Why is this unbelievable? The odds of these numbers coming up are no different to any other combination.
My odds of winning with the numbers 1, 2, 3, 4, 5, 6 sup 7 are exactly the same as any other random numbers that you pick.
But us humans seem to think that these numbers are less likely to come up than any other combination and that just is not true.
There are so many good examples of it, one of the best is a tactic that some of my poker machines love to take advantage of, a simple coin flip.
If I flip a coin, it comes up heads. I do this five times.
Heads
Heads
Heads
Heads
Heads
What is the chance that the next flip will be tails?
More or less likely than heads?
The coin and the universe don't care, the odds of the next coin flip are always 50:50.
My poker machines are programmed to show you the last five double up gambles, (red or black) and when you see a row of all one colour, the very first thing your brain says pick the opposite colour because it's "due".
Yes I am an agent of Satan, but my duties are largely ceremonial.
irritant (25-03-19)
Of course you coin could also land on edge
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However, even on a flat surface it is possible for a coin to land on its edge, with a chance of about 1 in 6000 for an American nickel. Angular momentum typically prevents most coins from landing on their edges unsupported if flipped.
I'm out of my mind, but feel free to leave a message...
irritant (25-03-19)
Yeah, I know, but I feel like an idiot because I actually played.
And, when I saw this I thought, "Well, screw me, if I knew it would be this..."
Just miffed I didn't think of these as possibilities. It's like you say, there is an amount of expectation I guess, and like your red and black example, with this one tends to think of "difficult" numbers, or numbers you "wouldn't normally choose" if that makes sense.
Yes, my large ego can't handle that I've been outwitted by a machine.
Last edited by irritant; 26-03-19 at 01:18 AM.
Don't feel bad. The machine didn't outsmart you.
It was nothing more that another human who programmed the machine to take advantage of your natural human behaviour.
I've done this myself. I wrote code for a playing field for an online multi user dungeon many years ago.
Most of the players of the game were bitchy little teenagers so I wrote to code deliberately to make them turn on each other. I'm machiavellian, I love watching other people burn each other, especially if it is for no good reason.
Greed and Trust. I wrote the game to work on trust. You had to trust a team mate but doing so bestowed him with incredible wealth. More than enough to share fairly and win as a team.
However, it was also much much easier to betray that trust and the software just encouraged the worst kind of greed. And 90% of the time the players would stab each other in the back.
If they did there was a subtle power balance programmed into the game that let the other players tear down anybody who betrayed them with a brutal vengeance.
Best part was I could watch players playing the game and friends tearing each other apart.
Yes I am an agent of Satan, but my duties are largely ceremonial.
Aaaah, good ol' "God Mode". I like it.
I know we said its possible and everything guys, but seriously, again the two-apart story?
11, 19, 21, 23, 25, 27 Bonus: 7
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