So far I get the numbers and torqued talk. BUT anything that requires guessing wrong and then switching is not a good bet.
Ignore Bait: Highest IQ, Many Questions, Odds makers invited...
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Depends on the odds.
If I gave you 3:1 odds just to pick a single door and stick with it, that’s a good bet.
2:1 is even money.
In the guessing and switching scenario, you are actually a 2:1 favorite. So, it’s almost always a good bet.
I seriously hope you don’t gamble a lot.
I bet on pool. I don't gamble at all. If I could read minds that might be different.
Which is another very good point.
This scenario makes a very good prop bet because people feel like switching is a bad thing.
Evidenced by the website listed earlier. Almost twice as many didn’t switch doors and they lost 65% of the time not switching.
And as evidenced by this thread, even people who are told the right answer, refuse to believe it.
One of the great prop bets of all time…
It’s all the same.
If you decide to play someone, and you’re not getting odds on your money (almost unheard of in pool) then any edge is a good bet.
As long as you win 51% of the time, it’s a good bet. If not, it’s a bad bet.
No different than any other thing in life.
Driving a car to work everyday. If the odds are high enough of being injured or killed and the pay you receive at the job you’re driving to doesn’t justify it, you shouldn’t be driving.
Life insurance is a literal line on your life just like a bookie sets a line on a game. You are paying them and giving them odds on their cash. They are expecting to make more off people than they pay out based on how long they expect you to live.
Your employer is betting they will make more revenue than they have to pay you and materials.
Literally everything in life is numbers and odds.
People just pay attention a little more when there’s direct cash or prizes being exchanged,
Have you considered testing it out? It’s not hard.
What mind reading?
But if it's pool there's a chance it's stealing.If somebody gives you even odds, it’s not gambling.
Kidding.
Little bit.
Nope. I'd rather steal...
What mind reading?
But if it's pool there's a chance it's stealing.
Kidding.
Little bit.
Nope. I'd rather steal...
If somebody gives you even odds on the three door challenge, where they are willing to stick with their initial choice every time, take it.
You’d be stealing…
The trick is that Monty KNOWS where the prize is and cannot reveal it. If he didn't know then changing your choice wouldn't matter.
I get lazy in these fast running threads and skipped after the first page or two. While it is certainly counterintuitive, part of the confusion is structuring the proposition wrong.
Starting out with one choice in three we can all agree our odds of being right are 33% and being wrong 66%, actually rounds to 67% but that isn't relevant here. Now comes the hocus-pocus. We can ignore that. What we need to focus on is that the first choice has a 33% chance of being right. Come hell or high water, if we don't change then the odds remain 33% on that choice.
Now one wrong door is opened so we know it is 0%. Nothing changed for our choice so it is still 33%. However, the remaining percentage has now shifted to one door, 66%!
The difference is where in the process choices are made.
I wish I had an old list I collected for years. Things that were counterintuitive had a fascination for me. In this case, misstating the equation after one door is opened is where the confusion comes in, or so I see it!
Poker lends itself to computer modeling far better than pool. We can put ten players of equal skill at a table and let them play a lifetime of hands in a few seconds. Oddly enough, the result isn't what is anticipated. There will be substantial winners and losers. Over the course of a lifetime, luck counts in poker. Those umpteen thousand hands aren't enough to eliminate luck.
However, we can adjust our model the tiniest bit, make one player only a few percentage points better, then that player becomes a huge lifetime winner in that game no matter how many times you run the simulation.
Short term it can be better to be lucky than to be good. Long term, skill rules!
Hu
Starting out with one choice in three we can all agree our odds of being right are 33% and being wrong 66%, actually rounds to 67% but that isn't relevant here. Now comes the hocus-pocus. We can ignore that. What we need to focus on is that the first choice has a 33% chance of being right. Come hell or high water, if we don't change then the odds remain 33% on that choice.
Now one wrong door is opened so we know it is 0%. Nothing changed for our choice so it is still 33%. However, the remaining percentage has now shifted to one door, 66%!
The difference is where in the process choices are made.
I wish I had an old list I collected for years. Things that were counterintuitive had a fascination for me. In this case, misstating the equation after one door is opened is where the confusion comes in, or so I see it!
Poker lends itself to computer modeling far better than pool. We can put ten players of equal skill at a table and let them play a lifetime of hands in a few seconds. Oddly enough, the result isn't what is anticipated. There will be substantial winners and losers. Over the course of a lifetime, luck counts in poker. Those umpteen thousand hands aren't enough to eliminate luck.
However, we can adjust our model the tiniest bit, make one player only a few percentage points better, then that player becomes a huge lifetime winner in that game no matter how many times you run the simulation.
Short term it can be better to be lucky than to be good. Long term, skill rules!
Hu
I deleted my previous posts as I didn’t explain it correctly.
This starts getting into what the odds are vs the play.
If he doesn’t know where the car is, and he can open it and you lose, then yes, you don’t get any different odds when he randomly opens the goat.
*However* the proper decision is now binging on if the player knows if Monty knows or not.
If the player knows that Monty doesn’t know where the car is before Month opens the door, then there is no right or wrong answer.
*But*, if the player doesn’t know if Monty knows, then he should always assume Monty knows and he should switch.
Because if Monty doesn’t know, the switch doesn’t matter. But if Monty does know, then the switch matters.
It’s like poker. There’s what you would do if you see your opponent’s cards vs what you should do without seeing them and the information you have.
So, if the player doesn’t know if Monty knows or not, or if he knows Monty knows, he should *always* swap.
If he does know Monty doesn’t know, it doesn’t matter if he swaps.
That’s still 2/3 scenarios.
You would never be “wrong” to swap. But you could be wrong not to swap.
Therefore, in the spirit of “is it to the player’s advantage to swap” the answer is still yes.
@vapoolplayer I don't seem to be able to reply to your posts but I think the whole proposition breaks down if there is a possibility that Monty can pick the door with the prize. In my example I was just saying that if Monty doesn't know where it is then there is no reason to switch. I didn't consider what would then happen if a door is opened.
Ya. I deleted them because I explained it incorrectly.
You are correct on the odds.
The only determining factor of the “proper” choice is what the player knows when Monty doesn’t know.
That’s just the game theory side of it.
This is the easiest way to think about it:
1/3 of the time you will initially pick the door with the car. When you switch you will get a goat.
2/3 of the time you will initially pick a door with one of the goats. Monty has two doors to open and has to open the remaining goat, leaving only the car. When you switch you get the car.
(1/3 * 0) + (2/3 * 1) = 2/3
1/3 of the time you will initially pick the door with the car. When you switch you will get a goat.
2/3 of the time you will initially pick a door with one of the goats. Monty has two doors to open and has to open the remaining goat, leaving only the car. When you switch you get the car.
(1/3 * 0) + (2/3 * 1) = 2/3
To expand on what you said, if Monty doesn’t know what’s behind any of the two doors he randomly chooses to open and it does have a goat behind it, then yes, at that point you’d have a 50-50 chance as to which of the remaining two doors the car is behind.
The problem is if he doesn’t know when he randomly chooses to open a door, there’s a 33.3% chance he could open the door with the car behind it.
The deception here is that he makes the audience/contestant think that he is just randomly choosing a door to open without knowledge, but that’s never the case. He knows the door he is choosing does not have the car behind it, and that’s why it changes the odds.
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In the Wikipedia entry you can read how the specifics of host behavior matter … go to the “other host behaviors” subsection in the link below.
en.wikipedia.org
Monty Hall problem - Wikipedia
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Something kind of ironic... People often cite that the player has a statistical advantage over the casino in blackjack, which is true, if played right; however, the problem lies in greed and finite resources.
People can play perfectly and lose all they have, or they can win big, but rarely do people stop playing when up big, they stop playing when they lose big, or all that they have.
I once had a friend that wanted to start playing blackjack and I told him this.
Whenever you play, you want to use a tiered structure of win/loss. So you go in with a set amount that you can lose. It doesn't matter what it is, you ALSO need to have an amount that you can win.
When you first tell people this, the greed starts to kick in, "but if I'm winning, why would I want to stop". The answer is you wouldn't, that's where the tiered structure comes in.
Once you get to that set amount that you give yourself to win, you pocket your starting amount and only play with the winnings. You are now incapable of losing, if you're disciplined. All of this is contingent on being disciplined.
So, your streak ends, you lose your winnings, you quit, even and go home.
Your streak continues, tier time. When you hit the next rung on the tier, you pocket a set amount of winnings and play with the rest. Now, you're guaranteed winner. If you lose the play amount, you go home, winner winner chicken dinner. If you continue to win, and get to the next tier, you pocket the winnings and play with the leftovers.
Now, I suggest, the higher the tier, the less you pocket and the more you risk because a) you're already guaranteed winner and b) if your streak continues, you're winning bigger and can set the individual bets higher.
So, you're something like 51% to get to the tier where you're guaranteed to NOT be a loser. Then every tier after that is gravy.
Requires discipline and a lack of greed that most are not capable of. Casinos stay in business because of greed, not because of a statistical advantage. Well, in most games and situations, the statistical advantage is there also...
Jaden
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That stems from the emotional side of things, which explains why some of the people here won't let the erroneous thinking go. They don't want to be wrong in their initial pick, so it's emotionally difficult to let it go.
Jaden