Game Show

[Pete C]

On the first go; you have a 1 in 3 chance; which stays at 1 in 3 unless you change; whereupon it changes to 1 in 2 when you flip.

And is 1 in 2 if you stick too. As soon as one door is removed,the odds for both change.

[HotStuff]

The prize is placed behind one of 3 doors at random, lets call the doors A, B & C. Therefore the chance of it being behind any of the 3 doors is 1/3rd.

Lets say you choose door A, the odds of the prize being behind door A is 1/3rd.

Therefore the odds of the prize being behind either door B or door C is 2/3rds.

Since there is only one prize atleast one of door B or door C will not have a prize behind it, therefore the host always has atleast one door he can open which doesn't have a prize behind it. The fact that the host opens a door doesn't change the odds. It's still 1/3rd for door A and 2/3rds for doors B or C. But the host has showed you it's not behind one of those two, so the other one that you haven't chosen and he hasn't opened has a 2/3rds chance of having the prize behind it.

[astroman]

No. The probability does not change.

You have a 1/3 chance of picking the correct door on the first go. That means that the probability that the door with the prize is one of the other two is 2/3.

Regardless of which of the other two doors the host opens (he always opens a door without the prize), the probability that the prize is behind one of the other two is still 2/3.

If we show this with the three doors, 1, 2 and 3. X marks the prize and O marks no prize, and assume that you always pick door 1 as your initial choice. There are three possible different scenarios as below, each with a probabilty of 1/3

1 2 3
X O O
O X O
O O X

If the prize is behind door 1, then by switching, you lose. If the prize is behind door 2, then the host shows you door 3. If you switch, you win. If the prize is behind door 3, the host shows you door 2, and if you switch you win.

Therefore, if you pick door 1 and stick, you win 1/3 of the time. If you pick door 1 then change, you win 2/3 of the time.

[Pete C]

The prize is placed behind one of 3 doors at random, lets call the doors A, B & C. Therefore the chance of it being behind any of the 3 doors is 1/3rd.

Lets say you choose door A, the odds of the prize being behind door A is 1/3rd.

Therefore the odds of the prize being behind either door B or door C is 2/3rds.

Since there is only one prize atleast one of door B or door C will not have a prize behind it, therefore the host always has atleast one door he can open which doesn't have a prize behind it. The fact that the host opens a door doesn't change the odds. It's still 1/3rd for door A and 2/3rds for doors B or C. But the host has showed you it's not behind one of those two, so the other one that you haven't chosen and he hasn't opened has a 2/3rds chance of having the prize behind it.

This argument is so flawed as to be laughable. I would advise you all to NEVER gamble.

By your logic, if a race has three horses and I select one, I just need to hope one goes lame, then bet on the other one. Trust me, you are confusing odds (based on probability) with mathematics.

I gamble a lot, so I understand odds. I am one a few people in the UK that plays craps seriously. I'll tell you why I play craps; with a double free odds game the casino has a 0.6 per cent advantage. That's all; it's the best odds in the house. Roulette, for example, gives the house a whacking advantage in the order of 20 per cent.

I do know what I'm talking about because on recent trips to the US I managed to buy my OH an MX5, and my last trip got me a Kawasaki ZRX. The car took around 12 hours, the bike around 5 days! When the house has a small advantage, you can win if you understand how the odds change.

Now, if I had three cups and hid a ball under one, your chances of finding it are 2/1. In truth, you'd be lucky if a bookie gave you 3/2. So, for the sake of the argument, give me a pound. I'll give you odds of 2/1 (which no gambling establisment will give you as they're true odds of probability) and if you pick the cup with the ball you get £3 back.

Now, if I have your pound, you pick a cup. The PROABILITY is still 3 in 1, so the ODDS are 2/1. Now, once you've picked, I give you another option. Forget the game show and think reality. If I show you that one cup hasn't got the ball, the DOES NOT change the proabbaility of it being under the cup you've picked. The PROBABILITY is till exactly the same. However, as I want your money, the odds will change to EVENS. This is because there's only two choices. You don't get a different PROBABILITY, you just get LESS money.

If I pay 2/1 on the original and EVENS on the other choice, you actually win LESS with the other choice. Odds deal with the probaility, and are a way of repaying risk.

PLEASE NOTE: ODDS HAVE NOTHING TO WITH PROBABILITY; THEY ARE DESIGNED TO OFFSET LOSS.

By taking three choices to two, you don't change the prbability of any one, you simply alter the risk. Changing odds does not change probability.

Over the years I've gambled a lot, but I don't try to do it too much because it is a risk. Anyone who thinks that changing their choice increases the chance of winning; please, take this advice.

Really...

Really...

NEVER GAMBLE

By the way, if you are sure I am wrong, I have dice and cards, and some cash, and fancy a Ford Mustang.

[HotStuff]

Pete, you may be a gambler, but either you are a troll or you have no grasp on logic.

[Sheepish]

That's not right though. The host opens another door regardless. Otherwise you'd get it right 100% of the time.

Yes, evidently I wasn't clear enough. The host always opens another door, but always chooses an empty door. There is no chance the host opens the door with the prize.

[Pete C]

Pete, you may be a gambler, but either you are a troll or you have no grasp on logic.

You're right. Care to test your logic with some cold hard cash? I am close to Camberley, and either the winner could take the money or give it to charity. I don't care, although I'll happily take the money. Maybe another person can open the doors/boxes? You can set a limit, a couple of hundred quid or something, it's down to you.

A troll? That's cheap!

[HotStuff]

You're right. Care to test your logic with some cold hard cash?

If we were to play a simulation of the game I've proposed yes, because on average I would beat you 2 to 1.

Three doors, you pick one, someone unbiased opens one of the other two which hasn't got the prize behind it and I'll take the other one. If you're right I owe you £1, if I'm right you owe me £1. After 90 goes I should be up about £30 roughly.

[Pete C]

If we were to play a simulation of the game I've proposed yes, because on average I would beat you 2 to 1.

Three doors, you pick one, someone unbiased opens one of the other two which hasn't got the prize behind it and I'll take the other one. If you're right I owe you £1, if I'm right you owe me £1. After 90 goes I should be up about £30 roughly.

As I said, I'm fine with it. Bascially, what you suggest is a 50:50guessing game. I'll put my money down.

EDIT: Make certain you've read my posts correctly, because I have said TWICE that the ODDS (you must have a potential loss) do change. Your losses will subsequently always be higher than mine, because while the PROBABILITY doesn't change, the odds do!

Also, realise that the way you are offsetting the betting means that for every bety I place at 2/1, you, taking the opposite stance, based on odds, have 2/3 liability. On the second bet, I have my original liability, but you then have an EVENS laibility too. Essentially, you need to bet £3 to win £3! I can't lose; only you can.

As I have said in two posts, don't confuse PROBABILITY with odds.

By the by, maybe read the original post. It talks on the likelihood of picking the right door. Odds are applied equally (unless you know of some system that differs).

[HotStuff]

As I said, I'm fine with it. Bascially, what you suggest is a 50:50guessing game. I'll put my money down.

EDIT: Make certain you've read my posts correctly, because I have said TWICE that the ODDS (you must have a potential loss) do change. Your losses will subsequently always be higher than mine, because while the PROBABILITY doesn't change, the odds do!

There are no odds in this case, if you are right I owe you £1, if I'm right you owe me £1. IT'S ALL DOWN TO PROBABILTY.

[Pete C]

There are no odds in this case, if you are right I owe you £1, if I'm right you owe me £1. IT'S ALL DOWN TO PROBABILTY.

Look, the whole debate is based on odds. I don't wantto be rude but you're being naive. Odds have a liability.

I pick door 1. Odds are 2/1 I put down £1. You put down £2.

The spare door is opened.

The odds are Evens. You are going against my origianl bet. You put down £1.

I put in £1. You put in £3. If I win, you must satisfy your liability. That's what bookies do. It's also why I said earlier you'd never get 2/1.

You see, again I don't want to be rude, but the whole f**king point of the so-called conundrum is that the ODDS change, which ALLEGEDLY makes it a better chance. However, the idiots that dreamed it up as a pub quiz question NEVER considered the liability of odds.

ODDS is ODDS; someone pays, either way. FACT.

[HotStuff]

Look, the whole debate is based on odds. I don't wantto be rude but you're being naive. Odds have a liability.

I pick door 1. Odds are 2/1 I put down £1. You put down £2.

The spare door is opened.

The odds are Evens. You are going against my origianl bet. You put down £1.

I put in £1. You put in £3. If I win, you must satisfy your liability. Tat's what bookies do. It's also why I said earlier you'd never get 2/1.

You see, again I don't want to be rude, but the whole f**king point of the so-called conundrum is that the ODDS change, which makes it a better chance. However, the idiots that dreamed it uyp s a pub quiz question NEVER considered the liability of odds.

ODDS is ODDS; someone pays, either way. FACT.

Did I mention odds in the original statement of the problem? No. It's a game show, the contestant doesn't have to make a stake. If there's something in that you don't understand please let me know.

[Pete C]

Did I mention odds in the original statement of the problem? No. It's a game show, the contestant doesn't have to make a stake. If there's something in that you don't understand please let me know.

Look, I tell you what; stick it.

I don't actually care; you've been rude and called me a troll. That's your bag. I didn't come here for this, so I guess you can have whatever you want.

I repeat my advice, really for your own good. Don't ever gamble. The question is based on odds, whether they're mentioned or not. If a horse is 10/1 and I stick £10 on it, if a bookie (or you) tried to give me £10 back, they'd be limping for it. For a long time.

Odds is the basis of the question; you can't ignore them.

Either way, I'm bored of this, but really ... for the sake of your health ... don't EVER gamble!

[HotStuff]

I don't believe I've been rude, I just wasn't sure whether you were being deliberately provocative or truely believed in your delusions.

Either way you're wrong. And no amount of Mustangs, Kawasakis or Mazdas will change that

Oh, and if you're still up for making the journey from Lingfield so I can prove you're wrong let me know. However you may want to read this first:

Monty Hall problem - Wikipedia, the free encyclopedia

[zazen999]

I see you boys have been playing nicely again?