there is a car, a goat named bill, and a goat named jeff. bill and jeff are identical twins.

pick a car – show jeff – switch – win bill – GOAT

pick a car – show jeff – dont switch – CAR

pick a car – show bill – switch – win jeff – GOAT

pick a car – show bill – don’t switch – win car – CAR

pick bill – show jeff – don’t switch – win bill – GOAT

pick bill – show jeff – switch – win car – CAR

pick jeff – show bill – don’t switch – win jeff – GOAT

pick jeff – show bill – switch – win car – CAR

or

there are three people who each get to pick one of the three boxes.

two cannot pick the same box.

it is revealed one of them picked the goat.

he’s out.

the remaining two are both given the option to switch.

they can both pick the same box.

its not revealed until they have both decided.

2 people – 2 options – 2 boxes – 1 car – 1 goat.

a is right – switches – GOAT

a is right – doesn’t switch – CAR

b is right – switches – GOAT

b is right – doesn’t switch – CAR

a is wrong – doesn’t switch – GOAT

a is wrong – switches – CAR

b is wrong – doesn’t switch – GOAT

b is wrong – switches – CAR

The 1st choice is for a car-prize ‘randomly’ placed behind one of 3 doors. Random means that each door has an exactly ‘equal chance/probability’ of hiding the car– thus, a contestant can easily and correctly figure he has a 1-of-3 {.33} chance of picking the right door.

But the 2nd choice becomes ‘non-random’, after Monty Hall opens another door. There is NOT an ‘equal’ chance of the car being behind the 2 remaining doors… as most people assume. The instinctive probability calculation 1-of-2 {.50} chance is FALSE because it “requires” a random basis of choice.

Monty Hall personally interferes with the game probabilities, much like someone substituting a biased/trick coin into a previously ‘fair’ coin toss series… the other player doesn’t realize the game has changed significantly.

Since Monty will always reveal the “Goat-Door” before the contestant makes his second decision, Monty artificially doubles the original chance/probability (to .66) of the car being behind the remaining door not first chosen by the contestant.

You’ll need a web programmer, because I’m sure as heck not going to do it.

Step 1: Randomize the placement of Goats/Car behind three doors (e.g. GGC, GCG, CGG).

Step 2: Participant chooses one of the doors.

Step 3: Show one of the two goats behind a door not chosen by the participant (not sure if this needs to be randomized).

Step 3: Participant is asked if he/she would like to stand or switch.

Step 4: The big reveal! Participant is informed of winning/loosing the game.

Step 5: Record the results in a huge spreadsheet and publish in shi-shi-poo-poo journal, noting me as co-author :-)

I’d appreciate some illumination on this.

A new commuter bike, with integrated generator lights and disk brakes, now that I’d think was worth doing the math for.

So, to get a better analysis of the situation, you’d want to watch Mr. Hall’s patterns for a while before trying your hand at the game.

I think it was Francis Bacon who first formally described the scientific method.

Computers can be used in mathematical problems and even some proofs like the ‘four colour problem’ where the computer was used to eliminate many of the mundane possible arrangements. The computer is used here as a tool. Theoretically this work could be done by humans.

The understanding comes from devising the proof (and possibly devising the code for programming of the computers so that it does the work you require).

So the use of computers does not apply to the advance of any real mathematical understanding.

As a society we have discovered a vast landscape of mathematics over the past 2500 years. It seems that our physical reality is a subset of this mathematical realm.

It is the scientist job to hypothesis what is the mathematics of our Physical World, then to prod nature to find out if it behaves as the hypothesised mathematics suggest.

Today the Standard Model and General Relativity describe the physical world to great accuracies. In fact there have not been experiments performed in the last 20 years or so that deviate from the mathematics of GR or the Standard Model of quantum mechanics.

Summing up the ‘scientific method’ is not relevant or applicable to computers churning through trials of a statistical problem and certainly no real understanding of the problem can come from such procedures.