Monty is a masculine given name, often a short form of Montgomery or Montague. It can be a surname as well.
One of the most famous game shows of all time was Let’s Make a Deal, hosted by Monty Hall. The show gained a second kind of fame when a dilemma in probability theory became known as the Monty Hall Problem.
What is Monty?
Aside from being a fun and engaging activity, Monty is a well-designed and entertaining game for players of all ages. The best part is that it’s relatively inexpensive and there is no need to worry about getting injured. In fact, the whole exercise can be a relaxing and enjoyable event that will help keep your brain healthy while improving your social skills. As you might have guessed, there are many versions of Monty available for purchase at various retailers and online. The name of the game is simply to choose the appropriate version for your needs. For instance, a more practical choice might be a less expensive mobile app. Alternatively, you could opt for a more comprehensive desktop solution, albeit one that will cost you a hefty premium. For the serious player, a home or office PC might be your ticket. To make your life easier, we’ve rounded up some of the best options on the market.
Origins
Monty is a male name, usually short for Montgomery, Montague and other similar names. It is also a surname and, as such, it can have both French and English origins.
There are a number of theories as to the origins of Monty, but the most common and probably most plausible is that it came from the name of a menswear firm founded by a man named Montague Maurice Burton. Mr Burton began the business in Chesterfield, Derbyshire in 1903, and by 1929 he had more than 500 shops across the country.
Another possible etymology is that it refers to Field Marshal Lord Montgomery, a British general who was affectionately known as “Monty” during World War II. During that time he became known for his long, fastidious military briefings.
This has led to speculation that the Pythons might have been influenced by Montgomery’s famous televised military briefings, although this isn’t entirely confirmed. However, it is likely that the members of the group had been aware of Montgomery’s reputation before they started working together.
The Pythons were formed in 1963, with two writing partnerships already in place: Cleese and Chapman and Jones and Palin. The remaining pair, Gilliam and Idle, were left to work independently, forming a new group that would become the world’s most influential comedy troupe.
The Pythons revolutionised comedy with a series of surrealist sketch comedy shows (Monty Python’s Flying Circus) and four feature films (And Now for Something Completely Different, The Holy Grail, Life of Brian and The Meaning of Life), as well as several stage shows and specials. It was their creative independence that made the group a pioneering force in comedy, discarding the established rules of television comedy and influencing the way performers entertained audiences for years to come.
Rules
Monty Hall was the host of a popular game show called Let’s Make a Deal. The game involved contestants selecting one of three doors, two of which contain goats and the other one containing a car.
Then, Monty opens one of the doors and reveals its contents. In two out of three cases, the player wins by changing their choice of door. However, there is a controversy over the rules of this game that makes it a fascinating probability puzzle.
There are a number of key assumptions that must be made in order to understand this problem. These include that Monty will always open a door and that he chooses at random.
These assumptions are reasonable, but it is not clear why he should only open the door he chose at the start of the game and not the one that contains the prize. It is likely that he is running short of time and is trying to get rid of the cars as quickly as possible, so he is not keen to waste any extra space by revealing the car in a door that the winner has already chosen.
If we apply a Bayesian approach to probability, we can explain this. It is based on the fact that, when you pick your door at the beginning of the game, you are giving the host a prior probability of the doors having a goat behind them.
But when you change your selection after Monty has opened a door that has a goat, then you give him a prior probability of the doors not having a goat behind them. Hence, you double the probability of winning by switching.
Variations
Monty Hall is the host of a game show. He stands before three closed doors, each of which conceals a different prize. You pick one door, hoping to win the prize behind it.
But then, Monty carefully opens a door that doesn’t contain the prize. He reveals a goat, and then lets you switch to another door.
Then, he shows you that there are 8 of the other 9 doors that also have goats behind them. But he doesn’t reveal which ones have the goats behind them, so you can’t tell which one you should choose. So you pick option B.
A number of variations on the Monty Hall problem have been proposed. Most of them are mathematically equivalent, although some are less popular.
First, a common solution of the problem is to assume that the winner is determined by mixed strategy equilibria. However, some studies suggest that it is not necessary to assume this. Instead, a simple game can be reduced to a single subgame perfect equilibrium if negative reciprocity is assumed.
For example, a variant that assumes that the host prefers not to give away the prize reduces the game to a situation in which the player wins by switching from her original choice. In this case, the probability that she chooses the correct door is equal to 2/3 (see Fig. 3b).
Alternatively, some researchers have suggested a variant in which the winner is determined by a conditional probability. This is a useful approach because it gives more attention to the perceived risk of switching.
Some people may prefer to stick with their initial choice because of a fear of making a mistake or not knowing the odds. Others may believe that it is more risky to switch, and these individuals might be right.
Odds of winning
The Monty Hall problem is a classic example of the fundamental flaws in our ability to weigh up probabilities. When presented with a situation in which we have to pick one good outcome against two bad ones, most people cannot recognise implied probability and therefore do not make a decision that is likely to produce an advantage.
The odds of winning are roughly half if you stick to your original choice, and are around 2/3 if you switch. It is counterintuitive, but it’s true.
Initially, Monty opens a door that has a goat behind it (this is why you have to choose a door), and you decide whether to stay or switch to the other closed door. If you stick with your original choice, you will win for scenarios 1, but lose for the other 2.
But if you switch, there’s a good chance Monty will open a door that has a car behind it. This is because you’ve now filtered your choices, curated by Monty Hall himself.
This is a much better strategy than sticking with your original choice. So why do so many people refuse to believe that it’s true?
Perhaps they think that the problem is a bit too simple. Or maybe they don’t understand the basic conditions of conditional probability.
The most likely explanation is that the’standard’ host strategy is not the right strategy to follow in this scenario. Some critics think that the ‘blind’ host strategy is the best way to play this game. But if you want to get the most out of the situation, it’s always a good idea to know what the right strategy is. If you do, you’ll be able to pick the best option in most cases.
