About Monty Hall Problem
The Monty Hall problem is the best example of showing how when we are presented with a simple challenge of making a choosing one favourable outcome against couple of unfavourable ones, we display our utter inability of correctly weighing up our success chances.
It’s a pretty crucial problem for sports bettors, as in simple terms, a sports bettor can never make any considerable money in the long run if he cannot successfully recognise the implied probability of different events and if the odds provided by a bookmaker hold value or not.
About the Monty Hall problem
There’s a brand-new car behind one of the three doors that you have to select one from, and there’s a goat present behind the other two. Your challenge is to make a correct guess about the door that has a car behind it, in order to win the vehicle, however, you are equipped with no prior knowledge enabling you to distinguish between the doors.
Once you select a door (and it’s not opened yet), one of the other two doors will be opened up to reveal at least one goat. You are now presented with one more option – Would you like to change the door that you had originally selected, or would you stick with that choice?
The Monty Hall problem got its name from the name of the person who used to host the popular 60s and 70s US show titled ‘Let’s Make a Deal.’ At core the Monty Hall Problem is basically a simple mathematical puzzle that effectively shows how people face difficulties when they’re presented with seemingly straightforward choices.
Using such a simple and cleverly posed teaser, the ‘Let’s Make a Deal’ show used to demonstrate how an average individual is capable of demonstrating counterintuitive behaviour whenever he is faced with probability puzzles; and the same holds true in case of casual sports bettors. When the same problem was put up in the Parade magazine, as many as 10,000 readers submitted complaints that the published answer was incorrect, and this included a large number of maths professors.
“66.6% is the exact probability of a car lying behind the remaining door”
The solution to the Monty Hall problem
The Monty Hall Problem’s solution is pretty simple – Always opt to switch the doors. Once the first door has been opened, it is guaranteed that the car would be behind the remaining two closed doors (even though there is no way of knowing which one that door exactly is). Majority of the show’s contestants intuitively believe that there is no advantage in switching the doors, presuming that every door has the same 1/3 probability of having a car behind it.
But that is incorrect. Your chances of winning a car actually get doubled if you opt to switch. Although it’s true that every door originally has a 33.3% chance of having a car behind it, once the first goat has been revealed, the probability of a car lying behind the last door rises up to an impressive 66.6%.
You can easily calculate these probabilities by thinking of picking between the original door (with 33.3% probability) and the sum of the probabilities of the two doors other than yours (33.3% + 33.3%). The reason for this is that after you have selected your door, the remaining two doors get paired up together, and the combined chance of a car behind any of those two doors is 66.6%. Once any one of those two doors has been removed from the equation, the combined chances still remain 66.6%, but now with the possibility of the car being behind the leftover door.
Carry out some search on the Internet and you may find several Monty Hall simulators to test this puzzle yourself!
Understanding when the odds are stacked against you!
The Monty Hall Problem very cleverly shows how you can easily fall into the trap of mistaking nonrandom information to be random in nature. This is further proved by the popular UK TV show titled ‘Deal No Deal’ as well. The show involves 26 unopened boxes that consist of different cash amounts - paying a sort of homage to the erstwhile ‘Let’s Make a Deal’ show by exploiting the weak grasp of the general public when it comes to the matters of probability (just like ‘Let’s Make a Deal’). It is based on the theory that contestants normally fail to comprehend when they’re in a statistically weaker or stronger position, acting solely based on their false gut feelings related to their chances of success.
All such notions are an integral part of the commonly made mistakes in the field of sports betting and gambling, wherein sports bettors and gamblers regularly act against their best interests, specifically in situations when they are puzzled by clever marketing methods, or are urged to indulge in sports betting simply as a lifestyle option instead of something which is to do with mathematics.
Please keep in mind that sports betting requires the basic skill of understanding if the offered odds by a bookmaker on a certain event represent the actual statistical probability of occurrence of that event or not. Regardless of whether it’s a game show, online sports betting or lottery play on television, you cannot book consistent profits if you don’t understand how to find and benefit from valuable bets.