Just because math scares you or you hate math doesn’t mean you can’t make a ton of money sports investing. Let me debunk a common math mistake made by many who bet on sports and show you a way to double your chances of being right.
DON’T RUN AWAY YET!!!! You knew this moment would come but relax and take a breath. I am going to make this really simple for you to grasp and understand. When we improve our statistical probability, we make more money. Simple, but scary, I know. However, instead of just relying on one’s own ‘gut feeling’ or ‘intuition’, what if there was a mathematical approach one could take to better our odds and make more money sports investing?
Basic Probability Theory Examples
It has long been understood that improving one’s odds can be increased by a better understanding of mathematics. Probability refers to the likelihood of something happening.
Here are some simple examples of probability mathematics:
- If you flip a standard coin, there is a 50% (or ½) chance that it will come up heads. There is also a 50% (or ½) chance that it will come u tails.
- If you roll a six-sided single die, the probability of rolling a 3 is 16.67% (or 1/6^{th})
- If I put 5 M&M’s (yum) in a bag, 4 being red M&M’s and 1 being a blue M&M, the probability or chance of your pulling out a red M&M from the bag is 80%.
Ok, simple enough so far? So if we were going to ‘bet’ or invest on the outcome of one of those examples it would only be profitable for us to do it if we were getting paid a fair price relative to the wager.
In our coin example, if I offered to pay you $1.00 every time you get a heads and you pay me $1.00 every time you get a tails, there is no point in playing. Over the long run, you will end up at break even.
Now, if I offer you $1.10 for every time you get a heads but you only have to pay me $1.00 when you get a tails, you should make this wager over and over and over again. You are essentially being the ‘house’ or casino and will make an absolute fortune over the long run.
Now we are going to explore a famous mind puzzle based upon the theory of probability to illustrate how one can tip the odds in your favor. It does require that we consider some challenging questions. Don’t panic, we will get through this together. Passengers, please make sure your seatbelts are fastened and place your tray tables into their upright and locked positions…
The Monty Hall Problem
In 1975 Steve Selvin, a professor and biostatistician at UC Berkley wrote a letter to Marilyn Vos Savant at Parade magazine posing a singular probability problem based on the popular 1970’s game show ‘Let’s Make a Deal’. The answer that Vos Savant gave in the article set off a firestorm of controversy among Mathematicians, which resulted in it being coined The Monty Hall Problem.
Here is the problem:
You are at the game show, and given a choice of selecting one of three doors. Behind one door is a brand new automobile, and behind the other two doors are goats. Let us presume you chose door #1. Upon choosing your door, Monty Hall adds suspense to the contest by opening door #3, which reveals a goat. He then asks you ‘would you like to switch doors, or stay with the door you have chosen?’ What should you choose?
Vos Savant’s response to Selvin was that the better choice would be to switch doors, as it increased the probability of success to 2/3rds as opposed to 1/3^{rd}.
On the surface it may seem that if we eliminate one of the three doors available, the chances have improved to 50/50 that one of the remaining doors has the car. Therefore, either choice is mathematically equal and the conclusion being that there is a 1 out of 2 probability of choosing correctly.
Lets dig a little deeper and see why that is in fact not correct.
How do our odds improve if we switch?
Lets examine the problem from a new perspective with this diagram so that you can see the probability theory in action:
Door #1 | Door #2 | Door #3 | Outcome | |
Game 1 | Auto | Goat | Goat | Switch & You Lose |
Game 2 | Goat | Auto | Goat | Switch & You Win |
Game 3 | Goat | Goat | Auto | Switch & You Win |
In the above example, let us assume you played three games in a row. Each time you chose Door#1 as your door. For purposes of demonstrating the outcome, there are three possible combinations for the doors to be in. The crossed out line indicates the door Monty has opened to reveal the goat, thus eliminating that door. The one thing that is the same in each example is that we know Monty has opened a door revealing a goat, and not the car. So in each example, we will know the location of one of the 2 goats.
In the first game shown above, if we chose door #1 and switched we would lose. We picked door #1 blindly (and it had the car!!!), and Monty shows us that there is a goat behind Door #3, so we are left deciding between our door, Door #1 and Door #2. If we decide to blindly switch our Door #1 for Door #2 the outcome would be a loss.
However, in game #2 & game #3, if we switched we would have won. We would have selected Door #1 (Goat) and then Monty would reveal the 2^{nd} goat behind either Door #2 or Door #3. In both cases, if we switch our Door #1 for the other remaining closed door, we win a car!
This example shows how our chances double by switching doors. If we stay with the one we selected, we only win the car 1 out of 3 times (33% chance of winning). If we switch to the unknown car, we win 2 out of 3 times (66% chance of winning).
What if we stay with our original door?
Let’s examine outcome in reverse. What if in the same scenario above, we chose to remain with Door #1? What would our chances look like then?
Door #1 | Door #2 | Door #3 | Outcome | |
Game 1 | Auto | Goat | Goat | Stay & You Win |
Game 2 | Goat | Auto | Goat | Stay & You Lose |
Game 3 | Goat | Goat | Auto | Stay & You Lose |
In this second illustration, we can see that staying only lets us win 1 out of 3 times. What we see is that it is designed to make the contestant believe they are getting a 50/50 chance with 2 doors left and that either choice is a good one. However, our odds can actually improve from 33% at the beginning to 66% once one door is revealed.
There is course the random factor to contemplate regarding Monty’s motivation in revealing what was behind door #3. Was he tipping his hand that Door #2 was not opened because it contained the car, or was he using a diversionary tactic to draw the contestant away from Door #1? Therefore the introduction of the human element into the equation highlights a new level of probability to consider.
We will save this for a future discussion but the importance here is that random information is not always random and its essential to use the data at our disposal to give ourselves the highest probability of success.
Understanding the Lesson
In the Monty Hall puzzle, we see that had the host not clued the contestant in to what was behind door #3, then the odds would have remained at 33% for each door. By revealing one of the goats behind door #3, the host improves our chances of selecting the right door because we now know that door #2 has a 66% chance of having the automobile instead of the goat. Our original choice of Door #1 has only a 33% chance of having the car, even when we remove one of the non-selected doors.
In the world of sports betting or sports investing, we understand that the odds offered by sportsbooks are not just simply the chances of one team winning versus another. They are designed to mislead us into taking the ‘less-likely’ outcome so the book can make a profit.
Knowing this allows us to greatly improve our chances of picking the correct outcome of an event. It is critical that we learn to adjust our thinking and go where the data points us, as opposed to where our heart directs us.
With all sports betting and sports investing, there is always an element of chance. We can improve our odds with gaining knowledge of probability theory, and a little head spinning mathematics. But don’t worry if math isn’t your thing or if this feels overwhelming…. That’s what you have me for 😉
This is an awesome post. Probability theory is super interesting and I look forward to further post on the subject.
Math does make my head hurt…but I’ll take it if I can win $$$
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