The most intuitively easy bet to understand is where two people put in the same amount of money on an event, where you either double your money or lose it.
This is typically for events with around a 50% chance of happening, like a coin toss.
Let’s say we have two people: Andrew and Bobby. They want to bet on a coin toss, also they are friends, so they want it to be fair.
Both of them are putting in $100, Andrew on heads, and Bobby on tails. If heads, Andrew will double his money winning $100 from Bobby. If tails, Bobby will double his money winning $100 from Andrew.
This implies odds of 2 for both of them which correlates well with the true probability of a coin toss, which is 50% for both heads and tails.
In practice, people rarely bet on coin tosses or games where the odds are 2 on both sides of the bet. So, let’s use a different example next before we explain how it relates to sports betting.
Andrew is really good at hitting the crossbar, so he wants to bet with Bobby on whether he can hit the crossbar or not.
Andrew can hit the crossbar often, 4 out of 5 times, or 80% of the time. This means that he misses 1 out of 5 shots, or 20% of the shots he takes.
Since Andrew hits more often than 50%, it would be unfair to Bobby if they both went in with $100 where the winner takes all.
For this to be fair, they need to adjust their stake sizes. For them to find the correct stake sizes they need to find the correct odds, which reflects the probability.
To get the odds from the probability, we use the inverse (1/(probability)) and the odds of Rob hitting the crossbar would be:
1/(4/5) = 1.25.
While the odds of him missing would be:
1/(1/5) = 5.
If you are wondering why the odds equals the inverse of the probability of the event, be sure to check this article out.
Andrew asks Bobby what odds he would give him if he were to bet $100. Bobby knows his stuff so he gives Andrew the odds of 1.25.
This means that Andrew would bet $100 and has the potential profit of $25, while Bobby would bet $25 with the potential profit of $100.
The reason to adjusting the stake sizes is so it would reflect the odds, which is similar to the underlying probability as we explained in the article about odds.
To clarify, odds is just a way of adjusting stake sizes in a bet between two parties to reflect the underlying probability.
In sports betting, it is important to understand that there is always two sides of a bet. And because people rarely bet on coin tosses, or events with the exact same probability, the odds are usually not the same for both sides of the bet.
The two sides of the bet are called backing and laying. Andrew is backing himself to hit the crossbar, while Bobby is laying the bet that Andrew will miss the crossbar.
If you have ever bet on a bookmaker’s site, you would be backing different outcomes like a home win, draw or away win.
In these cases, the bookmaker would always be laying bets against the bet you are backing. For clarity, laying bets means to bet on any event not to happen.
Laying bets with two outcomes is easy to understand, as laying one side of the bet means backing the other outcome.
The difficulty often arises when we have 3 or more outcomes. If we use football as an example, the usual thing to bet on is a full-time match winner. This consists of three outcomes: home win, draw or away win.
In this case;
- Laying a home win would mean backing a draw and away win.
- Laying a draw would mean backing a home win and away win.
- Laying an away win would mean a backing home win and draw.
NOTE: More advanced readers would also notice that instead of backing a home win and draw, one could place an Asian handicap (AHC) +0.5 on the home team.
If you are unfamiliar with AHC bets, this article explains what an Asian Handicap Bet is and how it works to bet on them.
Take some time and think of how this applies to a bookmaker and what really happens when you bet $100 on Liverpool to win at home with 1.2 odds?
This would mean that the bookmaker thinks that it is (1/1.2 = 0.8333 = 83.33%) chance that Liverpool would win or a chance of (1-0.8333 = 0.166666 = 16.66%) that Liverpool were to not win.
In this case, the bookmaker bets $20 on a draw and away win with the odds of (1/0.16666 = 6) against your $100 on the home win!
If this is hard to understand think back to Andrew and Bobby’s crossbar challenge.
Thinking this through, the probability against a home win should be the same as the probability for away win and draw.
The same goes for the odds. Let us start by showing you an example with the total probability equalling 1.
Let us see how this works with a random football match with 3 outcomes. We have the corresponding odds and probability like this:
The probability for not H is 1 - (1/2.5) = 1 – 0.4 = 0.6
The probability for U and B is 1/4 + 1/2.86 = 0.25 + 0.35 = 0.6
We now know that there are two sides to every bet. Now we need to separate practice from theory and look at how it works when you bet against a bookmaker.
Let us start with the coin toss. As we can see the odds are balanced with the probability since the probability for both heads and tails are 1/2 and the odds are 1/(1/2) = 2. The balance is shown with the colour blue.
If we go from a coin toss to a crossbar challenge where Andrew is hitting the ball, the underlying probability changes.
If the odds do not change, we would have a positive value bet on one side of the bet.
We would have a positive value on the backing side, while there would be a negative value on the laying side.
In this picture, green corresponds with a positive value, while red means a negative value.
The true odds for the event would be 1.25 for a hit and 5 for a miss, while we would get the odds of 2 for either outcome.
There would be positive value betting on Andrew hitting with 2 in odds because the odds are higher than what the underlying probability suggests.
Here we have the balanced-out odds of the crossbar challenge between Andrew and Bobby.
As we can see, the odds given are the same as the true odds from the underlying probability.
This would be fair odds and would essentially mean that Andrew and Bobby would break even in the long term.
These examples are as applicable to real sports events as they are to a crossbar challenge, so let us switch from a crossbar challenge (hit/miss) to a random football game (home win/not home win) using the same odds.
In reality, putting up odds equalling the underlying probability for every bet can be challenging.
So, let us see what happens if the odds are slightly wrong compared to the probability. Here the odds are adjusted to 1,33 and 4, while the probability still suggests odds of 1,25 and 5.
This will give you positive value if you were to bet on a home win, while laying a home win would give you negative value.
In this example, we see that the positive value and negative value switch places, making laying the bet the preferred choice.
As we can see from these two examples, if a bookmaker would operate with odds that reflects a total probability of 1, they would need to hit the exact probability every time.
Or, they would risk giving away an edge, it just depends on which side of the bet the edge is on.
So, what do bookmakers do to mitigate this risk factor? Well, the answer is simple; they make the stick bigger.
This picture shows the difference between the true probability and the corresponding odds, as well as how a bookmaker operates.
They basically calculate their odds from a total probability of more than what is theoretically possible.
This will give them more wiggle room for the odds which will make it easier to put up odds with a positive edge for them.
In other words, they use the margin to protect themselves from the uncertainty that exists when trying to predict the true odds.
Essentially, this will overvalue the probability, while undervaluing the odds consistently over time.
But, how can we find value, when they are always providing smaller odds than what is probable? Well, we find it when the blue double arrow goes outside the yellow area on the picture.
Then the odds would be either higher than 5 for laying a home win or higher than 1.25 for backing a home win.
In this picture we clearly see that in order to get an overvalued bet, in the case of a home win, the bookmaker would need to overestimate the probability of the contrary by a lot.
They still do this, and when we find these kinds of bets we would have an edge over the bookie.
This is what Trademate does for you, finding edges on thousands of events. To understand how this works, check out this article.
It is really important to understand that there are two sides to every bet and every bet should be looked at as a tug of war. The one who gets the better value than the true probability wins in the long term, so be sure to be on the right side of the bet. Trademate provides you with all the right tools to do this.
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