A Bit About Betting

I got to thinking about the way that the odds of a horse winning are expressed in betting circles and I sought the help of Gemini 2.0 Flash Experimental to explain it. Here is what it came up with.

Question: If probability of an event happening is given as 2 to 1 on, what does that mean?

When someone says the probability of an event is "2 to 1 on," they're expressing odds in fractional form, specifically "odds on." This means the event is considered more likely to happen than not.   

Here's how to break it down:

2 to 1: This represents the ratio of the likelihood of the event happening versus it not happening. In this case, it means for every 2 times the event is expected to occur, it is expected not to occur 1 time.

"On": This indicates that the first number in the ratio (2 in this case) is larger than the second number (1). This signifies that the event is favored or has a greater than 50% chance of happening.

To convert "2 to 1 on" to a probability:

Add the two numbers in the ratio: 2 + 1 = 3

Divide the first number by the total: 2 / 3 = 0.666...

Therefore, "2 to 1 on" translates to approximately a 66.7% probability or two-thirds chance of the event happening.

Example:

If you're told the odds of a horse winning a race are "2 to 1 on," it implies that out of every three similar races, the horse is expected to win two and lose one.

Key takeaway: "Odds on" always indicate a greater than 50% chance of an event occurring, with the specific probability determined by the ratio provided.

I then asked the following question:

Question: What's an example of a bet that isn't odds on?

You're right to ask for clarification! It's important to understand the difference. A bet that isn't "odds on" means the event is considered less likely to happen than not. This is often referred to as "odds against."

Here's how it works:

The ratio: In "odds against," the second number in the ratio is larger than the first. For example, "3 to 1 against" or "5 to 2 against."

Meaning: This signifies that the event is less favored or has a less than 50% chance of happening.

Example:

Let's say the odds of a particular football team winning their next match are "3 to 1 against."

This means that for every 3 times the team is expected not to win, they are expected to win only 1 time.

To convert this to a probability:

Add the two numbers: 3 + 1 = 4

Divide the second number by the total: 1 / 4 = 0.25

So, "3 to 1 against" translates to a 25% probability of the team winning.

Another example:

If the odds of rolling a 6 on a standard six-sided die are "5 to 1 against," this means that for every 5 times you're expected not to roll a 6, you're expected to roll a 6 only once. This aligns with the actual probability of 1/6 (approximately 16.7%).

In summary:

Odds on: The first number in the ratio is larger (e.g., 2 to 1 on). Indicates a greater than 50% chance.

Odds against: The second number in the ratio is larger (e.g., 3 to 1 against).1 Indicates a less than 50% chance.   

Understanding this distinction is crucial for interpreting betting odds and evaluating the likelihood of different outcomes.