It depends on who you ask. Remember that because no matter how well someone explains odds and probabilities, it always depends on who you ask.
Another way to put this question into context is to look at the context of what people tell you.
If you consult a thesaurus the chances are pretty good that it will list odds and probability as synonyms. The same is true for chances and probabilities.
So, yes, it is fair and accurate to say that odds, probability, and chances all refer to the same thing. But only in certain contexts.
Even gambling games may use the words slightly differently. I wouldn’t stake any bar bets on the explanations that follow because you’re more likely to start a brawl than win a bet.
Remember that no matter how right you think you someone else will be just as right as you.
1 – There are Probable Odds and Payout Odds
I’ve rarely heard anyone say “probable odds” but usually when someone asks “what are the odds” they mean “what are the probabilities (or chances).”
On the other hand, I like to use the game of roulette to illustrate the difference between payout odds and probability. In single-zero roulette you have a 1-in-37 chance of picking the right number where the ball lands on its next ride on the wheel.
And yet the best payout odds are 35-to-1. Either the casino can’t do math properly or the game ensures that – over time – the house retains some small percentage of the players’ wagers. And that’s how the house edge works in every gambling game.
2 – Probability Is a Distribution, Not a Prediction
Gambling books and articles quote statistics about the probabilities of games such as poker. The better books and articles include the standard disclaimer that the probabilities don’t guarantee anything. It’s a lot like reading a stock market prospectus disclaimer: “past performance doesn’t guarantee future results.”
Where do these probability estimates come from?
In some cases it’s a simple matter of calculating the probability distribution. There are 52 cards in a standard deck and only one Jack of Diamonds. The chance or probability or odds of drawing the Jack of Diamonds from any standard 52-card deck is 1-in-52.
The more complicated the game the harder it becomes to calculated the probabilities. So some people have turned to using computer simulations to estimate the probabilities. So they’ll run millions or billions of simulations and compute the average result.
Does it matter if a computed probability is based on simulations or precise calculations?
Probably not in most cases. Neither type of probability distribution guarantees you success – so they’re not predictions.
3 – Is Random Chance the Same as Probability?
A probability distribution is a computed value or set of values. It’s based either on the rules or conditions of a game or a set of scores.
But random chance is by very definition unpredictable. Some people say random chance is an act of nature (or an act of God). You can’t predict random chance.
Probability theory cannot predict the future but it points you to where random chance is most likely to produce the result you want.
When people say “this system has a 98% accuracy rate” they mean that it has failed 2% of the time in measured results. Random chance could lead to failures in the next 10 trials.
Is that luck or something else?
Random chance is always with us and it may be based on something mundane like the wear and tear on physical parts in an engine. But how much wear and tear the engine experiences depends on unpredictable things, like how much dirt gets into the engine, how often the engine is overheated, and more.
Probability theory cannot point you in the right direction when a lot of outside factors influence random chance. Any system with an expected 98% failure rate may experience 100% failure in conditions no one tested for.
In gambling, random chance leads to a roulette wheel landing on red 32 times in a row (in 1943) and on the number ten 6 times in a row (in 1959). These are both highly probable events but thanks to random chance they can happen.
In this example random chance is not the same as a probability.
4 – We Estimate the Likelihood of Random Events Happening
We use probability to estimate how likely an unpredictable event is to happen. A probability distribution is measured in the infinite range of values between 0 (no chance whatsoever the event will happen) and 1 (it will always happen every time).
There is nothing to gamble on if all the players know in advance that an event will (probability of 1) or will not (probability of 0) happen.
If everyone is ignorant of whether an event will happen – as is the case in honest gambling games – then what everyone wants is a best guess at what is most likely to happen.
The payout odds are set based on the estimate of what is most likely to happen – the calculated probability. And this is probably why so many people use odds and probability to refer to the same thing. They are closely connected to each other and we are accustomated to using either word to refer to the reward or the risk.
5 – The Words Can Be Ranked by Use
Although odds is used to refer to both the payout and the expectation for the outcome of a wager, neither chance nor probability are. It follows that odds is the most flexible or ambiguous of these words.
The odds of something happening are the same as the probability that it will happen.
When people speak of the chance of something happening they mean the expected probability that it will happen. But when speaking of chance in itself they mean an unpredictable thing.
Of the three words probability seems to have the least use, but sometimes people speak of an indefinite probability when they really mean an unpredictable probability. That is similar to chance.
Chance may be personified. “We’ll leave that to chance” has been used in literature and drama. This may be an echo of when people preyed to gods of chance.
The only common variation on probability is its plural form, probabilities, when people say “think of the probabilities” – implying there are several possible outcomes.
6 – Probability and Chance are Sometimes Connected with Possibility
If there is a chance or probability of something happen then that means there is a possibility. The possibility is a thing itself.
It’s tempting to say possibilities don’t pay so this word would never be confused with payout odds. But then when thinking of future potential gain people sometimes say, “think of the possibilities”. These could be probable outcomes or potential gains and rewards.
Of all these words probability is used to set a precision of expectation no matter how unreliable that may be. And probability is also used to compare the likelihood of two or more possible outcomes. Odds is more often used to compare the value of payouts.
7 – Most People Provide Sufficient Context
Honestly, I’ve never seen anyone use odds in two different ways in the same conversation without explaining the difference between the expectation of a probable outcome and the precise payment for a possible outcome.
While these words may seem confusing given the different ways they are all used, it’s generally easy to understand what they refer to.
If you are confused about anything it is about where and when it is appropriate to use each word. It’s almost always okay to use them how you wish as long as you provide clear supporting context about what you are referring to.
People ask how these words are used because they are used so loosely. Writers who talk about casino odds and probabilities know what they have in mind. I’ve rarely read a book or article that didn’t provide clear context.
I think the confusion people feel arises from the myriad ways writers use the words, even though the readers probably understand what each writer means. If you are asking whether there is a right or correct use for each word, that answer is it depends.