What do betting odds like 5/1 or 3.50 actually mean?
Shakespeare already wrote "ten to one" in the 1500s, long before anyone had a theory of probability to back it up.
Betting odds are a price tag attached to a chance. They tell you two things at once: how much you collect if you win, and, read backwards, how likely the thinks the result is.
In the British style, odds are fractional. "5/1" (said "five to one") means a net profit of 5 for every 1 you , and you also get your stake back. In gambling, odds are often given as the ratio of the possible net profit to the possible net loss, and that is exactly what are. The decimal style, popular in Europe and online, folds the stake into the number. A bet of 2 at "3 to 2" pays out 3 + 2 = 5, which is called "5 for 2", so are simply the total return per 1 staked. That makes 5/1 the same as 6.00, and 3/2 the same as 2.50. American "" odds use a third style: +X means a wager pays X to 100.
Try it
What a stake returns at different decimal odds
y = 4x + 0
Challenge · Find the decimal odds at which a stake of 50 returns 125 in total, then work out the implied probability: 1 divided by those odds.
Odds also hide a probability. If a bet pays "X for Y", it is fair when the true chance is Y divided by X. So of 2.50 correspond to a chance of 1 divided by 2.5, which is 40%, and evens (1-1) corresponds to 50%. This is called the . It is only what the odds suggest, not a fact about the world.
Beware two words that sound alike. "Odds" compare the outcomes for with the outcomes against, while "chances" compare the outcomes for with all outcomes. The odds of a randomly chosen day being a weekend are 2 to 5, but the chances are 2 in 7. People mix the two all the time.
The language is old. In the sixteenth century, well before probability theory existed, people already said "ten to one" about risks they only felt, and Shakespeare used it too.
Quiz me
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Recap
Odds compare outcomes for and against, chances compare outcomes for against all, and a price implies a probability.
💡 A trick to remember it · Flip the price upside down and the chance falls out: 2.5 flipped is 1 over 2.5, a two-in-five shot.
Surprising fact · Phrases like 'ten to one' were used in the sixteenth century, long before probability theory.
Connects to
- 📒 How do bookmakers set odds, and what is the overround?
- 🔮 What is a prediction market, and how does a price become a probability?
- 🎲 Did a gambling doctor write the first book on the odds of dice?
- 🎰 Why did gamblers lose millions betting against 26 blacks in a row?
- 🎲 How did an unfinished game of chance give birth to probability theory?
Sources (2)
No source, no claim. Every fact in this lesson (13 claims) cites at least one of these.