The most common and most likely answer to this crossword clue is the 11 letter word PROBABILITY
I've seen this crossword clue in The Guardian
P
R
O
B
A
B
I
L
I
T
Y
More clues leading to the result PROBABILITY
Buddy explains!

The straight part
We know that "Odds" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case odds = probability.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
Crossword Answer definitions
PROBABILITY noun- The state of being probable; likelihood.
- An event that is likely to occur.
- The relative likelihood of an event happening.
- A number, between 0 and 1, expressing the precise likelihood of an event happening.