Collocations for odds - noun

considerable, great, impossible, incredible, insurmountable, overwhelming, terrible
She struggled against terrible odds to overcome her illness.

good
high, low
long, short (esp. BrE)
Sometimes an outsider will win at long odds, but not often.
The bookmakers are offering only short odds on the favourite. (BrE)

offer, quote
lay
I'll lay odds we never see him again.

reduce, shorten
improve, increase
beat, defy, overcome
She defied the odds to beat the clear favourite/favorite.

calculate

fall, go down, lengthen (esp. BrE)
go up, increase, shorten (esp. BrE)
favour/favor sb

against the odds
The movie is a heart-warming tale of triumph against the odds.

odds against
The odds against making a profit in this business are huge.

odds of
They were offering odds of ten to one.

odds on
The odds on the outsider were 100–1.

against all odds, against all the odds
Against all the odds, we managed to get through to the final.

face impossible odds, face insurmountable odds
the odds are stacked against sb, the odds are stacked in favour/favor of sb
He will try hard to win, although he knows the odds are stacked against him.