Learn Russian: У нас мало шансов, но мы хотим играть. - We have few chances, but we want to play.

Because of the word мало (few/little). Words that express a quantity like сколько (how many), много (a lot), and мало require the noun following them to be in the Genitive case. Since "chances" is plural, we use the Genitive plural form шансов.

How do I know to add -ов to make the Genitive plural of шанс?

Шанс is a masculine noun that ends in a hard consonant (the letter с). For most regular masculine nouns ending in a hard consonant, the Genitive plural is formed by simply adding -ов. Another common example is студент, which becomes студентов.

The English translation says "We have...", so why doesn't the Russian sentence start with Мы?

To say "someone has something" in Russian, you usually use the structure У + [Genitive pronoun]. У нас literally means "by us" or "in our possession". While the literal phrase мы имеем (we have) exists, it is rarely used for everyday situations. У нас мало шансов is the most natural way to say this.

Why does хотим (we want) end in -им if its infinitive хотеть ends in -еть?