Both are correct. The gerund (playing) is more common in British English, while the infinitive ( to play) is more common in American English. For people who use both constructions, there can be a subtle difference in meaning.

From the Cambridge dictionay: There is a very small difference in meaning between the two forms. The -ing form emphasises the action or experience. e.g.: I like making jam The to-infinitive gives more emphasis to the results of the action or event. e.g.: I like to make jam every year We often use the -ing form to suggest enjoyment (or lack of it), and the to-infinitive form to express habits or preferences. The -ing form is more common than the to-infinitive form after hate and love.

As far as I know, both are equally correct!