Which is correct: He is playing the cricket or He is playing cricket?
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The quick answer
You can never say He is playing the cricket. One easy way to think of this is that 'cricket' is the name of the sport, and names in English don't combine with the definite article unless modified in some way.
The detailed answer: sport names as mass nouns
The names of sports and games typically don't appear with articles. Regular common nouns in English can't appear without an article unless they are plural, or abstract/mass nouns.
We can't say (1) where 'ball' has no article, but you can say (2) where 'balls' (plural) and 'water' (mass) have no article, and (3) where the abstract/mass noun 'skill' appears without an article. And of course, proper nouns like John usually appear without an article as in (4).
- *I threw ball.
- I threw water/balls.
- He showed skill at throwing.
- I saw John.
So from this we can conclude that the names of sports must either be proper nouns (despite not being capitalized in spelling) or abstract/mass nouns. It's actually quite hard to tease these two hypotheses apart in fact.
One argument in favour of them being abstract/mass nouns is that you can combine them with typical mass selecting determiners, which you can't do with proper nouns. So you can say (5) and (6).
- Most cricket is played in the summer.
- We played some cricket today.
But you can't say
- *Most John is around in the summer.
*We saw some John today.
(Note that these are not the same as the partitive construction with of as in We didn't see much of John.)
"He is playing cricket" is correct.
"The" is a definite article, which means you use it if a noun needs to be specified in a certain way, such as "He is playing the game of cricket".
In casual conversation where there is no need to specify anything in particular, you would simply say "He is playing cricket".