Is there any rule that says you can't play with two rackets in badminton?
That is, one racket in each hand, so for example you don't have to hit a backhand; you can just do forehands.
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Unlike International Tennis Federation (ITF) which specifically bans using more than one racket under the rule 4. THE RACKET, Case 5:
Is a player allowed to use more than one racket at any time during play?
Badminton World Federation (BWF) laws don't state anything specific on using more than one racket. However, like ITF, they use the singular form of the noun racket in the laws, based on which we can safely assume using more than one racket is prohibited.
One more thing to consider is would it really help to use two rackets? If you play with two rockets, it will be more difficult to serve effectively (you need to note there is a rule on Service, too) and it might injure your hands when you try to dive to receive a shuttle.
I'm not an expert but can use either hand effectively. The difficulty I see, is in anticipating a return shot your stance will be set, with one raised racket.
From that point you are restricted in what you can deploy in a fraction of a second. If your body is committed to one racket before your opponent smashes, that's your best option. I have occasionally switched hands in play, more to give my predominant arm a rest than be more competitive.
The other difficulty of having a racket in your free hand is it will get in the way all the time, as that arm is used extensively for counterbalancing both for balance and strength.
There's also no real argument for doing forehand shots all the time, back-hands can be equally powerful with practice.
Not specifically but you can deduce the answer is you are allowed 1 racket per person.
4.3 The racket:
[The racket] shall be free of attached objects and protrusions, other than those used solely and specifically to limit or prevent wear and tear, or vibration, or to distribute weight, or to secure the handle by cord to the player's hand, and which are reasonable in size and placement for such purposes
The International Badminton Federation shall rule on any question of whether any racket, shuttle or equipment or any prototype used in the playing of Badminton complies with the specifications. Such ruling may be undertaken on the Federation's initiative or on application by any party with a bona fide interest, including any player, technical official, equipment manufacturer or Member Association or member thereof.
I imagine the Federation would rule this illegal.