How to deal with conditioned based validation in laravel?

I have a situation and unfortunately not sure how to sort it out in proper way. I have below script

$validator = Validator::make(
    $request->all(), 
    [
        'game_id' => 'required|integer'
    ],
    $messages
);

if ($validator->fails()) {    
    $response = $validator->messages();
}else{
    $response = $gameService->setStatus($request);
} 

Now each game has different type, I wanted to add validation on behalf of type. For example if a game is Task Based then I would add validation for time which would be mandatory only for Task based game otherwise it would be an optional for other types.

I have three types of games

1 - level_based 2 - task_based 3 - time_based

In the type table, each game has type.

So is there any way to add validation? I want to do it, inside validation function.

Thank you so much.

via Chebli Mohamed