Sparse neural networks have been widely applied to reduce the computational demands of training and deploying over-parameterized deep neural networks. For inference acceleration, methods that discover a sparse network from a pre-trained dense network (dense-to-sparse training) work effectively. Recently, dynamic sparse training (DST) has been proposed to train sparse neural networks without pre-training a dense model (sparse-to-sparse training), so that the training process can also be accelerated. However, previous sparse-to-sparse methods mainly focus on Multilayer Perceptron Networks (MLPs) and Convolutional Neural Networks (CNNs), failing to match the performance of dense-to-sparse methods in the Recurrent Neural Networks (RNNs) setting. In this paper, we propose an approach to train intrinsically sparse RNNs with a fixed parameter count in one single run, without compromising performance. During training, we allow RNN layers to have a non-uniform redistribution across cell gates for better regularization. Further, we propose SNT-ASGD, a novel variant of the averaged stochastic gradient optimizer, which significantly improves the performance of all sparse training methods for RNNs. Using these strategies, we achieve state-of-the-art sparse training results, better than the dense-to-sparse methods, with various types of RNNs on Penn TreeBank and Wikitext-2 datasets. Our codes are available at https://github.com/Shiweiliuiiiiiii/Selfish-RNN.