We present an approach for generating playable games that blend a given set of games in a desired combination using deep generative latent variable models. We refer to this approach as latent combinational game design -- latent since we use learned latent representations to perform blending, combinational since game blending is a combinational creativity process and game design since the approach generates novel, playable games. We use Gaussian Mixture Variational Autoencoders (GMVAEs), which use a mixture of Gaussians to model the VAE latent space. Through supervised training, each component learns to encode levels from one game and lets us define new, blended games as linear combinations of these learned components. This enables generating new games that blend the input games as well as control the relative proportions of each game in the blend. We also extend prior work using conditional VAEs to perform blending and compare against the GMVAE. Our results show that both models can generate playable blended games that blend the input games in the desired proportions.