The ESP Game (Ahn and Dabbish 2004) was designed to harvest human intelligence to assign labels to images – a task which is still difficult for even the most advanced systems in image processing. However, the ESP Game as it is currently implemented encourages players to assign “obvious” labels, which are most likely to lead to an agreement with the partner. But these labels can often be deduced from the labels already present using an appropriate language model and such labels therefore add only little information to the system. We present a language model which, given enough instances of labeled images as training data, can assign probabilities to the next label to be added. This model is then used in a program, which plays the ESP game without looking at the image. Even without any understanding of the actual image, the program manages to agree with the randomly assigned human partner on a label for 69% of all images, and for 81% of images which have at least one “off-limits” term assigned to them. We then show how, given any generative probabilistic model, the scoring system for the ESP game can be redesigned to encourage users to add less predictable labels, thereby leading to a collection of informative, high entropy tag sets. Finally, we discuss a number of other possible redesign options to improve the quality of the collected labels.