 In this example, the only option that isn’t dominated is the option in which you do not play the game with God. If you choose that option, you get 2 utiles for sure. If, on the other hand, you choose to play the game and pick integer \(k\), then choosing integer \(k+1\) will be guaranteed to get you more utility: either \(2^{k+1}\) utiles compared with \(2^k\) or \(2 - \frac{1}{2^k}\) utiles compared with \(2 - \frac{1}{2^{k-1}}\). However, the option in which you get 2 utiles for sure seems a lousy option given the other possibilities available. One way to see this is as follows: Take a probability distribution over the two possibilities (i) and (ii) between which God will choose if you choose to play; then, providing it doesn’t assign all probability to God choosing (i), there will be some option you can take if you play the game that has greater expected utility than the option of not playing the game. If  Naive Dominance  is correct, however, not playing the game is the only rational option. This seems to tell against  Naive Dominance.