Suppose you place three even-money bets (e.g., red vs. black, or even vs. odd) on a roulette wheel (with no 0 or 00). You use a martingale strategy, starting with a unit bet of $1. What is the expected value of the three bets?

Suppose your car is worth $10,000. Every year, there’s a 1% chance you’ll get into an accident. If you do get into an accident, there’s a 20% chance that your car is totalled, a 30% chance that the repairs cost $5,000, and a 50% chance that the repairs cost $1,000. What is the maximum you should be willing to pay for insurance against accidents?

Design a gambling game. The game should reward players not just for accurate calculations of expected value, but for knowledge of something other topic, like the news game that we discussed in class. For instance, a game might encourage players to bet on where earthquakes will occur, with payouts proportional to the quake magnitude.

Using some portion of the MIT main campus as a game world, draw a simplified map. Write pseudocode for four search strategies for a monster stalking a player: “smart”, “dumb”, “suspenseful”, and “fun”. The smart strategy should use an efficient search mechanism to seek out the player; the dumb strategy should use an efficient (but still sensible) search strategy; and the suspenseful strategy will scare the player. The fun strategy is more open-ended: assume that the monster is not a monster at all, but some other player or object in the game whose goal is something other than stalking.

Choose a game you like and critique its AI. How does it work? Could it be improved? Should it be improved? Discuss some different ways the AI could operate and speculate about how it would impact gameplay.