Design dice betting strategy under time limit

You have T = 10 minutes and initial bankroll B = $1,000 to play a repeated betting game with a fair six‑sided die. Before each roll, you may stake any fraction of your current bankroll on exactly one offered wager: (A) “roll is 6” pays 6:1, (B) “roll is 5 or 6” pays 2.2:1, or (C) “roll is odd” pays 1.1:1. Rolls take 3 seconds and outcomes are independent. Unlimited number of bets within the time limit. a) Which wager (s) have positive expected value? Show EV calculations. b) For your chosen wager, compute the optimal bet fraction to maximize expected log wealth (Kelly) and propose a more conservative fraction to keep the probability of a 50% drawdown below 5%. c) Outline a practical staking policy for the time‑limited setting and explain when you would stop betting. d) After n = 60 “odd” bets you observed k = 36 wins. Provide a fast 95% confidence interval for p and interpret it. e) Discuss the return–variance trade‑offs and how your allocation changes if rolls slow down or T is shorter.