75% + 1. State the main interpretation of the probability of an event and give an example (Please give a non- circular answer, without using "chances", "likelyhood" etc.). 2. You are dealt big slick AK (or KA). What is the probability that another player has pocket aces, kings queens or big slick (i.e. AA-QQ or AK; single no. for answer)? 3. The game is to flip a fair coin. If you get heads, you win 6 dollars; if tails, you lose 4 dollars. Let the random variable X be your win. Find the expected value # - E(X) and standard deviation o of this bet. 4. Little Lottery: A lottery ticket costs 1 dollar. If you win, you are paid 101 dollars by the lotto commission. The probability of winning is 1.0%. What the expected value (round to nearest cent)? 5. Suppose you can buy as many lottery tickets as you want in previous exercise. What is the (Kelly) optimal bet if your bankroll is 1 million dollars? What does this mean in practice? 6. Find the probability of being dealt a holdem hand with two hearts. What is the probability of flopping a flush given that you have 2 hearts? (Express as % and round to 2 digits) 7. Find the probability of a flopping a set in holdem given that you have a pocket pair (Express as % and round to 2 digits). 8. Draw a single card. Let A be the event that you get an ace and let B be the event that you get a spade. Are A and B independent events? Explain in terms of conditional probabilities. Your answer should verify an equation! 9. Find the probability of being dealt a blackjack from a six deck shoe. 10. Find the expected value in % of an insurance bet if you have removed 6 small cards from a single deck (and the dealer has an ace up). 11. You have 90JO and the turn board is QQTO5024. Assume a straight or better is good. The pot is 100$ and villain bets $50. What is the expected value of a call? What are the pot odds? What would you do in this situation? 12. You have TOTO and the turn board is T2925424. You have flopped a set but the turn makes a flush likely. Assume the villain has A&. The pot is 90$ and villain bets $30. What is the expected value of a call? What are the pot odds? What would you do in this situation? 13. Suppose you are the house in European Roulette. A bet on a single number pays 35:1. What is the optimal bet as a percentage of the bankroll? 14. A dice game involving rolling 2 dice pays 6 units if you roll a total of 7, pays zero if you roll a 2 or 12, and you lose one unit otherwise. Find the expected value and standard deviation of a unit bet. 15. You bet 20 percent of your 100 dollar bankroll on a 60%-40% even money bet (using the Kelly optimal. bet). Use the natural log utility function (corresponding to full Kelly) to find the expected value and
