ROULETTE is a casino game where a numbered wheel spins and a steel ball falls in
ID: 3205310 • Letter: R
Question
ROULETTE is a casino game where a numbered wheel spins and a steel ball falls into a location marked by one particular colored number. In the United States there are 18 locations colored red, 18 locations colored black and 2 locations colored green. The red and black locations are numbered 1-36 and the green locations are labeled "0" and "00" as shown in the picture to the right. The wheel therefore has 38 locations in total. Note that the odd and even values are not evenly distributed within each color. For any particular wager a player makes, an expected profit can be calculated from: Expected profit = (Prob, of winning) x (winning payout amount) - wager One potential wager is to "bet on black" where you make a wager and if the ball lands in a black location you win an additional amount equal to the wager for a total payout equal to twice the wager. For example, if you bet $1 and win the casino gives you a $2 payout. If the ball lands on red or green you would lose your wager and the payout would be $0. What is the expected profit from making a $3 "bet on black"? (Round to closest penny) To "let it ride" is to make a bet and if it wins to make the same bet with the entire payout amount. For example, if you bet $1 on black and win the casino gives you $2, you then "let it ride" by betting that $2 on black and if you win again the casino would give you $4. If the ball were to land on red or green on either spin of the wheel you would lose your wager and the final payout would be $0. What is the expected profit for betting $6 on black and if you win, "letting it ride" once? I.E., betting on black and if you win betting your winnings on black again? (Keep in mind that if you lose the first bet you are done; round to closest penny) Another potential wager is to "bet on odd" which has the same payout as betting on black, but wins only when the ball lands in a location with an odd number of either color. If the ball lands on an even numbered location or a green space you lose your wager and the payout would be $0. What is the expected profit from placing two bets on a single spin - $6 on black and $6 on odd? (Round to closest penny) you may find it helpful to use a tree diagram. In Europe Roulette is more popular than in the US. European wheels do not have a "00" location, but the payout amounts for betting on black, red, odd, even, etc. are the same. Provide an explanation for the increased popularity of roulette in Europe based upon the comparison of an example expected profit calculation. Be clear and precise.Explanation / Answer
(a) expected profit = 3*18*2/38 -3 = 108/38-3*20/38 = 48/38
(b)Expected profit = 12*W + 18*WW - 6*L
=12*18/38 + 18*(18/38)^2 -6*20/38
(c)Expected profit = (12*18/38 - 6*20/38) + (12*18/38 - 6*20/38)
(d)Since the expected profit increases as in the denominator we have 37 locations only than 38 which increases expected profit and hence is the increased popularity
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