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Question: question 29...

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Question 2.9

lt Wieelr With a bet of $5 on black and a bet of $2 on the specific group of four numbers pictured in Figure 2.1 (13, 14, 16, 17). What is the bettors expectation on this combined bet? Conclude, as suggested in the text, that the bettors expected loss is 5.26 cents for every dollar bet. 2.9 A European roulette wheel has 37 sectors including a zero but no double zero. Furthermore if the zero comes up, any wager on even money bets (red, odd, 2nd 18, etc.) remains for one more spin. If the desired even money event occurs on this next spin, the original wager is returned (no gain or loss). Otherwise house odds are as listed in Table 2.1. (a) Compute the expectation of a $1 bet on red with such a wheel. (b) Compute the expectation of other types of $1 bets. (o) Conclude that European roulette has a measure of skill not present in American roulette. 2.10 A coin is flipped then a single die is rolled. Payoffs in this successive game are as indicated below. What is the expectation of this game horand to a nlaver to make it a fair
ddds WIf L I Uu form r : 1 wheré It should be clear from comparing the casino owners are very fond of the game of roulette (a forth will elaborate on this theme). true odd cominge ng ex TABLE 2.1 True and House Odds in American Roulette True odds House odds Type of bet Color (Red or Black) Parity (Even or Odd) 18#5 (1-18 or 19-36) 12 #s (columns or dozens) 6 #s (any 2 rows) 4 #s (any 4 number square) 3 #s (any row) 2 #s (adjacent) Single #s 20:18 20:18 20:18 26:12 32:6 34:4 35:3 36:2 37:1 17:1 35:1
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