A popular casino table game is three-card poker. One aspect of the game is the \

Question

A popular casino table game is three-card poker. One aspect of the game is the "pair plus" bet in which a player is paid a dollar amount for any hand of a pair or better, regardless of the hand the dealer has. The table shows the profit and probability of various hands of a player playing the $7 pair plus bet.

12/5525

a) what is the expected profit when playing the $8 pair plus bet in three card poker.

b) what is the standard deviation.

c) You play the game for 6 hours with the average of 33 hands per hour, how much would you expect to lose?

Outcome Profit Probability Straight Flush 250

12/5525

Three of a kind 165 1/425 Straight 35 36/1105 Flush 27 274/5525 Pair 8 72/425 Other -8 822/1105

Explanation / Answer

The table shows the expected profits when placing 8 pair plus bet

So,

Expected profit

= 250 (12 / 5525) + 165 (1 / 425) + 35 (36 / 1105) + 27 ( 274 / 5525 ) + 8 ( 72 / 425 ) - 8 (822 / 1105 )

= -1.185 is the average expected loss from each game

Thus,.Playing for 6 hours at 33 hands per hour,

expected losses = 6 * 33 * -1.185

= -234.69

Calculation for standard deviation is as shown

Profit Prob Product (Profit - Mean) ( P - M ) ^2 Product 250 0.002171946 0.542986 251.1853394 63094.07471 137.0369 165 0.002352941 0.388235 166.1853394 27617.56702 64.98251 35 0.032579186 1.140271 36.18533937 1309.378785 42.65849 27 0.04959276 1.339005 28.18533937 794.4133552 39.39715 8 0.169411765 1.355294 9.185339367 84.37045928 14.29335 -8 0.743891403 -5.95113 -6.814660633 46.43959955 34.54602 1 Var 332.9144 Mean -1.18533937 Std.Dev 18.24594

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