A popular casino table game is threecard poker One aspect of

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?

Solution

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