Answer:
Ok, the probability of winning is:
For the first draw, we have 13 diamonds in a 52 card deck, the probability of drawing a diamond is:
p1 = 13/52
for the second draw we have 12 diamonds and 51 cards in the deck, now the probability is:
p2 = 12/51
the total probability is equal to the product of the individual probabilities, this is:
P = p1*p2= (13/52)*(12/51) = 0.059
now, the expected value can be calculated as follows.
EV = (P1*X1 + P2*X2)
where P1 is the probabilty of event 1, and X1 is the event 1,
In this case X1 is the event of winning $29, then P1 = 0.059
X2 will be the event of loosing $4, so P2 = 1 - 0.059 = 0.941
Then the expected value for 1 round of the game is:
EV = (0.059*$29 - 0.941*$4) = -$2.05
So if you play 891 times, expected value of 891 times the expected value for 1 round, this is:
891*EV = 891*(-$2.05) = -$1826.55
So you loss around $1826.55
