Probability Application - Essay Example

These probabilities help me evaluate the chance of losing all my cash in case I call the $10,000 bet and ultimately, the decision that I will make.
Assuming I call the $10,000 bet, there are 44 possible outcomes but in the end, they will result in five distinct winning-hands (a draw is not possible in this game).

Four of a kind: The opponent’s possible best hand will occur if the last card dealt is a 10 of hearts giving him four tens. The probability of this win is:
P=Pr⁡(10 of hearts)

P=1/44
Full house: The opponent gets a Full-house provided that a three, four, or nine is dealt. For him to win, neither a straight-flush nor a four kind should occur. The probability of this win is:

P={Pr⁡(a three)+Pr⁡(a four) + Pr(a nine)} * Pr(not a four-kind)
P=(3/44+3/44+3/44)*43/44=387/1936

Flush: I will hold a flush if a diamond is dealt. To win with the flush neither of the above hands occurs. The probability of winning with the flush is:
P=Pr(diamond)*Pr(not full house)*Pr(not four of a kind)
P=(7/44*43/44*1549/1936)=0.12440

Straight: I will hold a straight hand if an eight is dealt. To win with the straight neither of the above hands occurs. The probability of winning with the straight is:
P=Pr(eight)*Pr(not flush)*Pr(not full house)*Pr(not four of a kind)
P=(3/44*43/44*1549/1936*0.87560)=0.04668

Three of a kind: The opponent will hold a three of a kind if all the above cards are not dealt. The probability of winning with three of a kind is equal to the probability of the above hands not occurring, given by:
P={Pr(not straight)*Pr(not flush)*Pr(not full house)*Pr(not four of a kind)}
OR: P=1-{Pr⁡(straight)+Pr⁡(flush)+Pr(full house)+Pr(four of a kind)}
P=1-(0.04668+0.12440+387/1936+1/44)=0.60630

My total probability of winning is: 0.12440+0.04668=0.17108
My opponent’s probability of winning is: 0.60630+387/1936+1/44=0.82892
I have a 17% chance of winning against my opponent’s 83%. I, therefore, have a higher chance of losing than winning in case I match the opponent's $10,000 bet. The best move is to fold and keep the $10,000 as opposed to calling. Read More