Question

Project#1. Conduct a Monte Carlo simulation and estimate the probability of a royal-flush in poker, if 5 cards are selected at random from a deck of 52 cards?Write the simulation Rcode.

Answer 1

Royal Flush is a sequence of Ace, King, Queen, Jack and ten from a suit.

Out of five cards first card can be any of the above five cards from a suit. This means that there are 20 such cards from a deck of 52 cards.

So the probability of first card= 20/52

Now the second card must have to be the remaining 4 cards from the same suit as of first card's suit.

Hence probability of second card= 4/51

Similarly,

Probability of third card= 3/50

Probability of fourth card= 2/49

Probability of fifth card= 1/48

Hence the probability of a royal flush= (20/52)*(4/51)*(3/50)*(2/49)*(1/48)

= (20*4*3*2*1) / (52*51*50*49*48)

= 0.000001539

= 0.0001539%