Statistical Mechanics of Poker: in statistical mechanics, microstates associated
ID: 3209340 • Letter: S
Question
Statistical Mechanics of Poker: in statistical mechanics, microstates associated with classical or quantum mechanics are effectively partitioned into microstates. The definition and specification of these microstates is to some extent up to us. although obviously, some choices will be more useful than others, being more naturally associated with typical sorts of bulk measurements or leading to more reproducible predictions. But the situation is Somewhat analogous to a card game like poker, where the microstates correspond to the particular cards dealt to given players and in a certain order, while the macro states correspond to the classification of the hands, such as one pair, two pair, three of a kind, straight, flush, etc. These aerostats are human inventions, but obviously, some choices of microstates will be easier to remember than others, or will typically lead to more interesting games, etc. Consider a game of five-card stud, where a player receives five years with no Oporto unity for substitutions} from a standard deck of cards. The Boltzmann entropy is associated with the number of microstates compatible with a given microstate. which is then here proportional to the probability for getting dealt a specified type of hand. These probabilities then determine the rank of the possible hands in the game. What is the probability of getting dealt a full house, exactly 3 cards with the same face value and the remaining 2 cards both sharing a common face value? What is the probability of getting dealt a flush, with all live cards having the same suit? Of course, you can easily find these odds online, but it Ls more fun and informative to actually work them out yourself. But if history had played out differently, we could have introduced other types of poker hands: Calculate the probability of being dealt a skip-straight, in which the live cards constitute a sequence of successive even values or odd values for example 2, 4, 6, 8, 10. Face cards are ordered as usual (where Jack = 11. Queen 12. King = 13, and aces can be taken to have either a value of I or 14}. [PRACTICE] Calculate the probability of being dealt a rouge et noir, in which, when cards are arranged in non-descending order, the colors of the cards alternate for example, a 2 of hearts, a 5 of clubs, a 7 of diamonds, a 10 of spades, and a jack of hearts. [PRACTICE] Calculate the probability of being dealt a Fibonacci straight, in which the five cards constitute successive terms from near the beginning of the Fibonacci sequence. (Again, an ace can count as cither high or low). Explicitly define your own new type of five-card poker hand, and calculate its probability in a game of five-card stud. Where would this type of hand fall in the rankings of standard poker hands (which now you can look up)?Explanation / Answer
Here you have to find the probability of flush in poker hand.
You have to choose 5 cards from 52 cards.
possibilities for 5 cards is
52C5 =2598960
a)
For full house 3 cards are same cards( eg. 3,3,3) and others two cards also same cards(eg .2,2)
We choose 1 card from 13 cards( 3)
13C1=13
3,3,3 are different suit so 4C3=4
Other card 2 is choose from remaining 12 crads so 12C1=12
And suit for this other cards is 4C2=6
So probability of full house = 13*4*12*6 / 2598960
=3744/2598960
=0.001441
b)
The total number of cards in sequence 1 to K is 13. you choose 5 cards ( eg 4,7,9,10,J)
13C5=1287
For flush choose each cards from same suit . total number of suit is 4 you choose 1 suit
4C1=4
probability of flush =1287*4 / 2598960
=5148/2598960
=0.001981
c)
In straight and royal flush are subtract from above .
10C1 * 4C1=40
probability flush skip straight = (5158 - 40 )/2598960
=0.001965