Question
Imagine a game like poker but played with 4 card hands. Which should be a better hand: one pair or ``melting pot'', which is four cards all of different ranks and different suits? There are 13?(4choose2)?(12choose2)?4?4=82368 one pair hands (choose the rank of the pair, choose the two suits of of four for that pair, choose the ranks of the other two cards, and choose the suit of one of them and then the other). There are fewer than 13?12?11?10=17160 melting pot hands (choose the rank of the spade, the rank of the heart, the rank of the diamond, and the rank of the club; this total includes some straights hence the qualifier "fewer than"). So melting pot should beat one pair. could any one explane that specially whats the poker game ruls in this question thanks
Explanation / Answer
Imagine a game like poker but played with 4 card hands. Which should be a better hand: one pair or ``melting pot'', which is four cards all of different ranks and different suits? There are 13?(4choose2)?(12choose2)?4?4=82368 one pair hands (choose the rank of the pair, choose the two suits of of four for that pair, choose the ranks of the other two cards, and choose the suit of one of them and then the other). There are fewer than 13?12?11?10=17160 melting pot hands (choose the rank of the spade, the rank of the heart, the rank of the diamond, and the rank of the club; this total includes some straights hence the qualifier "fewer than"). So melting pot should beat one pair. could any one explane that specially whats the poker game ruls in this question thanks LET ME ANSWER THE II PART OF YOUR QUESTIONN FIRST could any one explane that specially whats the poker game ruls in this question thanks IT IS LOGICAL THAT THE HAND WITH LESSER PROBABILITY OF OCCURRENCE SHOULD WIN OVER A HAND WITH HIGHER PROBABILITY OF OCCURRENCE. POKER RULES ARE BASED ON THIS PRINCIPLE. THE ONLY VARIATIONS ARE SOME PLAY A 3 HAND POKER AND SOME PLAY WITH 5 CARD HAND ACCORDINGLY , THE WINNING ARRANGEMENTS ARE NOTIFIED IN THEIR SEQUENTIAL ORDER BASED ON THE ABOVE PRINCIPLE. SINCE POSSIBILITIES FOR TOTAL NUMBER OF HANDS THAT COULD BE DEALT ARE SAME IN ALL CASES, INSTEAD OF DIVIDING WITH THAT LARGE NUMBER TO GET PROBABILITIES IN DECIMALS , WE JUST TAKE THEIR FREQUENCY OF OCCURRENCE TO DETERMINE THE WINNING ORDER. FREQUENCY OF A GETTING ONE PAIR IN 4 CARDS . I. TO GET A PAIR ... THE PAIR CAN BE OF ANY ONE OF 13 RANKS ......13 POSSIBILITIES CHOICE OF THE PAIR AS ABOVE FROM 4 SUITS CAN BE DONE IN C[4,2] WAYS ......6 WAYS . THE OTHER 2 CARDS CAN BE ANY OF THE REMAINING 50....50*49 WAYS SO FREQUENCY = 13*6*50*49 =191100 2. TO GET A MELTING POT 4 DIFFERENT SUITS CAN BE SELECTED OUT OF FOUR IN ONLY 1 WAY .....1 POSSIBILITY 4 DIFFERENT RANKS CAN BE SELECTED OUT OF 13 IN C[13,4] WAYS = 715 SO FREQUENCY = 715*1 = 715 SO OBVIOUSLY MELTING POT SHALL RANK HIGH ABOVE A PAIR AMONG THE WINNERS..... Imagine a game like poker but played with 4 card hands. Which should be a better hand: one pair or ``melting pot'', which is four cards all of different ranks and different suits? There are 13?(4choose2)?(12choose2)?4?4=82368 one pair hands (choose the rank of the pair, choose the two suits of of four for that pair, choose the ranks of the other two cards, and choose the suit of one of them and then the other). There are fewer than 13?12?11?10=17160 melting pot hands (choose the rank of the spade, the rank of the heart, the rank of the diamond, and the rank of the club; this total includes some straights hence the qualifier "fewer than"). So melting pot should beat one pair. could any one explane that specially whats the poker game ruls in this question thanks LET ME ANSWER THE II PART OF YOUR QUESTIONN FIRST could any one explane that specially whats the poker game ruls in this question thanks IT IS LOGICAL THAT THE HAND WITH LESSER PROBABILITY OF OCCURRENCE SHOULD WIN OVER A HAND WITH HIGHER PROBABILITY OF OCCURRENCE. POKER RULES ARE BASED ON THIS PRINCIPLE. THE ONLY VARIATIONS ARE SOME PLAY A 3 HAND POKER AND SOME PLAY WITH 5 CARD HAND ACCORDINGLY , THE WINNING ARRANGEMENTS ARE NOTIFIED IN THEIR SEQUENTIAL ORDER BASED ON THE ABOVE PRINCIPLE. SINCE POSSIBILITIES FOR TOTAL NUMBER OF HANDS THAT COULD BE DEALT ARE SAME IN ALL CASES, INSTEAD OF DIVIDING WITH THAT LARGE NUMBER TO GET PROBABILITIES IN DECIMALS , WE JUST TAKE THEIR FREQUENCY OF OCCURRENCE TO DETERMINE THE WINNING ORDER. FREQUENCY OF A GETTING ONE PAIR IN 4 CARDS . I. TO GET A PAIR ... THE PAIR CAN BE OF ANY ONE OF 13 RANKS ......13 POSSIBILITIES CHOICE OF THE PAIR AS ABOVE FROM 4 SUITS CAN BE DONE IN C[4,2] WAYS ......6 WAYS . THE OTHER 2 CARDS CAN BE ANY OF THE REMAINING 50....50*49 WAYS SO FREQUENCY = 13*6*50*49 =191100 2. TO GET A MELTING POT 4 DIFFERENT SUITS CAN BE SELECTED OUT OF FOUR IN ONLY 1 WAY .....1 POSSIBILITY 4 DIFFERENT RANKS CAN BE SELECTED OUT OF 13 IN C[13,4] WAYS = 715 SO FREQUENCY = 715*1 = 715 SO OBVIOUSLY MELTING POT SHALL RANK HIGH ABOVE A PAIR AMONG THE WINNERS.....