EPTOkay, so i recently played a family game called Tripoly, in which there is 8 ways to win money:
1. you can win the poker round
2. you can win any of the 7 placers on the board consisting of:
a. King of hearts
b. Queen of Hearts
c. Jack of hearts
d. Ten of hearts
e. Ace of hearts
f. King and Queen of hearts (both same suite)
g. Kitty (explained below)
h. 8, 9, 10 suited
Depending on the number of players, you can have different amounts of cards as all of the cards must be used up. However, if there are n players you must deal out as if there were n+1 because a extra set of cards is dealt for the dealer to see if he wants to either auction the hand off or switch his own hand for it( he is not allowed to see this set). So how the game in one turn generally goes is the dealer either switches or auctions the hand, then a poker round goes, which is basically 5 card stud, and then the dealer selects his lowest rank card of any suite, and if the next person has the next card in that suite, they play it and so on until you reach the ace. If no one has the next card of the suite, the player who put down the last card gets to choose the lowest card of a different suite and so on. If the player has the ace and it is played, they get to choose the next suite. If at any time any of the said outcomes to win is placed down, you get the money in that pot, (i.e i play a 10h i get that cash. Or if i play both 10h, Kh, and Qh, i get all the cash from the independants, as well as the KQh pot.).
Last night i played where everyone typically had 7 cards in their hand, and i tried using my limited knowledge having taken a discrete math course to try to compute the following odds. So here are my questions.
1. probability of getting either a 10h, Jh, Qh, Kh, or Ah in a :
a. 7 card hand
b. 8 card hand
c. 9 card hand
without getting another of the said cards in the same hand (i.e cant have JQh in the same hand.
1a. probability of getting two of 10h, Jh, Qh, Kh, or Ah in a:
a. 7 card hand
b. 8 card hand
c. 9 card hand
getting a KQh or any other of the cards in the same hand.
1b. probability of getting 3 of 10h, Jh, Qh, Kh, or Ah in a:
a. 7 card hand
b. 8 card hand
c. 9 card hand
without getting a KQh in the 3 cards or any of the other cards in the same hand (i.e {10h, Jh, Qh,x, y, z, a})
1c. probability of getting 4 of 10h, Jh, Qh, Kh, or Ah in a:
a. 7 card hand
b. 8 card hand
c. 9 card hand
without getting a KQh in the 4 cards.
2. probability of getting a KQh in a:
a. 7 card hand
b. 8 card hand
c. 9 card hand
without having any of the other "important hearts" in the hand.
2a. probability of getting a KQh in a
a. 7 card hand
b. 8 card hand
c. 9 card hand
with having 1, or 2 other "important hearts" in the hand.
3. Probability of getting a 8, 9, 10 of the same suite in a:
a. 7 card hand
b. 8 card hand
c. 9 card hand
