Texas 42, Interesting Probability Question?

Question

Texas 42 is a game played with double six dominoes similar to the card game spades. There are 4 players each with a partner sitting across from each other at the table. There are 28 total dominoes and each player draws 7. There are 7 total suits. (blanks, aces, deuces, treys, fours, fives, and sixes) and 7 of each suit. An example suit of fours would be (4-0, 4-1, 4-2, 4-3, 4-4, 4-5, 4-6). Each player bids on the number of points they think they can earn based on a total possible points of 42. If a player wins the bid, he/she must call “trumps” and say what the “spade” suit would be.
It is often termed “getting trump f****d” when an opposing player holds important “trumps” that can easily “set ” the other team making them lose the hand.
Here is the scenario:
If player A bids on a hand, holding 5 of the above four suit dominoes. This player can get “set” if one of the two opposing players (not his partner) hold BOTH the other 2 four-suit dominoes. Keep in mind that if 1 of the four suit dominoes is in player B’s hand and the other 1 four suit domino is in player C’s hand, or if both of the 2 four-suits are in his partner’s hand, then player A will NOT get “set”.
Remember, each player holds 7 dominoes, and player A hopes that the distribution of BOTH the other 2 fours is not in ONE opposing player’s hand.
What is the probability of player A getting “set”?

Answer 1

There are 21 dominoes whose locations you don't know. For both the two "set" dominoes to be in one hand, the other two hands must have none. The probability of two hands having no "set" dominoes (and, therefore, some other hand having both) is:



19/21 x 18/20 x 17/19 x ... x 7/9 x 6/8 =



(19!/5!) / (21!/7!) = (7 x 6) / (21 x 20) = 0.1



Since there are two hands you are concerned about, the total probability one of your opponents has both is double that, or 0.2, or 20%.



The probability your partner has the other two is 10%, and the probability of the split being 1-1-0 or 1-0-1 or 0-1-1 is 70%.

Answer 2

something tells me you need a break from dominoes

Answer 3

odds of drawing 7 doubles