There are C(4,2) ways of choosing each Ace and each SXNA. You might do it exactly (with no extra aces or extra cards of suit x):Ĩ aces: 2222 and 8 suit-X-non-aces (SXNA): 2222 with four other cards (neither Aces nor of suit X - I'll call these "Off" cards): 4 I'll write this as case 1: 1) 2222 2222 4 ![]() the number of TJQK in suit X, without regard to a specific rank:.the number of aces of a suit, without regard to a specific suit.Winning configuration count for your choice of suit x:Įach digit in the configuration represents either Scott Johnson.įirst calculate how many ways you can select a "winning hand": This result supports the full calculation by L. When I ran this the output was: 58 / 100000000Ĭombining these results gives an average of about 295 times in five hundred million hands, or 1/1694915. Results = pool.map(simulate, range(poolSize)) Scott Johnson's full calculation), so I wrote a Python script to estimate the probability: import randomįrom multiprocessing.dummy import Pool as ThreadPoolĬards = * 4 The calculation of this seemed quite involved (although see L. Consequently the required cards for the hand are A♣ A♦ A♥ A♠ A♣ A♦ A♥ A♠ Tx Kx Qx Jx Tx Kx Qx Jx for some suit x, which leaves four cards unspecified. Melds in Pinochle are allowed to reuse cards (as long as they are different types of melds), and so the aces for the runs can be reused in the arounds. ![]() In double-deck Pinochle this is only half the aces, so is much more common and is only worth 100 points. In standard Pinochle this is all of the aces in the deck and is worth 1000 points. "A thousand aces" is a term from standard (single-deck) Pinochle, and refers to two "arounds" of aces (i.e. Consequently we're interested in the chance of being dealt two sets of ATKQJ both in the same suit. Trumps is decided by a bidding mechanism, but for this answer we'll assume that the bidding was won by the player in question, and trumps were chosen to match the hand. Rules BackgroundĪ double run is two sets ATKQJ in whichever suit is declared trumps. TLDR: This will happen roughly once every 1.7 million hands. Melds in Pinochle are allowed to reuse cards (as long as they are different types of melds), and so the aces for the runs can be reused for the double run. "A thousand aces" is a term from standard (single-deck) Pinochle, and refers to two "rounds" of aces (i.e. Trumps is decided by a bidding mechanism, but for this question we'll assume that the bidding was won by the player in question, and trumps were chosen to match the hand. ![]() Wikipedia and this rules page).Ī double run is two sets ATKQJ in whichever suit is declared trumps. What are the odds of getting a hand containing:Ī♣ A♦ A♥ A♠ A♣ A♦ A♥ A♠ Tx Kx Qx Jx Tx Kx Qx Jx for some suit x, and another four unspecified cards.ĭouble-deck Pinochle is a four player game using a deck of 80 cards (four lots of ATKQJ in each of ♣♦♥♠) (cf.
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