Flush In Crib Hand

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Traditional Cribbage is a card game that has been around since the 17th Century. It involves creating hands composed of pairs, runs, flushes, and sums to 15. Here at eCribbage.com, you can play 2 player, 3 player, and 4 player games. You can also play teams, muggins, and jokers.

Flush In Your Hand Crib


What features make eCribbage.com the best?

These are standard hand rankings for most poker games and apply to all high-hand poker variations including Texas Hold'em, Omaha and Stud. You'll find a printable poker hand rankings chart below the hand rankings as well as answers to some of the most frequently asked questions about poker hands and poker hand ranking. If the dealer is discarding for the crib, they should “salt” it with the best possible cards, but at the same time retain good cards in their hand that can be used for high scoring. Conversely, for the non-dealer, it is best to lay out cards that will be the least advantageous for the dealer.

How to play (2 player):

The players cut to see who gets the first 'crib'. Players are dealt 6 cards each, and both have to discard 2 cards into the crib. Then a community card is cut that will play for both hands in the show. If a jack is cut for the cut card, the player with the crib immediately gets 2 points. (This is called His Nobs). Now on to the play:

The play

Players take turns playing (pegging) their cards one at a time and announcing the total sum of the cards. Face cards count for 10. If the sum is equal to 15 or 31, that player gets 2 points. If the player forms a pair, they get 2 points. A triple pair is worth 6 points, and a quadruple pair is worth 12 points. If either player forms a run of 3 or more, they get to claim that many points as well. Runs do not necessarily have to be played in order. For example if 4,7,5,6 was played, whoever laid the 6 would get to claim a run for 4 points.

You are not allowed to play a card to make a sum over 31, so if you play to 28 and your opponent only has cards of over 3, they will say GO and you will continue to play as many cards as you can up to 31. You also claim one point for playing the last card of every trick. Whoever played the last card in the trick, their opponent starts the next trick. When all cards have been played, you move on to the show.

The show

The show is where you count all the hands up. The player that does not have the crib counts first, then the player with the crib counts their hand, and then finally the crib is counted. Scores count for the following:

  • 2 points for every pair
  • 3 points for every run of 3.
  • 4 points for every run of 4.
  • 5 points for a run of 5.
  • 2 points for each sum to 15.
  • 4 points for a flush
  • 1 additional point for a 5 card flush.
  • 1 point for 'His Heels', if you have a jack and the suit matches the cut card.

  • How to play (3 player):

    3 player crib is very similar to 2 player crib except players are dealt 5 cards each instead of 6. They only throw one card each to the crib, and one card is taken off the top of the deck and placed in the crib.

    eCribbage.com also provides the variant where the dealer (the player with the crib) can deal themself 6 cards, and the rest of the players 5. The dealer throws 2 cards to their crib, and the rest of the players throw 1 card to the crib.

    Flush

    How to play (4 player):

    4 player crib is very similar to 2 player crib except players are dealt 5 cards each instead of 6. Every player throws one card to the crib. The play goes clockwise through all players. There is also a 2 vs 2, team cribbage game that is described on the team cribbage page.


    In cribbage, the probability and maximum and minimum score of each type of hand can be computed.

    Distinct hands[edit]

    • There are 12,994,800 possible hands in Cribbage: 52 choose 4 for the hand, and any one of the 48 left as the starter card.

    (524)×48=12,994,800{displaystyle {52 choose 4}times 48=12,994,800}

    Flush In Crib Handle

    • Another, and perhaps more intuitive way of looking at it, is to say that there are 52 choose 5 different 5-card hands, and any one of those 5 could be the turn-up, or starter card.
      Therefore, the calculation becomes:

    (525)×5=12,994,800{displaystyle {52 choose 5}times 5=12,994,800}

    • 1,009,008 (approximately 7.8%) of these score zero points,[1] or 1,022,208 if the hand is the crib, as the starter must be the same suit as the crib's four cards for a flush.
    • Not accounting for suit, there are 14,715 unique hands.[2]

    Maximum scores[edit]

    Flush
    • The highest score for one hand is 29: 555J in hand with the starter 5 of the same suit as the Jack (8 points for four J-5 combinations, 8 points for four 5-5-5 combinations, 12 points for pairs of 5s and one for his nob).
    • The second highest score is 28 (hand and starter together comprise any ten-point card plus all four 5s, apart from the 29-point hand above).
    • The third highest score is 24 (A7777, 33339, 36666, 44447, 44556, 44566, 45566, 67788 or 77889).
    • The highest score as a dealer from the hand and crib is 53. The starter must be a 5, the hand must be J555, with the Jack suit matching the starter (score 29), and the crib must be 4466 (score 24), or vice versa.
    • The highest number of points possible (excluding pegging points) in one round is 77. The dealer must score 53, the opponent must then have the other 4466 making another 24 point hand for a total of 77.
    • The highest number of points from a hand that has a potential to be a '19 hand' is 15. It is a crib hand of one suit, 46J and another ten card, with a 5 of that suit cut up. The points are 15 for 6, a run for 9, nobs for 10, and a flush for 15. Any of the following cards in an unlike suit yields a '19 hand'; 2,3,7,8,and an unpaired ten card.
    • The most points that can be pegged by playing one card is 15, by completing a double pair royal on the last card and making the count 15: 12 for double pair royal, 2 for the 15, and 1 for the last card. This can happen in two ways in a two-player game. The non-dealer must have two ten-value cards and two 2s, and the dealer must have one ten-value card and 722, in which case the play must go: 10-10-10-go; 7-2-2-2-2. For example:
    Alice
    (dealer)
    Bob
    PlayerCardCumulativeScoreAnnounced
    Bob10'ten'
    Alice20'twenty'
    Bob303 points (run)'thirty'
    Alice1 point to Bob (30 for one)'go'
    Alice7'seven'
    Bob9'nine'
    Alice112 points'eleven for two'
    Bob136 points'thirteen for six'
    Alice1515 points (double pair royal,
    fifteen, last card)
    'fifteen for fifteen'
    • Alternatively, the players can each have two deuces, with one also holding A-4 and the other two aces. Then play might go 4-A-A-A-2-2-2-2.
    • The maximum number of points that can be scored in a single deal by the dealer in a two player game is 78 (pegging + hand + crib):
      Non-dealer is dealt 3 3 4 4 5 J and Dealer is dealt 3 3 4 4 5 5. Non-dealer discards J 5 to the crib (as ill-advised as this may be). Dealer discards 5 5 to the crib. Note that the J is suited to the remaining 5. The remaining 5 is cut.
      Play is 3 3 3 3 4 4 4 4 go. The dealer scores 29 total peg points.
      The dealer's hand is 3 3 4 4 5 = 20
      The dealer's crib is J(nobs) 5 5 5 5 = 29
      The total score for the dealer is 29 + 20 + 29 = 78.
      Note that the correct play for both players is to keep 3 3 4 5 worth 10 points and discarding J 4 and 4 5 to the crib respectively, meaning in reality, this hand would never take place. A more realistic hand would be both players being dealt 3 3 4 4 J J with both discarding J J and a 5 cut. In this case, with pegging as described above, the total score would be 20 (hand) + 21 (crib) + 29 (pegging) = 70 points.
    • The maximum number of points that can be scored in a single deal by the non-dealer in a two player game is 48 (pegging + hand), with the following example :
      Non-dealer is dealt 5 5 4 4 crib crib and Dealer is dealt 4 4 5 9 crib crib. Cut card is a 6.
      Play is 5 5 5 4 4 4 4, with the Non-dealer pegging 24. The Non-dealer scores 24 in the hand for a total of 48 points.
    • The maximum number of points that can be scored with a four-card flush is 21, which is achieved with a hand of 5 5 10 J Q or 5 5 J Q K: a pair, six fifteens, a three-card sequence, and the flush. A five-card flush of 5 10 J Q K scores 18 if the Jack is not the starter.

    Minimum scores[edit]

    • The dealer in two-player, 6-card cribbage will always peg at least one point during the play (the pegging round), unless the opponent wins the game before the pegging is finished. If non-dealer is able to play at each turn then dealer must score at least one for 'last'; if not, then dealer scores at least one for 'go'.
    • While 19 is generally recognized as 'the impossible hand', meaning that there is no combination of 5 cards that will produce a score of 19 points, scores of 25, 26, 27, and greater than 29 are also impossible in-hand point totals.[1] Sometimes if a player scores 0 points in their hand they will claim they have a '19-point hand.'[3]

    Minimum while holding a 5[edit]

    If a player holds a 5 in their hand, that player is guaranteed at least two points, as shown below:

    A 0-point hand must have five distinct cards without forming a run or a fifteen combination. If such a hand includes a 5, it cannot hold a 10 or a face card. It also cannot include both an A and a 9; both a 2 and an 8; both a 3 and a 7; or both a 4 and a 6. Since four more cards are needed, exactly one must be taken from each of those sets. Let us run through the possible choices:

    • If the hand includes a 9, it cannot hold a 6, so it must hold a 4. Having both a 4 and a 9, it cannot hold a 2, so it must hold an 8. Holding both a 4 and an 8, it cannot hold a 3, so it must hold a 7. But now the hand includes a 7-8 fifteen, which is a contradiction.
    • Therefore, the hand must include an A. If the hand includes a 7, it now cannot contain an 8, as that would form a 7-8 fifteen. However it cannot hold a 2, as that would form a 7-5-2-A fifteen. This is a contradiction.
    • Therefore, the hand must include a 3. Either a 2 or a 4 would complete a run, so the hand must therefore include a 6 and an 8. But this now forms an 8-6-A fifteen, which is a contradiction.

    Therefore, every set of five cards including a 5 has a pair, a run, or a fifteen, and thus at least two points.

    Interestingly, a hand with two 5s also can score only two points; an example is 2 5 5 7 9, which would be most likely a crib hand, and would not score a flush because of the pair, although said hand can be a non-crib four-card flush if either 5 is the starter. A hand with three 5s scores at least eight points; a hand with all four 5s scores 20 points and is improved only with a 10, J, Q, or K (scoring 28 except for the 29 hand previously described.)

    It is also true that holding both a 2 and a 3, or an A and a 4 (pairs of cards adding up to five) also guarantees a non-zero score:

    • If a hand includes both a 2 and a 3 and is to score 0 points, it cannot have a face card, an A, a 4, or a 5. This requires three cards from the 6, 7, 8, and 9, and any such selection will include a fifteen.
    • If a hand includes both an A and a 4 and is to score 0 points, it cannot have a face card or a 5. It also cannot have both a 2 and a 3; both a 6 and a 9; or both a 7 and an 8. If the hand includes a 2, it cannot have a 9 (9-4-2 fifteen). Thus it must have a 6. It then cannot have an 8 (8-4-2-A fifteen) or a 7 (7-6-2 fifteen). If, however, the hand includes a 3, it cannot include an 8 (8-4-3 fifteen) or a 7 (7-4-3-A fifteen). These are all contradictions, so every hand containing both an A and a 4 scores at least two points.

    Odds[edit]

    • The table below assumes the card(s) discarded to the crib are randomly chosen. Given this assumption, the odds of getting a 28 hand in a two-player game are about 1 in 170984, and a perfect 29 hand 1 in 3,248,700.[3]
    • However, if we assume that the player will always keep J555 if those cards are included in the hand, the odds of getting a perfect 29 hand starting with a six-card hand are 1 in 216,580, while the odds after discarding from a five-card hand are 1 in 649,740.[4]

    Flush In Crib Hand


    Scoring Breakdown, assuming random discard(s) to the crib[1]

    ScoreNumber of hands
    (out of 12,994,800)
    Percentage of handsPercentage of hands at least as high
    01,009,0087.7647100
    199,7920.767992.2353
    22,813,79621.653291.4674
    3505,0083.886269.8142
    42,855,67621.975565.928
    5697,5085.367643.9525
    61,800,26813.853838.5849
    7751,3245.781724.7311
    81,137,2368.751518.9494
    9361,2242.779810.1979
    10388,7402.99157.4181
    1151,6800.39774.4266
    12317,3402.44214.0289
    1319,6560.15131.5868
    1490,1000.69341.4355
    159,1680.07060.7421
    1658,2480.44820.6715
    1711,1960.08620.2233
    182,7080.02080.1371
    19000.1163
    208,0680.06210.1163
    212,4960.01920.0542
    224440.00340.0350
    233560.00270.0316
    243,6800.02830.0289
    25000.0006
    26000.0006
    27000.0006
    28760.00060.0006
    2940.000030.00003
    • Mean = 4.7692
    • Standard deviation = 3.1254
    • Skewness = 0.9039
    • Excess kurtosis = 1.4599

    Note that these statistics do not reflect frequency of occurrence in 5 or 6-card play. For 6-card play the mean for non-dealer is 7.8580 with standard deviation 3.7996, and for dealer is 7.7981 and 3.9082 respectively. The means are higher because the player can choose those four cards that maximize their point holdings. For 5-card play the mean is about 5.4.

    Slightly different scoring rules apply in the crib - only 5-point flushes are counted, in other words you need to flush all cards including the turn-up and not just the cards in the crib. Because of this, a slightly different distribution is observed:

    Scoring Breakdown (crib/box hands only)

    ScoreNumber of hands (+/- change from non-crib distribution)
    (out of 12,994,800)
    Percentage of handsPercentage of hands at least as high
    01,022,208 (+13,200)7.8663100
    199,792 (0)0.767992.1337
    22,839,800 (+26,004)21.853491.3658
    3508,908 (+3,900)3.916269.5124
    42,868,960 (+13,284)22.077865.5962
    5703,496 (+5,988)5.413743.5184
    61,787,176 (-13,092)13.753038.1047
    7755,320 (+3,996)5.812524.3517
    81,118,336 (-18,900)8.606018.5393
    9358,368 (-2,856)2.75789.9332
    10378,240 (-10,500)2.91077.1755
    1143,880 (-7,800)0.33774.2648
    12310,956 (-6,384)2.39293.9271
    1316,548 (-3,108)0.12731.5342
    1488,132 (-1,968)0.67821.4068
    159,072 (-96)0.06980.7286
    1657,288 (-960)0.44090.6588
    1711,196 (0)0.08620.2179
    182,264 (-444)0.01740.1318
    190 (0)00.1144
    207,828 (-240)0.06020.1144
    212,472 (-24)0.01900.0541
    22444 (0)0.00340.0351
    23356 (0)0.00270.0317
    243,680 (0)0.02830.0289
    250 (0)00.0006
    260 (0)00.0006
    270 (0)00.0006
    2876 (0)0.00060.0006
    294 (0)0.000030.00003
    • Mean = 4.7348

    As above, these statistics do not reflect the true distributions in 5 or 6 card play, since both the dealer and non-dealer will discard tactically in order to maximise or minimise the possible score in the crib/box.

    Card combinations[edit]

    • A hand of four aces (AAAA) is the only combination of cards wherein no flip card will add points to its score.
    • There are 71 distinct combinations of card values that add to 15:
    Two
    cards
    Three
    cards
    Four cardsFive cards
    X5
    96
    87
    X4A
    X32
    95A
    942
    933
    86A
    852
    843
    77A
    762
    753
    744
    663
    654
    555
    X3AA
    X22A
    94AA
    932A
    9222
    85AA
    842A
    833A
    8322
    76AA
    752A
    743A
    7422
    7332
    662A
    653A
    6522
    644A
    6432
    6333
    554A
    5532
    5442
    5433
    4443
    X2AAA
    93AAA
    922AA
    84AAA
    832AA
    8222A
    75AAA
    742AA
    733AA
    7322A
    72222
    66AAA
    652AA
    643AA
    6422A
    6332A
    63222
    553AA
    5522A
    544AA
    5432A
    54222
    5333A
    53322
    4442A
    4433A
    44322
    43332
    Note: 'X' indicates a card scoring ten: 10, J, Q or K

    Hand and Crib statistics[edit]

    Flush In Crib Hand

    If both the hand and the crib are considered as a sum (and both are drawn at random, rather than formed with strategy as is realistic in an actual game setting) there are 2,317,817,502,000 (2.3 trillion) 9-card combinations.(524)×(484)×44=2,317,817,502,000{displaystyle {52 choose 4}times {48 choose 4}times 44=2,317,817,502,000}

    • As stated above, the highest score a dealer can get with both hand and crib considered is 53.
    • The only point total between 0 and 53 that is not possible is 51.

    Scoring Breakdown

    ScoreNumber of hand-crib pairs
    (out of 2,317,817,502,000)
    Percentage of hand-crib pairs to 6 decimal placesPercentage of hand-crib pairs at least as high
    014,485,964,6520.624983100
    13,051,673,9080.13166299.375017
    280,817,415,6683.48678999.243356
    323,841,719,6881.02862895.756566
    4190,673,505,2528.22642494.727938
    570,259,798,9523.03129186.501514
    6272,593,879,18811.760883.470222
    7121,216,281,6245.2297671.709422
    8290,363,331,43212.52744666.479663
    9151,373,250,7806.53085353.952217
    10254,052,348,94810.96084347.421364
    11141,184,445,9606.09126736.460521
    12189,253,151,3248.16514530.369254
    1398,997,926,3404.2711722.204109
    14127,164,095,5645.48637217.932939
    1559,538,803,5122.56874412.446567
    1677,975,659,0563.3641859.877823
    1732,518,272,3361.4029696.513638
    1842,557,293,0001.8360935.110669
    1917,654,681,8280.7616943.274576
    2022,185,433,5400.9571692.512881
    218,921,801,4840.3849231.555712
    2210,221,882,8600.4410131.17079
    234,016,457,9760.1732860.729776
    245,274,255,1920.2275530.55649
    251,810,154,6960.0780970.328938
    262,305,738,1800.0994790.25084
    27750,132,0240.0323640.151361
    281,215,878,4080.0524580.118998
    29401,018,2760.0173020.06654
    30475,531,9400.0205160.049238
    31184,802,7240.0079730.028722
    32233,229,7840.0100620.020749
    3382,033,0280.0035390.010686
    3471,371,3520.0030790.007147
    3519,022,5880.0008210.004068
    3644,459,1200.0019180.003247
    379,562,0400.0004130.001329
    3810,129,2440.0004370.000916
    391,633,6120.000070.000479
    405,976,1640.0002580.000409
    411,517,4280.0000650.000151
    42600,9920.0000260.000085
    43127,6160.0000060.00006
    44832,7240.0000360.000054
    45222,2200.000010.000018
    4642,5600.0000020.000009
    4724,3520.0000010.000007
    48119,7040.0000050.000006
    496,16800
    5038400
    51000
    524,32000
    5328800
    • Mean: 9.50397
    • Median: 9
    • Mode: 8

    See also[edit]

    References[edit]

    1. ^ abcSteven S. Lumetta (2007-05-15). 'Amusing Cribbage Facts'. Archived from the original on 2018-01-16. Retrieved 2008-03-03.
    2. ^Tim Wood (2008-08-05). 'All Possible Cribbage Hands'. Archived from the original on 2013-02-09. Retrieved 2008-08-05.
    3. ^ abWeisstein, Eric W. 'Cribbage'. MathWorld. Retrieved 2008-03-02. All scores from 0 to 29 are possible, with the exception of 19, 25, 26, and 27. For this reason, hand scoring zero points is sometimes humorously referred to as a '19-point' hand.
    4. ^Cribbage Corner (2008-05-05). 'Perfect cribbage hand odds'. Retrieved 2008-05-05.

    How Do You Count A Flush In Crib

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