Cribbage Flush In The Crib

Cribbage Pro player “sm15” sent me a message asking about the pegging advantage of playing a flush. That’s a great question, and got me thinking about flushes in general.

• Cribbage flush If the four cards in your hand are of the same suit, you score four for a flush (a cribbage flush, unlike in poker, doesn't beat three of a kind!). If the starter card is also of the same suit, you score five. However, in the crib you cannot score a four-card flush; all five must be the same suit.
• Oct 04, 2012 Remember that a flush in the crib only counts if the cut card is the same suit as the cards in the crib, so it’s significantly less common than a flush in the hand. Around 0.17% of cribs hold a flush (1 in 588). Even when dealer tosses two suited cards in her crib she still only ends up with a flush 0.81% of the time (1 in 123).
• Aug 19, 2017 A flush of four or five cards. For a four-card flush, all four cards must be in the player's own hand, as opposed to being the shared Crib Card. A five-card flush must obviously use all five cards. The number of points is equal to the number of cards in the flush.
• Here are the (interesting) rules for scoring a set of cards in Cribbage. Points are combined. If all four cards in the players hand are the same suit, this is a called a flush and scores 4 points. If the turned up card is also the same suit, the flush scores 5 points. (No points are scored for a flush of four cards that comprises three in the.

How likely is your opponent to have a flush?

There is a special rule for a flush in the crib. Normally, if you have four or more cards of the same suit in your hand, including the turn up card, you can score a flush. In the crib, however, a flush only scores if all four cards AND the turn up are the same suit. In other words, only a 5-card flush counts in the crib.

About 3.0% of dealer’s hands are flushes. Pone’s hand holds a flush about 3.3% of the time.
Pone’s initial lead gives a clue as to whether or not they have a flush. A lead 5 is only 1.4% likely to be part of a flush. A lead 2 or 3 is 4.0% likely to be part of a flush. Basically if a lead card is more likely to be part of a trap (see the “Should you pair your opponent’s lead?”), it’s less likely to be part of a flush.

How likely are you to have a flush in your crib?

Remember that a flush in the crib only counts if the cut card is the same suit as the cards in the crib, so it’s significantly less common than a flush in the hand. Around 0.17% of cribs hold a flush (1 in 588). Even when dealer tosses two suited cards in her crib she still only ends up with a flush 0.81% of the time (1 in 123). When pone tosses suited cards in the crib she ends up giving dealer a flush 0.77% of time time (1 in 130).

Should you toss suited cards in the crib?

If it’s not going to make a difference to your hand, you might as well toss suited cards as dealer, and off-suit cards as pone. Usually all things are not equal, though, and pone might be faced with the choice of splitting up her hand to avoid giving dealer a flush. Changing your hand to avoid throwing suited cards is a pretty subtle play. When pone tosses suited cards into dealer’s crib she has a 0.77% chance of giving dealer 5 points, which works out to an average of 0.04 points.
Do situations exist where that 0.04 would make a difference? Sure. When pone discards 8-6 she gives dealer, on average, 0.01 points more than if she’d discarded 8-9. But if pone’s 8-9 is suited it might make sense for her to toss an off-suit 8-6 instead. That would offset the extra points from the 8-6, penalizing dealer an average of 0.03 points. Those three-one-hundredths-of-a-point could win you the game, but you've probably got more important cribbage-related things to worry about.
The Jack is a special case. Imagine you’re playing as pone and your hand holds: J♣, J♦, 6♦, 7♠, 8♠, 4♦. The right toss is probably the 4 and a Jack. But which Jack? If you toss dealer the J♦/4♦ you’ll give her a 10/46 (10 diamonds left in the deck after the Jack, 6, and 4, and 46 cards left in the deck) chance of scoring 1 for his knobs, plus a 0.77% chance of giving her 5 points for a flush. That works out to about 0.256 points.
If you toss the J♣/4♦ you’re giving her a 12/46 (12 clubs left in the deck / 46 cards left in the deck) chance of scoring 1 for his knobs, which works out to about 0.261 points. Throwing the off-suit Jack gives dealer an extra 0.005 points that you’d just as soon she not have! So if you’re going to toss a Jack into your opponent’s crib, consider tossing the suit that shows up most often in your hand, even if it might give dealer a flush.

How big is the pegging advantage?

To answer sm15's original question, the results depend on the hand being played, and who’s playing it (dealer or pone). For instance, we've seen that when dealers play a suited 6-7-8-9 they peg about 1% more points, while their opponents peg about 9% fewer points. A dealer holding suited A-4-Q-K will peg about 1% fewer points, while her opponent will peg about 7% fewer. And when pone holds A-4-Q-K she’ll peg the same number of points whether or not its suited, but dealer will peg 5% fewer points if pone’s A-4-Q-K is suited. (All of these statistics are based on several hundred examples of pone playing suited versions of those hands)
Taking into account every possible hand, dealer will peg about 1% fewer points if her cards are suited than if they’re not; and dealer’s opponent will peg about 4% fewer points if the cards are suited. If pone’s cards are suited, pone will peg the same as if they weren't suited, but her opponent will peg about 1.5% fewer points. So the pegging advantage to a flush is more about limiting your opponent’s pegging than it is about increasing your own.

Questions?

What do you think, sm15? Is that what you were expecting? Does anyone else have any questions they’d like answered?
Editor's Note: This is a guest post by Aaron Harsh continuing the series on cribbage strategy and tips. Aaron lives in Portland, Oregon with his wife Stacy and daughter Audrey. He spends his evenings analyzing cribbage strategy for Fuller Systems, and his days analyzing television viewership for Rentrak Corporation's Advanced Media & Information group. You can play him on Cribbage Pro Online as user 'aaronhars', or in person at American Cribbage Congress grassroots club #28 (Oregon's Finest).

Two cards from each player set aside for the dealer.

Board with pegs and 121 numbered holes used to keep score in a cribbage game.

The card flipped over by the dealer after the opponent cuts the deck at the start of each round. The players use the cut card when scoring their hands. Sometimes called the Starter Card.

Cribbage Flush In The Crib Combo

When the loser scores 60 points or they are said to be double-skunked. In match play, this is the equivalent of losing 4 games.

Common expression used by players when counting the points in their hand. For example, “fifteen-two, fifteen-four, and a pair is six”.

Four cards of the same suit in the hand or crib. In the hand, scores four points. Scores an additional point if the cut card is also the same suit. In the crib, scores five points but only if the cut card is of the same suit.

The final hole, hole number 121, on the cribbage board.

A player says “go” when they can’t play a card without exceeding a total count of 31. The opponent scores a point on a go.

The cards dealt to each player.

When the cut card is a Jack, the dealer scores “two for His Heels”.

Jack of the same suit as the cut card, either in the hand or crib. The player scores “one for His Nobs”.

See Skunked.

A series of games. For example, players may play a best of seven match.

An impossible score in the hand or crib. For this reason, players often joke that they have “nineteen” when they have a zero-score hand.

Two cards of the same rank.

Three cards of the same suit. Three-of-a-kind.

To score 121 points or more and win the game.

The dealer’s opponent is called the pone.

What Makes A Flush In Cribbage

Three or more cards in sequence. For example, 4-5-6 is a three card run. Scores one point per card. Also called a Straight.

When the loser scores only 61 to 90 points the are said to be skunked. In match play, this is the equivalent of losing 2 games.

See Cut Card

See Run

Another term for three cards of the same suit. Three-of-a-kind.

Expression routinely said by player who makes the count 31 and in so doing scores 2 points.

Cribbage Flush In The Crib Cover

Highest possible hand score. Comprised of four 5s and His Nobs.