1

We had a hand that was 3 - 7's with an ace in hand and then the cut card came up as an ace. How many points would this be.

We were confused and figured it was 12 or 24 points?

3

Neither, as it scores 20 points in the Show. The Rules of Cribbage specify that one scores "pairs" and "fifteens" as combinations.

The Show

Each player then counts the score of the four cards in his hand plus the turned up card. The non-dealer shows first and this is important because it can often make the difference between winning and losing.

  • Fifteen - All combinations of cards that add up to fifteen count 2 points.

  • A pair, a pair royal or a double pair royal - count 2, 6 or 12 respectively.

....

Note that:

  • the term pair royal is shorthand for the three combinations of two (ie a pair) available from three by omitting each one in turn.

    This can be visualized by placing the three cards in a triangle and noting that the three sides are the pairs available to be scored.

  • the term double pair royal is shorthand for the six combinations of two (ie a pair) available from four by omitting two in turn.

    This can be visualized by placing the four cards in a diamond, and noting that not only the four sides, but also the two diagonals are the (now six) pairs available for scoring.

Then so this hand scores (as there are no runs, flushes, or "his nobs") as:

  • with 1st ace, omitting each seven in turn:

    fifteen-2, fifteen-4, fifteen-6*,

  • with 2nd ace, again omitting each seven in turn:

    fifteen-8, fifteen-10, fifteen-12*;

  • for the sevens, again omitting each seven in turn:

    a pair royal of sevens makes 18;

  • for the aces:

    and a pair of aces makes 20.

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