How many cribbage points are in a full deck of cribbage?

Answer 1

If you had 52 cards in your hand...

QUADS (you cannot have pairs or trips any more since all the cards are in your hand)

You would have 13 sets of quadruples. A quadruple is composed of 6 unique pairs (if you lay the four cards out in a square then the unique pairs are the top two, bottom two, left, right, and the two diagonals). Each of the six pairs is worth 2 points = 12 points. (13 cards x 12 points) = 156 points.

RUNS

You would have 4 cards at each place comprising 13 card runs (4^13) = 67,108,864 points.

SUITS

You cannot have anything less than all cards counted (same with runs, above). Therefore you have 13 clubs, 13 hearts, 13 diamonds and 13 spades = 52 points.

Next are the fifteens. Yes this was crunched manually.

Combination Givens and Multipliers:

There is one unique combination of 4 of the same card. (one way to have four 2's)

There are four unique combination of 3 of the same card. (four ways to have three 5's)

There are six unique combinations of 2 of the same card. (six ways to have two 7's)

There are four unique one-card "combinations" of a card (there are four 9's in a deck)

These multipliers (1, 4, 6 or 4) will be used below based on the composition of each unique sum-15 structure.

Note for Tens: there are 16 unique ten-point cards (4 each of 10s, jacks, queens, kings)

Card combinations in a construct are always made "going even then down" to avoid double counting. Example we count 10+5. But never 5+10. The even part is we'd count 7+7 then down = 7+7+1. Pattern reveals itself quickly.

Construct Format:

cards that add to fifteen (card + card + card)

then ...

then the "combination givens" multipliers based on the extent to which cards in the construct repeat

= total number of combinations

then the reminder that each combination that adds to 15 is worth 2 points

and the total # of points

Using the first construct in the TENS section as an example:

T+5 (one of the 10point cards like 10/J/Q or K and one of the 5s)

...

16 possible Ts x 4 possible 5s

= 64 combinations

times 2 points per combination

= 128 points

TENS

T+5...16x4 = 64 @ 2pts = 128 pts

T+4+1...16x4x4 = 256 @ 2pts = 512 pts

T+3+2...16x4x4 = 256 @ 2pts = 512 pts

T+3+1+1...16x4x6 = 384 @ 2pts = 768 pts

T+2+2+1...16x6x4 = 384 @ 2pts = 768 pts

T+2+1+1+1...16x4x4 = 256 @ 2pts = 512 pts

TENS TOTAL = 3200

NINES

9+6...4x4 = 16 @ 2pts = 32 points

9+5+1...4x4x4 = 64 @ 2pts = 128 pts

9+4+2...4x4x4 = 64 @ 2pts = 128 pts

9+4+1+1...4x4x6 = 96 @ 2pts = 192 pts

9+3+3...4x6 = 24 @ 2pts = 48 pts

9+3+2+1...4x4x4x4 = 256 @ 2pts = 512 pts

9+3+1+1+1...4x4x4 = 64 @ 2pts = 128 pts

9+2+2+2...4x4 = 16 @ 2pts = 32pts

9+2+2+1+1...4x6x6 = 144 @ 2pts = 288 pts

9+2+1+1+1+1...4x4x1 = 16 @ 2pts = 32 pts

NINES TOTAL = 1520

EIGHTS

8+7...4x4 = 16 @ 2pts = 32pts

8+6+1...4x4x4 = 64 @ 2pts = 128 pts

8+5+2...4x4x4 = 64 @ 2pts = 128 pts

8+5+1+1...4x4x6 = 96 @ 2pts = 192 pts

8+4+3...4x4x4 = 64 @ 2pts = 128 pts

8+4+2+1...4x4x4x4 = 256 @ 2pts = 512 pts

8+4+1+1+1...4x4x4 = 64 @ 2pts = 128 pts

8+3+2+2...4x4x6 = 96 @ 2pts = 192 pts

8+3+2+1+1...4x4x4x6 = 384 @ 2pts = 768 pts

8+3+1+1+1+1...4x4x1 = 16 @ 2pts = 32 pts

8+2+2+2+1...4x4x4 = 64 @ 2pts = 128 pts

8+2+2+1+1+1...4x6x4 = 96 @ 2pts = 192 pts

EIGHTS TOTAL = 2562

SEVENS

7+7+1...6x4 = 24 @ 2pts = 48 pts

7+6+2...4x4x4 = 64 @ 2pts = 128 pts

7+6+1+1...4x4x6 = 96 @ 2pts = 192 pts

7+5+3...4x4x4 = 64 @ 2pts = 128 pts

7+5+2+1...4x4x4x4 = 256 @ 2pts = 512 pts

7+5+1+1+1...4x4x4 = 64 @ 2pts = 128 pts

7+4+4...4x6 = 24 @ 2pts = 48 pts

7+4+3+1...4x4x4x4 = 256 @ 2pts = 512 pts

7+4+2+2...4x4x6 = 96 @ 2pts = 192 pts

7+4+2+1+1...4x4x4x6 = 384 @ 2pts = 768 pts

7+4+1+1+1+1...4x4x1 = 16 @ 2pts = 32 pts

7+3+3+2...4x6x4 = 96 @ 2pts = 192 pts

7+3+3+1+1...4x6x6 = 144 @ 2pts = 288 pts

7+2+2+2+2...4x1 = 4 @ 2pts = 8 pts

7+2+2+2+1+1...4x4x6 = 96 @ 2pts = 192 pts

7+2+2+1+1+1+1...4x6x1 = 24 @ 2pts = 48 pts

SEVENS TOTAL = 3416

SIXES

6+6+3...6x4 = 24 @ 2pts = 48 pts

6+6+2+1...6x4x4 = 96 @ 2pts = 192 pts

6+6+1+1+1...6x4 = 24 @ 2pts = 48 pts

6+5+4...4x4x4 = 64 @ 2pts = 128 pts

6+5+3+1...4x4x4x4 = 256 @ 2pts = 512 pts

6+5+2+1+1...4x4x4x6 = 384 @ 2pts = 768 pts

6+5+1+1+1+1...4x4x1 = 16 @ 2pts = 32 pts

6+4+4+1...4x6x4 = 96 @ 2pts = 192 pts

6+4+3+1+1...4x4x4x6 = 384 @ 2pts = 768 pts

6+4+2+1+1+1...4x4x4x4 = 256 @ 2pts = 512 pts

6+3+3+3...4x4 = 16 @ 2pts = 32pts

6+3+3+2+1...4x6x4x4 = 384 @ 2pts = 768 pts

6+3+3+1+1+1...4x6x4 = 96 @ 2pts = 192 pts

6+3+2+2+2...4x4x4 = 64 @ 2pts = 128 pts

6+3+2+2+1+1...4x4x6x6 = 576 @ 2pts = 1152 pts

6+3+2+1+1+1+1...4x4x4x1 = 64 @ 2pts = 128 pts

6+2+2+2+2+1...4x1x4 = 16 @ 2pts = 32 pts

6+2+2+2+1+1+1...4x4x4 = 64 @ 2pts = 128 pts

SIXES TOTAL = 5760

FIVES

5+5+5...4 @ 2 pts = 8 pts

5+5+4+1...6x4x4 = 96 @ 2pts = 192 pts

5+5+3+2...6x4x4 = 96 @ 2pts = 192 pts

5+5+3+1+1...6x4x6 = 144 @ 2pts = 288 pts

5+5+2+2+1...6x6x4 = 144 @ 2pts = 288 pts

5+5+2+1+1+1...6x4x4 = 96 @ 2pts = 192 pts

5+4+4+2...4x6x4 = 96 @ 2pts = 192 pts

5+4+4+1+1...4x6x6 = 144 @ 2pts = 288 pts

5+4+3+3...4x4x6 = 96 @ 2pts = 192 pts

5+4+3+2+1...4x4x4x4x4 = 1024 @ 2pts = 2048 pts

5+4+3+1+1+1...4x4x4x4 = 256 @ 2pts = 512 pts

5+4+2+2+2...4x4x4 = 64 @ 2pts = 128 pts

5+4+2+2+1+1...4x4x6x6 = 576 @ 2pts = 1152 pts

5+4+2+1+1+1+1...4x4x4x1 = 64 @ 2pts = 128 pts

5+3+3+3+1...4x4x4 = 64 @ 2pts = 128 pts

5+3+3+2+1+1...4x6x4x6 = 576 @ 2pts = 1152 pts

5+3+3+1+1+1+1...4x6x1 = 24 @ 2pts = 48 pts

5+3+2+2+2+1...4x4x4x4 = 256 @ 2pts = 512 pts

5+3+2+2+1+1+1...4x4x6x4 = 384 @ 2pts = 768 pts

5+2+2+2+2+1+1...4x1x6 = 24 @ 2pts = 48 pts

5+2+2+2+1+1+1+1...4x4x1 = 16 @ 2 pts= 32 pts

FIVES TOTAL = 8488

FOURS

4+4+4+3...4x4 = 16 @ 2pts = 32 pts

4+4+4+2+1...4x4x4 = 64 @ 2pts = 128 pts

4+4+4+1+1+1...4x4 = 16 @ 2pts = 32 pts

4+4+3+3+1...6x6x4 = 144 @ 2pts = 288 pts

4+4+3+2+1+1...6x4x4x6 = 576 @ 2pts = 1152 pts

4+4+3+1+1+1+1...6x4x1 = 24 @ 2pts = 48 pts

4+4+2+2+2+1...6x4x4 = 96 @ 2pts = 192 pts

4+4+2+2+1+1+1...6x6x4 = 144 @ 2pts = 288 pts

4+3+3+3+2...4x4x4 = 64 @ 2pts = 128 pts

4+3+3+3+1+1...4x4x6 = 96 @ 2pts = 192 pts

4+3+3+2+1+1+1...4x6x4x4 = 384 @ 2pts = 768 pts

4+3+2+2+2+2...4x4x1 = 16 @ 2pts = 32 pts

4+3+2+2+1+1+1+1...4x4x6x1 = 96 @ 2pts = 192 pts

4+2+2+2+2+1+1+1...4x1x4 = 16 @ 2pts = 32 pts

FOURS TOTAL = 3504

THREES

3+3+3+3+2+1...1x4x4 = 16 @ 2pts = 32 pts

3+3+3+3+1+1+1...1x4 = 4 @ 2pts = 8 pts

3+3+3+2+2+2...4x4 = 16 @ 2pts = 32 pts

3+3+3+2+2+1+1...4x6x6 = 144 @ 2pts = 288 pts

3+3+3+2+1+1+1+1...4x4x1 = 16 @ 2pts = 32 pts

3+3+2+2+2+2+1...6x1x4 = 24 @ 2pts = 48 pts

3+3+2+2+2+1+1+1...6x4x4 = 96 @ 2pts = 192 pts

3+2+2+2+2+1+1+1+1...4x1x1 = 4 @ 2pts = 8 pts

THREES TOTAL = 640

There are no TWOS or ONES when we follow the "going even then down" rule: They never add up to fifteen: 2+2+2+2+1+1+1+1 = 12.

Grand Total for the Fifteens = 29,090 points.

Final Tally:

Quads = 156

Runs = 67,108,864

Suits = 52

Fifteens = 29,090

TOTAL: 67,138,162 points in a cribbage deck.

Sorry, no knobs or points for turning a Jack. But there are gimmies. What did I miss?

Cheers.

But with whom would you be playing?

************************* boyydz here **********************

There are some errors in the above answer. First, each of the 4^13 13-card runs is worth 13 points. Thus, the total run value is 4^13*13 = 872,415,232!

In the fifteens:

EIGHTS: Missed 8+3+3+1...4x6x4 = 96 @ 2 pts = 192 pts. Also, the given numbers actually total 2560, not 2562. Thus total for EIGHTS should be 2752.

SEVENS: Missed 7+3+2+2+1...4x4x6x4 = 384 @ 2 pts = 768 pts. Missed 7+3+2+1+1+1...4x4x4x4 = 256 @ 2 pts = 512 pts. Thus, the correct total for SEVENS is 4696.

SIXES: Missed 6+4+3+2...4x4x4x4 = 256 @ 2 pts = 512 pts. Missed 6+5+2+2...4x4x6 = 96 @ 2 pts = 192 pts. Missed 6+4+2+2+1...4x4x6x4 = 384 @ 2 pts = 768 pts. Thus, the correct total for SIXES is 7232.

FIVES: Missed 5+3+3+2+2...4x6x6 = 144 @ 2 pts = 288 pts. Thus, the correct total for FIVES is 8776.

FOURS: Missed 4+4+3+2+2...6x4x6 = 144 @ 2 pts = 288 pts. Missed 4+3+3+2+2+1...4x6x6x4 = 576 @ 2 pts = 1152 pts. Missed 4+3+2+2+2+1+1...4x4x4x6 = 384 @ 2 pts = 768 pts. Thus, the correct total for FOURS is 5712.

The earlier answer missed 5440 points for 15s, and it overtotaled by 2. Thus the correct total score for 15s is 34,528.

The earlier answer was correct - the pairs are worth 13x12 = 156.

Thus, the total for pairs, runs, and 15s is 156 + 872,415,232 + 34,528 = 872,449,916, which is the answer I would give. If you want to add 13 points for each of 4 13-card flushes (doesn't really make sense to me, since your entire hand must be one suit to count a flush), that makes 872,449,968.

Answer 2

Alot