[Guest]

My first question on these forums. Hope you like it.

There's an addicting solitaire-type game on Facebook called "Catch 21". Here are the rules:

You have a standard deck of cards (no jokers) with 4 columns to play in. You flip the cards over one at a time into any of the four columns, adding the cards in a given column up like blackjack. When you hit "21", the column is cleared and you can start a new set in it's place. You cannot play a card that would put you over 21. Face cards are worth 10 and aces are worth 1 or 11.

Scoring:

A "21" is worth 50 points

If you play five cards adding up to 21 or less, you get 100 points.

The two black jacks are worth 75 points each and automatically clear any column you play them in.

What is the highest number of points you can get in a single deck? And what combination of cards do you use to get there?

[Guest]

Note: If you play the real game, you know you also get more points the faster you burn through the deck. For the purposes of this question, we're not considering speed.

[bonanova]

1. Since you're looking for the score with a single deck why does speed come into play?
   
2. Play the spade A then the spade J, clearing the column.
   Is your score 125 [50 for the AJ 21 and 75 for the black J] or 75 [21 is not scored]?
   

I can get 950.

[Guest]

1. Since you're looking for the score with a single deck why does speed come into play?
   
2. Play the spade A then the spade J, clearing the column.
   
   Is your score 125 [50 for the AJ 21 and 75 for the black J] or 75 [21 is not scored]?
   

I can get 950.

1. I'm saying speed doesn't come into play. In the computer game, you get bonus points for going faster. We're leaving that part out.

2. If you play a jack of spades or clubs to get to 21, you only get the 75 points. However, if the jack of spades or clubs is the 5th card you play, you get 100 points for using five cards instead of 75 for the jack.

[bonanova]

Everything can be played into a single column.

Red suits:

5,6,J [50] 4,7,10 [50] 3,8,Q [50] A,K [50] 2, 9 left over later in the deck 400 points

Black suits:

J [75] 4,7,10 [50] 3,8,Q [50] A,K [50] 2, 5, 6, 9 left over later in the deck 450 points

Cards from any suit:

6,5,5,2,2 [100] with the remaining 9,9,9,9,6,2,2 at the bottom of the deck 100 points

[Guest]

Ok, first of all, let's assume you will maximize the value of the two black jacks and play them by themselves.

The remaining 50 cards have a total combined face value of 360 (assuming the aces are used as 11s which is a must for a top score). Divide that by 21 and you get 17.14.

That means you can get the maximum points if you can arrange the cards in 17 separate stacks of 21 (50 points each) plus the two black jacks (75 points each), that gives a total of 1000 points.

There are many ways to get 17 stacks of 21, here's one as proof:

1. 10 - A

2. 10 - A

3. 10 - A

4. 10 - A

5. J - 2 - 9

6. J - 2 - 9

7. Q - 2 - 9

8. Q - 3 - 8

9. Q - 3 - 8

10. Q - 3 - 8

11. K - 4 - 7

12. K - 4 - 7

13. K - 5 - 6

14. K - 5 - 6

15. 5 - 5 - 7 - 4

16. 6 - 7 - 8

17. 2 - 4 - 6 - 9

Then add in the two black jacks played individually for a total of 1000 points.

Note, this leaves a lone 3 which can be left by itself or played with one of the black jacks.

[superprismatic]

A slight modification of Magic Man's nice post yields a higher score:

50pts -> 2. 10 - A
50pts -> 3. 10 - A
50pts -> 4. 10 - A
50pts -> 5. J - 2 - 9
50pts -> 6. J - 2 - 9
50pts -> 7. Q - 2 - 9
50pts -> 8. Q - 3 - 8
50pts -> 9. Q - 3 - 8
50pts -> 10. Q - 3 - 8
50pts -> 11. K - 4 - 7
50pts -> 12. K - 4 - 7
50pts -> 13. K - 5 - 6
50pts -> 14. K - 5 - 6
50pts -> 15. 6 - 7 - 8
50pts -> 16. 5 - 7 - 9
100pts -> 17. 2 - 3 - 4 - 5 - 6
75pts -> 18. J(black)
75pts -> 19. 4 - J(black)

 50pts -> 1. 10 - A

For a total of 1050 points.

Edited August 1, 2011 by superprismatic

[Guest]

Excellent post superprismatic, I knew mine could be topped if I could squeeze in a 5 card/100 point play, I just didn't see it.