Type Collecting card combinations
What could be simpler than a game of perfect information
where you deal the cards out in a row and then pick them up one by one? (Or two, or three, as the case may be.)
Simple? Yes - but there's more to this Nim-type game than meets the eye.
Use a 24-card pack consisting of A-K-Q-J-10-9 in each suit.
Shuffle the cards thoroughly and deal them all out, face up, with just enough overlap to enable each
card to be identified. For example:
Take cards one, two or three at a time from right to left
To take cards that form scoring combinations (sets and sequences, as in Rummy) but without taking more cards than
Non-dealer examines the layout and decides whether to play first or second. If second, dealer must play first.
You each in turn draw either one, two or three consecutive cards from the top end of the row until none remain.
(The top end is the one with the fully exposed card -
in the illustration.)
You must place the cards you take face up on the table before you, clearly arranged by suit and rank, so your opponent
can always see what you have taken so far.
The scoring combinations are sets of three or more cards of the same rank and sequences
of three or more cards of the same suit. Any individual card may, if possible, be counted twice, once in a set and
once in a sequence. Your score for the deal consists of two part-scores multiplied together.
First, for combinations, score as follows:
sets: three of a kind 2 points, four of a kind = 8 points
suit-sequences: of three 3, four 4, five 6, six 12 points
Next, total your score for combinations and multiply this by the total number of cards drawn by your
opponent. This gives you your score for the deal.
Theoretically, if you don't make any combination at all you score nothing, since one of the multipliers is zero.
In this case, however, the scores are reversed. The player who took no combination scores whatever the other one
makes, and the other one scores nothing.
Given the layout illustrated above, non-dealer went first, and the number taken at each pair of turns was:
2-2, 2-3, 1-1, 2-3, 1-3, 2-2.
Non-dealer therefore took :
scoring 8 for four Aces, plus 4 for the diamond sequence,
times 14 cards taken by dealer, total 168.
The dealer took :
8 for four Tens, plus 4 for the Kings and Jacks, plus 4 for
the spade sequence, plus 3 for the heart sequence, plus 6 for the
clubs, total 25, times 10 cards taken by non-dealer, total 250.
It's interesting to see what the results would be if the same layout were played in various different ways. Assuming
that non-dealer chose to go first, then
a. if each player always took one card, dealer would win by 96 to 60; b. if they each always took two, non-dealer would win by 144 to 120; and c. if they each always took three, non-dealer would win by 96 to 84.