Many games have more than pure entertainment value. Indeed some are
clearly exploiting ideas we now consider to be mathematics.
The card game known as solitaire or patience is one such example. [See
Klondike.]
Solitaire is quite complicated. The seven open cards at
the start might include an Ace. What is the chance that there is no ace
at start? It is (12/13)7 - approximately 0.571. If there is an
Ace it can be moved to the ordered-pile section. Whether there are
other moves or no moves, or the probability that a shuffle results
in a winnable game are all answerable by mathematical analysis. Should that
prove to be intractable statistical simulation could yield an answer.
The bicyclecards web site says this about Klondike/Solitaire/Patience:
it is one of the most difficult Solitaire games to win.
In standard Klondike the twenty-four cards that remain are cycled
through by looking at the 3rd first. If it isn't used, the 6th card is
examined. The process is repeated, and the case where the shuffle is not
solvable may be revealed so, if every 3rd card is unplayable.
A related game deals out all the remaining twenty-four cards, as
four-long stacks following the 2nd through 7th open cards. Play in this
form starts whenever a one-rank-lower card of opposite color is visible
for some tip open card.
Other games likewise presenting fundamental ideas are Casino and Rummy.
Four suits partition a deck of 52 cards. Thirteen Spades, Hearts,
Diamonds, and Clubs are one division. Another is the
picture-card/number-card separation.
Besides recognizing the suit, the number value of a card enables
familiarity with quantity, and comparisons of two or more cards.
Card games usually involve random outcomes. Nevertheless players' skills
impact the final result.
Probability is presented using simple cases like tossing a coin and
observing whether the outcome is a head or a tile. Coins are modeled by
two alternatives, although standing on edge is technically possible
though extremely rare in practice.
An ancient game involved tossing a six-sided cube. Whichever single
number occurs, a model of probability of any single value being the
outcome, has each occurring one-sixth of the cases.