Frustration (card game)

Frustration is an early 20th century Eastern European patience or card solitaire resembling the banking game of Treize which has its roots in the 1700s. Frustration is similar to but opposite of Hit or Miss.

History

Frustration appears to have been played by the Romani people of Eastern Europe before the Second World War, but came to light in American in the 1990s where it became the subject of mathematical investigation. The game relies purely on luck rather than on skill, and has been both mathematically analyzed and discussed in popular media.^[1] It is an example of a derangement problem in combinatorial mathematics, which can be understood using a combinatorial tool called a rook polynomial. The probability of winning the game has been determined exactly, and is approximately 1.6233%.^[2] The same technique can be applied to variations of the game that use different numbers of suits, and different numbers of cards per suit.

This instantiation of Frustration does not appear in any games compendium; the patience described in the 1993 work, The Complete Book of Card Games, is a double pack game that is played quite differently.^[3]

Rules

As in the Hit or Miss, the player deals the cards from a 52-card deck, and says "ace" when drawing the first card, "two" for the second, then "three, four... nine, ten, jack, queen, king", then starts again with "ace".

The game is lost if the rank of a dealt card matches the rank uttered by the player while dealing it. The game is won if the sequence is successfully repeated four times (and the entire deck is thus dealt out) without any word/card match causing a loss.

References

^ Vos Savant, Marilyn (21 August 1994). "Ask Marilyn: A hat check problem", Parade Magazine. Retrieved 23 October 2020.
^ Doyle, Peter G.; Grinstead, Charles M.; Laurie Snell, J. (2 April 2009). "Frustration Solitaire", arXiv:math/0703900. Retrieved 23 October 2020,
^ The Complete Book of Card Games (1993), p. 73.

Bibliography

_ (1993). The Complete Book of Card Games. London: Ward Lock.

External links

Estimating the probability of winning Frustration Solitaire by simulating 100,000 games in Mathematica

[1] Vos Savant, Marilyn (21 August 1994). "Ask Marilyn: A hat check problem", Parade Magazine. Retrieved 23 October 2020.

[2] Doyle, Peter G.; Grinstead, Charles M.; Laurie Snell, J. (2 April 2009). "Frustration Solitaire", arXiv:math/0703900. Retrieved 23 October 2020,

[3] The Complete Book of Card Games (1993), p. 73.

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