11,051 Pages

This page contains card game-related numbers. Numbers related to the tile-based games Mahjong and Rummikub are also included.

## List of card game-related numbers

• There are 104 playing cards in a typical rummy deck without jokers.
• The board game of Rummikub uses 106 tiles.
• There are 108 playing cards in an UNO deck.
• There are 108 or 110 playing cards in a rummy deck with jokers.
• The highest possible game value (Grand ouvert with all four jacks) in the German card game of Skat is 264.
• A common variant of the German card game of Schafkopf uses 24 cards, of which six cards will be given to each of the four players, resulting in 134,596 hands.
• There are $$9!=362,880$$ possible ways to arrange a sequence of moves that fills a $$3\times 3$$ tic tac toe board and $$255,168$$ possible games of tic tac toe if only counting valid games. (where rotations and reflections of other games are counted as different games) There are $$81,792$$ possible games which end with a win on the ninth move, $$46,080$$ possible draws, $$72,576$$ possible games that end in a win at the eighth move, $$47,952$$ that finish on the seventh, $$5,328$$ that end on the sixth and $$1,440$$ that end on the fifth.
• In the card game of poker, a poker hand can be any combination of 5 cards of a standard 52-card deck. Therefore, the number of possible combinations is equal to 52C5 = 2,598,960.
• It is also equal to the number of possible combinations in a 5/52 lottery available in some U.S. states, such as Arizona, Indiana and Kentucky, where you must pick 5 cards out of 52, or they are generated by a terminal.
• Its prime factorization is 24 × 3 × 5 × 72 × 13 × 17.
• A common variant of the German card game of Doppelkopf uses 40 cards (two copies of 20 types), of which 10 cards will be given to each of the four players, resulting in 8,533,660 hands.
• The German card game of Schafkopf uses 32 cards, of which eight cards will be given to each of the four players, resulting in 10,518,300 hands.
• The German card game of Skat uses 32 cards, of which 10 cards will be given to each of the three players, and two cards remain on the table, resulting in 64,512,240 hands.
• The German card game of Doppelkopf uses 48 cards (two copies of 24 types), of which 12 cards will be given to each of the four players, resulting in 287,134,346 hands.
• The Chinese tile game of Mahjong uses 136 tiles (four copies of 34 types), of which 13 tiles will be given to each of South, West and North, resulting in 98,521,596,000 hands.
• The Chinese tile game of Mahjong uses 136 tiles (four copies of 34 types), of which 14 tiles will be given to East, resulting in 326,520,504,500 hands.
• The Anglo-American card game of contract bridge uses 52 cards, of which 13 cards will be given to each of the four players, resulting in 635,013,559,600 hands.
• A common variant of the German card game of Schafkopf uses 24 cards, of which six cards will be given to each of the four players, resulting in 2,308,743,493,056 card distributions.
• The German card game of Skat uses 32 cards, of which 10 cards will be given to each of the three players, and two cards remain on the table, resulting in 2,753,294,408,504,640 card distributions.
• The German card game of Schafkopf uses 32 cards, of which eight cards will be given to each of the four players, resulting in 99,561,092,450,391,000 card distributions.
• A common variant of the German card game of Doppelkopf uses 40 cards (two copies of 20 types), of which 10 cards will be given to each of the four players, resulting in 293,631,119,403,639,732 card distributions.
• The German card game of Doppelkopf uses 48 cards (two copies of 24 types), of which 12 cards will be given to each of the four players, resulting in 2,248,575,441,654,260,591,964 card distributions.
• The Anglo-American card game of contract bridge uses 52 cards, of which 13 cards will be given to each of the four players, resulting in 53,644,737,765,488,792,839,237,440,000 card distributions.

## Approximations of these numbers

For 134,596:

Notation Lower bound Upper bound
Scientific notation $$1.34596 \times 10^5$$
Arrow notation $$51\uparrow3$$ $$367↑2$$
Steinhaus-Moser Notation 6[3] 7[3]
Copy notation 1[6] 2[6]
Taro's multivariable Ackermann function A(3,14) A(3,15)
Pound-Star Notation #*(36)*3 #*(37)*3
BEAF {52,3} {53,3}
Hyper-E notation E5 E[53]3
Hyperfactorial array notation 8! 4!1
Fast-growing hierarchy $$f_2(13)$$ $$f_2(14)$$
Hardy hierarchy $$H_{\omega^2}(13)$$ $$H_{\omega^2}(14)$$
Slow-growing hierarchy $$g_{\omega^4\times5+\omega\times4}(13)$$

For 53,644,737,765,488,792,839,237,440,000:

Notation Lower bound Upper bound
Scientific notation $$5.364\times10^{28}$$ $$5.365\times10^{28}$$
Arrow notation $$12\,712\uparrow7$$ $$12\,713\uparrow7$$
Steinhaus-Moser Notation 21[3] 22[3]
Copy notation 4[29] 5[29]
Chained arrow notation $$12\,712\rightarrow7$$ $$12\,713\rightarrow7$$
Taro's multivariable Ackermann function A(3,92) A(3,93)
Pound-Star Notation #*(8,4,6)*8 #*(8,4,6)*9
PlantStar's Debut Notation [17] [18]
BEAF & Bird's array notation {12712,7} {12713,7}
Hyper-E notation 5E28 6E28
Bashicu matrix system (0)(0)(0)[2964] (0)(0)(0)[2965]
Hyperfactorial array notation 27! 28!
Strong array notation s(12712,7) s(12713,7)
Fast-growing hierarchy $$f_2(88)$$ $$f_2(89)$$
Hardy hierarchy $$H_{\omega^2}(88)$$ $$H_{\omega^2}(89)$$
Slow-growing hierarchy $$g_{\omega^{7}}(12\,712)$$ $$g_{\omega^{7}}(12\,713)$$
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