cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A002761 Number of ways of getting a royal flush, other straight flush, 4 of a kind, full house, other flush, other straight, 3 of a kind, 2 pair, a pair or nothing in 5-card poker.

Original entry on oeis.org

4, 36, 624, 3744, 5108, 10200, 54912, 123552, 1098240, 1302540
Offset: 1

Views

Author

N. J. A. Sloane, Koreen M Mielke (mielkk72(AT)VAXA.CIS.UWOSH.EDU)

Keywords

References

  • J. Scarne, Scarne's Complete Guide to Gambling, Simon and Schuster, 1961, p. 582.

Links

Crossrefs

Cf. A002806, A002847.

Formula

From Jianing Song, Apr 06 2019: (Start)
a(n) = A002806(11-n) for 1 <= n <= 10.
Sum_{i=1..10} a(i) = binomial(52,5) = A017768(5). (End)

A014353 Chance of getting nothing, a pair, 2 pair, 3 of a kind, other straight, other flush, full house, 4 of a kind, other straight flush, or a royal flush in poker is 1 in a(n) (rounded to nearest integer).

Original entry on oeis.org

2, 2, 21, 47, 255, 509, 694, 4165, 72193, 649740
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • J. Scarne, Scarne's Complete Guide to Gambling, Simon and Schuster, 1961, p. 582.

Links

Crossrefs

Cf. A002761, A002806.

A143314 Number of hands of n cards containing a straight flush (for n=1 to 52).

Original entry on oeis.org

0, 0, 0, 0, 40, 1844, 41584, 611340, 6588116, 55482100, 380126920, 2177910310, 10644616240, 45049914588, 167011924492, 547315800984, 1597026077496, 4173458163098, 9813490226056, 20841357619302, 40096048882028
Offset: 1

Views

Author

Gerard P. Michon, Aug 06 2008

Keywords

Comments

With a regular deck of 52 playing cards (4 suits of 13 cards: 23456789TJQKA) a "straight flush" consists of 5 cards of the same suit with consecutive values. The ace (A) is considered to come either before the deuce (2) or after the king (K).
The first terms of the sequence are zero because there are no straight flushes in a hand of fewer than 5 cards.

Examples

			a(5) = 40 because each suit allows 10 straight flushes (2 of which contain an ace).
a(44) = 752538149 = C(52,44) - 1 because there's only one way to avoid a straight flush with 44 cards (namely, 2346789JQKA in every suit).
a(45) = 133784560 = C(52,45) because every hand of 45 cards (or more) includes a straight flush.
a(52) = 1 because there's only one "hand" of 52 cards.

Links

Crossrefs

Cf. A002761, A002806, A002834, A002879.

Formula

The generating function is a polynomial: (1+x)^52 - ((1+x)^13 - x^5(1+x)(10 + 61x + 156x^2 + 215x^3 + 169x^4 + 65x^5 + 12x^6 + x^7))^4.

A216076 Number of ways in which each hand can be obtained in a game of 5-card poker, starting with the most probable category.

Original entry on oeis.org

1302540, 1098240, 123552, 54912, 10200, 5108, 3744, 624, 40
Offset: 1

Views

Author

V. Raman, Sep 01 2012

Keywords

Comments

a(1): high card
a(2): pair
a(3): two pair
a(4): three of a kind
a(5): straight
a(6): flush
a(7): full house
a(8): four of a kind
a(9): straight flush

Crossrefs

Cf. A002761, A002806, A002847 (reverse of this sequence).
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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