| Version: | 1.0 |
| Date: | 2024-10-06 |
| Title: | A Posteriori Probs of Suits Breaking Evenly Across Four Hands |
| Maintainer: | Barry Zeeberg <barryz2013@gmail.com> |
| Depends: | R (≥ 4.2.0) |
| Imports: | combinat, graphics, stats, utils |
| Description: | We quantitatively evaluated the assertion that says if one suit is found to be evenly distributed among the 4 players, the rest of the suits are more likely to be evenly distributed. Our mathematical analyses show that, if one suit is found to be evenly distributed, then a second suit has a slightly elevated probability (ranging between 10% to 15%) of being evenly distributed. If two suits are found to be evenly distributed, then a third suit has a substantially elevated probability (ranging between 30% to 50%) of being evenly distributed.This package refers to methods and authentic data from Ely Culbertson https://www.bridgebum.com/law_of_symmetry.php, Gregory Stoll https://gregstoll.com/~gregstoll/bridge/math.html, and details of performing the probability calculations from Jeremy L. Martin https://jlmartin.ku.edu/~jlmartin/bridge/basics.pdf, Emile Borel and Andre Cheron (1954) "The Mathematical Theory of Bridge",Antonio Vivaldi and Gianni Barracho (2001, ISBN:0 7134 8663 5) "Probabilities and Alternatives in Bridge", Ken Monzingo (2005) "Hand and Suit Patterns" http://web2.acbl.org/documentlibrary/teachers/celebritylessons/handpatternsrevised.pdfKen Monzingo (2005) "Hand and Suit Patterns" http://web2.acbl.org/documentlibrary/teachers/celebritylessons/handpatternsrevised.pdf. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Encoding: | UTF-8 |
| VignetteBuilder: | knitr |
| Suggests: | knitr, rmarkdown, testthat (≥ 3.0.0) |
| RoxygenNote: | 7.3.1 |
| Config/testthat/edition: | 3 |
| NeedsCompilation: | no |
| Packaged: | 2024-10-17 17:37:56 UTC; barryzeeberg |
| Author: | Barry Zeeberg [aut, cre] |
| Repository: | CRAN |
| Date/Publication: | 2024-10-21 11:41:20 UTC |
compareProbs
Description
organizes invoking evenBreakDriver() for 4 deck sizes, and presenting the results in a table
and in a graph scatter plot of 2 sets of distribution probabilities
Usage
compareProbs(verbose)
Arguments
verbose |
Boolean if TRUE print output data |
Value
returns no value, but has side effects of printing a table and a graph
of the probability of a given distribution of a single suit across 4 hands,
conditioned on the number of suits that are known to be evenly distributed.
Author(s)
Barry Zeeberg
Examples
compareProbs()
evenBreak
Description
compute the probability of a given distribution of a single suit across 4 hands
Usage
evenBreak(D4,n1,n2,n3,PERM)
Arguments
D4 |
one quarter of the size of the deck, normally = 13 |
n1 |
the number of cards in the suit in the hands of player 1 |
n2 |
the number of cards in the suit in the hands of player 2 |
n3 |
the number of cards in the suit in the hands of player 3 |
PERM |
the number of permutations |
Value
returns the probability of a given distribution of a single suit across 4 hands
Author(s)
Barry Zeeberg
Examples
n1<-3
n2<-3
n3<-3
n4<-13-(n1+n2+n3)
PERM<-length(unique(combinat::permn(c(n1,n2,n3,n4))))
PERM
evenBreak(13,n1,n2,n3,1)*length(unique(combinat::permn(c(n1,n2,n3,n4))))
evenBreakDriver
Description
loop through all possible distributions of a single suit across 4 hands
Usage
evenBreakDriver(D4)
Arguments
D4 |
one quarter of the size of the deck, normally = 13 |
Value
returns a table of the probability of a given distribution of a single suit across 4 hands,
conditioned on the number of suits that are known to be evenly distributed.
Author(s)
Barry Zeeberg
Examples
evenBreakDriver(13)