Jump to content

File:Probability of winning Snakes and Ladders by turns.svg

Page contents not supported in other languages.
This is a file from the Wikimedia Commons
From Wikipedia, the free encyclopedia

Original file (SVG file, nominally 500 × 312 pixels, file size: 37 KB)

Summary

Description
English: Probability of winning a game a Snakes and Ladders within n turns. Location of snakes and ladders placed according to this paper.
Date
Source

Mathematica source code: 

ladders = {{1, 38}, {4, 14}, {9, 31}, {21, 42}, {28, 84}, {36, 44}, {51, 67}, {71, 91}, {80, 100}};
snakes = {{16, 6}, {47, 26}, {49, 11}, {56, 53}, {62, 19}, {64, 60}, {87, 24}, {93, 73}, {95, 75}, {98, 78}};
maxNum = 100;
numDieSides = 6;
f := If[0 <= #2 - #1 <= numDieSides, If[#1 != #2, 1/numDieSides, If[#1 + numDieSides <= maxNum, 0, (numDieSides + #1 - maxNum)/numDieSides]], 0] &;
p = Table[f[i, j], {i, 0, 100}, {j, 0, 100}];
pTranspose = Transpose[p];
transports = Union[snakes, ladders];
For[i = 1, i <= Length[transports], i++, pTranspose[[transports[[i, 2]] + 1]] = pTranspose[[transports[[i, 1]] + 1]] + pTranspose[[transports[[i, 2]] + 1]]]
For[i = Length[transports], i > 0, i--, pTranspose = Delete[pTranspose, transports[[i, 1]] + 1]]
p = Transpose[pTranspose];
For[i = Length[transports], i > 0, i--, p = Delete[p, transports[[i, 1]] + 1]]
points = {{0, 0}};
pPower = IdentityMatrix[Length[p]];
For[x = 0, x <= 250, x++, points = Union[points, {{x, (pPower = pPower.p)[[1, Length[p]]]}}]]
ListPlot[points, Joined -> True, Frame -> True, PlotRange -> {{0, 250}, {0, 1}}, ImageSize -> 500]

After saving the image as an SVG from Mathematica, edit the raw SVG text by adding "width='500' height='312'" to the end of the SVG tag.
Author Self

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
You may select the license of your choice.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

inception

21 October 2011

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current15:46, 21 October 2011Thumbnail for version as of 15:46, 21 October 2011500 × 312 (37 KB)Bender2k14{{Information |Description ={{en|1=Probability of winning a game a Snakes and Ladders within ''n'' turns. Location of snakes and ladders placed according to [http://dx.doi.org/10.2307%2F3619261 this paper].}} |Source

Global file usage

The following other wikis use this file:

Retrieved from "https://en.wikipedia.org/wiki/File:Probability_of_winning_Snakes_and_Ladders_by_turns.svg"