Casio fx-CG50: Plotting the Betting Equation
Introduction
The program BETPLOT plots two equations:
The betting equation, based on logistic equation:
y1(x) = p(x) = 1 / (1 + α*x^β)
α, β: parameters
x: data point, odds given by the booker
p(x): probability, probability that a favorite event happens/wins
The expected profit equation:
y2(x) = p(x) * x - (1 - p(x))
Casio fx-CG 50 Program: BETPLOT
The characters α, β, and # are found in the CHAR sub menu (outside of the PRGM menu). If you have a monochrome calculator or just don't want color, ignore the color commands.
The program then graphs the resulting equation. The variables Y1 and Y2 (with the bold Y) represent functions of X.
"BETTING EQN."
"DAVID SUMPTER"
Red "1÷(1+αX^β)"◢
"INCREMENT"?→1
"# STEPS"?→S
"α"?→A
"β"?→B
"(1+A×X^B)^-1"→Y1
"X×Y1-(1-Y1)"→Y2
Y=type
SetG-Color Black, 1
SetG-Color Green, 2
Seq(K,K,0,S×I+I,I)→List 1
(1+A×List 1^B)^-1→List 2
List 2×List1-(1-List 2)→List 3
ClrText
"COL. 1: X"
"COL. 2: P(X)"
"COL. 3: EXP. WIN"◢
List→Mat(List 1,List 2,List 3)◢
ViewWindow 0,S×I,I,Min(List 2)-1,Max(List 2),0.25
AxesOn
GridOn
DrawGraph
Examples
Example 1:
α = 1.3, β = 1.01
Example 2:
α = 1.16, β = 1.25
Source:
Sumpter, David. The Ten Equations That Rule the World: And How You Can use Them Too. Flatiron Books: New York. 2021. ISBN 978-1-250-24696-7
Eddie
All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
