Pictured:
Pic 1: Casio fx-991CN X (China)
Pic 2: Casio fx-570SPX II Iberia (Spain)
Pic 3: Casio fx-92 Collège (France)
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All original content copyright, © 2011-2026. 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.
High Rollers: When Only Even Numbers Remain – Game Strategy
Introduction
In the famous game show High Rollers, which aired from 1975-1980, hosted by Alex Trebek and then again from 1987-1988 hosted by Wink Martindale. The main objective of the game is to eliminate numbers 1 through 9 by rolling dice.
On the game show, there are two rounds*. On the main game, two opponents play against each other. The winner goes on to the Big Numbers where the winner tries to clear all the numbers.
* There were variants, but this was prevailing game modes.
For detailed information: https://en.wikipedia.org/wiki/High_Rollers
Just Even Numbers Left: 2, 4, 6, and 8
From this point, only rolls with even sums are valid. The strategy changes depending on what round is being played.
In a two-player game: You either win by either rolling the last number off the board or getting your opponent to roll an unplayable number. As the game goes on, the chance of rolling an unplayable number increase.
In the Big Numbers bonus round: To win the big prize, typically a $ 10,000 cash jackpot, the only you win is to clear all the numbers.
Ways to roll even numbers:
2: 1,1
4: 1,3; 2,2; 3,1
6: 1,5; 2,4; 3,3; 4,2; 5,1
8: 2,6; 3,5; 4,4; 5,3; 6,2
10: 4,6; 5,5; 6,4
12: 6,6
If both dice has the same number, i.e. 2,2, it is considered a double and it wins the player an Insurance card, which counts as a free roll. At worst, rolling doubles acts as a “roll again”.
With a board consisting of the even numbers 2, 4, 6, and 8, the best way
Roll |
Main Game: Against an Opponent |
During the Big Numbers Bonus Round |
2 |
Only one move: remove the 2 |
Only one move: remove the 2 |
4 |
Only one move: remove the 4. 4 becomes an unplayable roll. |
Only one move: remove the 4. 4 becomes an unplayable roll. |
6 |
Remove the 2 and 4. This eliminates 2, 4, 10, and 12 as valid rolls, leaving only the 6 and 8. |
Remove the 6. This leaves 2, 4, and 8. All even rolls are still good. A roll of 6 can eliminate the 2 and 4 the next roll. |
8 |
Remove the 2 and 6. This eliminates the 2, 6, and 10, leaving only the 4, 8, and 12 (12 wins the game). |
Remove the 8. This leaves 2, 4, and 6. All even rolls are still good. A roll of 8 can eliminate the 2 and 6 the next roll. |
10 |
Remove the 4 and 6. This leaves 2, 8, and 10 as valid rolls on the next turn (10 wins the game). The chance of rolling a 2, 8, or 10 is 1/6 (≈ 16.7%). |
Remove 2 and 8. This leaves 4, 6, and 10 as valid rolls on the next turn (10 wins the game). The chance of rolling a 4, 6, or 10 is 2/9 (≈ 22.2%). |
12 |
Remove on 2, 4, and 6. This leaves only the 8. Chance of rolling 8 is 5/36 (≈ 13.9%). |
Remove the 4 and 8. This leaves the 2 and 6. A roll of 8 can eliminate both the 2 and 6 on the next roll. The chance of rolling a 2, 6, and 8 is 11/36 (≈ 30.6%). |
Source
“High Rollers” Wikipedia. Edited November 10, 2025. Retrieved February 14, 2026. https://en.wikipedia.org/wiki/High_Rollers
Eddie
All original content copyright, © 2011-2026. 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.
Numworks (Python): Parallelograms Described by Vectors
Introduction
The script drawpgram.py draws a parallelogram constructed by a pair of two-dimensional vectors. Both vectors original from the origin of the Cartesian plane ([0, 0]). Let the two vectors be labeled as [x1, y1] and [x2, y2].
This script also calculates the area and perimeter of the constructed parallelogram consisting of the end points (0,0), (x1, y1), (x2, y2), and (x1+x2, y1+y2).
Then the perimeter of the parallelogram is calculated as:
perimeter = 2 * (norm([x1, y1] + norm[x2, y2]) = 2 * (√(x1 + y1) * √(x2, y2))
And the area is calculated as:
area = abs(det([[x1, y1] [x2, y2]])) = abs(x1 * y2 – x2 * y1)
Numworks Script: drawpgram.py
Modules used: Math, PyPlot
Script page: https://my.numworks.com/python/ews31415/drawpgram
# Draw a parallelogram with two vectors
# Edward Shore, 2/15/2026
# Numworks
# drawpgram.py
from math import *
from matplotlib.pyplot import *
print("Draw a parallelogram with 2 vectors")
x1=eval(input("x1? "))
y1=eval(input("y1? "))
x2=eval(input("x2? "))
y2=eval(input("y2? "))
# Area
area=abs(x1*y2-x2*y1)
# Perimeter
perim=2*((x1**2+y1**2)**(1/2)+(x2**2+y2**2)**(1/2))
minx=min([x1,x2,x1+x2,0])
maxx=max([x1,x2,x1+x2,0])
miny=min([y1,y2,y1+y2,0])
maxy=max([y1,y2,y1+y2,0])
axis((minx-1,maxx+1,miny-1,maxy+5))
plot([0,x1],[0,y1],'blue')
plot([0,x2],[0,y2],'purple')
plot([x1,x1+x2],[y1,y1+y2],'purple')
plot([x2,x1+x2],[y2,y1+y2],'blue')
str1="area = {0:.6f}".format(area)
text(minx-1,maxy+4.5,str1)
str2="perim = {0:.6f}".format(perim)
text((minx+maxx)/2,maxy+4.5,str2)
show()
Notes:
1. I use eval(input( “prompt” )) and importing the Math module to allow for expressions to be entered, such as expressions involving pi (π). If I use float(input( “prompt” )) instead, only numbers would be allowed.
2. For the purposes of display, the results are rounded off to six decimal places ({0:.6f}) and displayed in a line. The full precision results of area and perimeter are stored in the variables area and perim, respectively.
Examples
Example 1: [2, 4], [5, 2]
Example 2: [-3, 1], [5, 3]
Example 3: [-6, 0], [0, -4]
Source
Margalit, Dan and Joseph Rabinoff. 2025. “Determinants and Volumes” Interactive Linear Algebra LibreTexts. Accessed February 8, 2026. https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/04%3A_Determinants/4.03%3A_Determinants_and_Volumes
Eddie
All original content copyright, © 2011-2026. 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.
RPN: Solving T * w + Z = Y * w + X (featuring DM42, HP 67)
Introduction and Code
This is inspired in part by the new Casio fx-92 being released where it has added the linear equation:
ax + b = cx + d
( https://tiplanet.org/forum/viewtopic.php?p=280173&sid=2174c3a99692ac8898ff3957db84031a#p280173 (in French), retrieved February 6, 2026)
Solve the equation for w:
T * w + Z = Y * w + X
where the solution is w = (Z – X) ÷ (Y – T)
The values for T, Z, Y, and X are taken directly from the four-level classic RPN stack.
HP 42S/DM42/HP 41C (programmed with a DM42) Code
LBL “TZYX1”
x<>y
R↓
-
R↓
-
R↑
x<>y
÷
RTN
HP 67 Code
001: LBL A; 31, 25, 11
002: x<>y; 35, 52
003: R↓; 35, 53
004: -; 51
005: R↓; 35, 53
006: -; 51
007: R↑; 35, 54
008: x<>y; 35, 52
009: ÷; 81
010: RTN; 35, 52
Stack Results:
Start |
Finish |
T |
Z - X |
Z |
Z - X |
Y |
Y |
X |
(Z – X) ÷ (Y – T) = W (solution) |
Examples
Example 1: 5 * w + 20 = 10 * w + 30
T: 5
Z: 20
Y: 10
X: 30
Solution: w = -2
Example 2: 3 * w – 18 = -2 * w + 16
T: 3
Z: -18
Y: -2
X: 16
Solution: w = 6.8
Example 3: 5 * w + 3 = w + 2
T: 5
Z: 3
Y: 1
X: 2
Solution: w = -0.25
Eddie
All original content copyright, © 2011-2026. 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.