High Rollers: When Only Even Numbers Remain – Game Strategy

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.

OT: Race to the Finish Line Board Game

OT:   Race to the Finish Line Board Game 

What Is Needed

Your printer - preferably a color printer

Scissors

Markers:  the file contains four markers you can cut out (gray box), but any sort of small marker will do

A single die (use one of the dice from a pair of dice).  Alternates: playing cards of Ace through Six (Ace counts as one), six index cards labeled one through six (shuffle each time), or a calculator that can generate random integers 1-6

Rules

The object is simple:  get your marker to the finish line.  This game for at least 2 players.  You can determine the order which turns are taken. 

There are several spaces:

Green:  Lucky Space, Roll Again!  The player who lands on this space takes another turn. 

Red:  Stop!, Lose a Turn:  The player that lands here has his/her next turn skipped.

Blue:  Chance?  Draw one of the blue chance cards (see the bottom on the file).  You can add or transfer the chance cards to index cards, customize it any way you want. For young children, play without the chance cards if you want. 

I hope this game provides some entertainment in these tough times (and beyond).  Feel free to comment some creative ideas. 

You can download the jpeg and pdf files here (zip drive): 

https://drive.google.com/open?id=1LPJc5rh-2b17wtu9A6UtyaY5fkJ8Oxvl


(P.S. There is no cost)

Take care, stay sane, stay healthy, and love,


Eddie

All original content copyright, © 2011-2020.  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.

TI-84 Plus and Casio fx-CG50: Which Die Wins?

TI-84 Plus and Casio fx-CG50: Which Die Wins?

Introduction:  Which Die Wins? 

The program DICEODDS compares a pair of dice against each other.  Each die, having values on its six faces and a different distribution of those values, is rolled against each other.  The program determines which die has a better chance of winning.

The face of each die can have any value, and values can repeat.  These dice can and usually are  different from the standard dice (1, 2, 3, 4, 5, 6).

Example 1:

Die 1 is your standard die:  {1, 2, 3, 4, 5, 6}
However, Die 2 has all threes:  {3, 3, 3, 3, 3, 3}

If we roll Die 1 against Die 2, Die 1 wins if a 4, 5, or 6 is rolled.  The odds of Die 1 having a higher value is 1/2. 

Example 2:

Die 1:  {3, 3, 3, 4, 4, 4}
Die 2: {2, 2, 2, 2, 7, 7}

Die 1 wins when a 2 is rolled on Die 2, which occurs 4/6 or 2/3 of the time.  If a 7 is rolled from Die 2, then Die 2 wins, and this has a probability of 1/3. 

DICEODDS compares each value of Die 1 against Die 2 on a single roll of each die.

This is an idea based on a article from James Grime, mathematician who is part of Numberphile. (see Source below)  Numberphile has a YouTube channel which discusses mathematics.   

Grime starts the article by presenting a game where two players choose one of three dies.  The red die has five 3s and one 6, the blue die has three 2s and three 5s, and the olive has one 1 and five 4s.  By comparing dies against each other, the red has a better chance of winning over blue, the blue has better chance of winning over olive, and olive has a better chance of winning over red.  It happens that the dice in this game represent paper-rock-scissors.

Grime also covers games where a chosen die is rolled twice during a game.  There is Efron Dice, a game involving choosing one of four dice (all 3s, half 0s and half 4s, half 1s and half 5s, half 2s and half 6s).  Grime also presents a game involving five dice, each die with an equal chance of winning. 

Dice are considered to be non-transitive when in a game of comparing dice, no die is dominant.

Running DICEODDS

DICEODDS compares two dice on a single role and their probability of winning.  The user is allowed to either enter their own values or generate two random dice, with values ranging from 0 to 9.  Values can repeat, and if you want, do not have to be positive integers.  The screen shots below are from the Casio fx-CG50 version of DICEODDS. 

TI-84 Plus Program DICEODDS

"2019-06-03 EWS"
Menu("WHICH DIE WINS?","RANDOM DICE",1,"ENTER DICE",2)
Lbl 1
seq(randInt(0,9),X,1,6)→L₁
seq(randInt(0,9),X,1,6)→L₂
Goto 3
Lbl 2
Disp "ENTER DIE OF 6 VALUES"
Input "DIE 1: ",L₁
Input "DIE 2: ",L₂
Lbl 3
0→P
For(I,1,6)
sum(L₁(I)>L₂)/6*1/6→F
P+F→P
End
ClrHome
Disp "DIE 1,2",L₁,L₂,"ODDS DIE 1 WINS",P▶Frac,"ODDS DIE 2 WINS",(1-P)▶Frac

Casio fx-CG50 Program DICEODDS - (text file format)

'ProgramMode:RUN
"2019-06-04 EWS"
Menu "WHICH DIE WINS?","RANDOM DICE",1,"ENTER DICE",2
Lbl 1
6->Dim List 1
6->Dim List 2
For 1->I To 6
RanInt#(0,9)->List 1[I]
RanInt#(0,9)->List 2[I]
Next
Goto 3
Lbl 2
"ENTER DIE: 6 VALUES"
"DIE 1:"?->List 1
"DIE 2:"?->List 2
Lbl 3
0->P
For 1->I To 6
Sum (List 1[I]>List 2)/6*1/6->F
P+F->P
Next

ClrText
Red Locate 1,1,"DIE 1:"
Blue Locate 1,2,"DIE 2:"
For 1->I To 6
6+2*I->J
Red Locate J,1,List 1[I]
Blue Locate J,2,List 2[I]
Next
Locate 1,4,"ODDS DIE 1 WINS:"
Red Locate 1,5,P
Locate 1,6,"ODDS DIE 2 WINS:"
Blue Locate 1,7,1-P

Source:

Grime, James "The Bizzare World of Nontransitive Dice: Games for Two or More Players" from:
Pritici, Micrcea (editor) "The Best Writing on Mathematics 2018"  Princeton University Press: Princeton, NJ.  2019  ISBN 978-0-691-18276-6

The article can also be found on the web:  https://singingbanana.com/dice/article.htm
(Retrieved June 5, 2019)

Eddie

All original content copyright, © 2011-2019.  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.

HP 32SII and HP Prime: Throwing Dice

HP 32SII and HP Prime: Throwing Dice

Note: Symbols that are produced by Unicode should, but may not show up on all browsers. Please make sure your browsers are updated to the latest version.  

⚀ ⚁ ⚂ ⚃ ⚄ ⚅

Let Em’ Roll

One way to simulate a pair of dice being thrown is to generate two random integers between 1 through 6.  The integers are either shown as a pair or vector of integers.  For calculators that do not have a list capacity or want a more compact representation, the program for the HP 32S II (which can easily apply almost to any other programming calculator), in the format A.0B, where A is one die and B is the other.   For example, 3.06 represents a 3 and a 6 being thrown.

The formula would be:   RandInt(1,6) + RandInt(1,6)/100

On certain Sharp calculators, such as the Sharp EL-W516T, the R.DICE function generates a single digit between 1 and 6.

HP 32 SII Program: Dice Generator

D01 LBL D

D02 RANDOM

D03 6

D04 *

D05 1

D06 +

D07 IP

D08 1

D09 %

D10 RANDOM

D11 6

D12 *

D13 1

D14 +

D15 IP

D16 +

D17 RTN

HP Prime:  Graphical Representation of Dice

We can also use the Unicode representation of dice.

Unicode Character	Decimal	Hexadecimal
⚀	9856	2680
⚁	9857	2681
⚂	9858	2682
⚃	9859	2683
⚄	9860	2684
⚅	9861	2685

Unicode characters need to be in strings.  The HP Prime program RDICE returns a list, the roll in compact format, along with the Unicode representation.  This is only one of many ways to do it.

An example output of RDICE is {4.02, “⚃”, “⚁”}

HP Prime Program: RDICE

EXPORT RDICE()

BEGIN

// rolling dice A.0B

LOCAL A, B, C, D;

A≔RANDINT(1,6); C≔9855+A;

B≔RANDINT(1,6); D≔9855+B;

RETURN {A+B/100, CHAR(C), CHAR(D)};

END;

Have fun and roll those dice,

Eddie

All original content copyright, © 2011-2018.  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.  Please contact the author if you have questions.

High Rollers: Game Show and Possible Sums with the TI-84 Plus

High Rollers:  Game Show and Possible Sums with the TI-84 Plus

If you have a group of numbers, what are the possible sums you can make?  We’re talking about combinations of 1, 2, to as many numbers you have.  This is one of the key elements of the classic game show High Rollers (1970s, 1987-1988), a dice rolling game based on Shut The Box. 

To whet your appetite, click on the links below to see classic episodes (the links should be good as of 3/15/2017).  The first two links are from episodes from the 1978-1980 series with Alec Trebek (with facial hair) and the last two links are from episodes from the 1987-1988 series with Wink Martindale. We’ll get to the game show later in this blog entry. (no ownership implied, these are from other YouTube accounts)

https://www.youtube.com/watch?v=nsxQoDM0rd0&t=1172s

https://www.youtube.com/watch?v=urzJINgMu3E

https://www.youtube.com/watch?v=j951e0r0EB8

https://www.youtube.com/watch?v=OeD__GYvZZk

The Program POSSUMS

The program POSSUMS calculates all possible sums created by a set of numbers (2, 3, or 4).  With n numbers available, there are 2^n – 1 possible sums.

For n = 2, with let A and B represent the numbers.   There are 2^2 -1  = 3 possible sums:

A, B, A + B

For n = 3 (A, B, C), there are 2^3 – 1 = 7 possible sums:

A, B, C, A + B, A + C, B + C, A + B + C

For n = 4 (A, B, C, D) there are 2^4 – 1 = 15 possible sums:

A, B, C, D, A + B, A + C, A + D, B + C, B + D, B + C, A + B + C, A + B + D, A + C + D, B + C + D, A + B + C + D

The program POSSUMS allows all possible sums, including repeats.

TI-84 Plus Program POSSUMS

Menu("SUMS FROM AVAIL. NUMBERS","2",2,"3",3,"4",4)

Lbl 2

Prompt A,B

{A,B,A+B}→L₁

Goto 5

Lbl 3

Prompt A,B,C

{A,B,C,A+B,A+C,B+C,A+B+C}→L₁

Goto 5

Lbl 4

Prompt A,B,C,D

{A,B,C,D,A+B,A+C,A+D,B+C,B+D,C+D,A+B+C,A+C+D,A+B+D,B+C+D,A+B+C+D}→L₁

Goto 5

Lbl 5

SortA(L₁)

Pause L₁

Examples

3 Numbers:  A = 2, B = 3, C = 5

Result:  {2, 3, 5, 5, 7, 8, 10}

Notes:  There are two 5s, meaning 5 can be made by two combinations (5, 2 + 3)

4 Numbers:  A = 1, B = 6, C = 7, D = 9

Result:  {1, 6, 7, 7, 8, 9, 10, 13, 14, 15, 16, 16, 17, 22, 23}

Notes:  7 can be made two ways (7, 6 + 1); 16 can be made two ways (7 + 9, 1 + 6 + 9)

The Game Show High Rollers

 

High Rollers was a game show that aired in three series: 1974-1976, 1978-1980, and 1987-1988.  The premise of the game was to clear as many numbers, ranging from 1 to 9.  In the original 1974-1976 series, each number was attached to a prize.  In the more famous 1978-1980 and 1987-1988 series, the numbers were aligned (seemingly at random) on a 3 x 3 grid.  Each column represented a prize or a group of prizes. 

In the main game there are two contestants.  You would win by either rolling the last number off the board or most likely, force your opponent to roll a number that can’t be cleared.  Obviously the total on the dice is used to clear numbers.  For example, a roll of a 6 (the total counts, not the pips on the individual dies), can clear any of the following combinations: 6 itself, 1 and 5, 2 and 4, or 1 and 2 and 3.  Starting with the 1978 series, rolling doubles earned the contestant an insurance marker, basically an extra life.

Winning two games entitled the champion to play the Big Numbers.  The object remained the same, get rid of the numbers 1 to 9 for a major cash prize or car.

One thing to note:  unlike Shut the Box, High Rollers offered no provision should the last number remaining on the board be a 1.

Below are all the possible combinations that can be cleared with each roll.  There are 61 combinations.  Statistically, rolling a 7 is the most likely event, followed by 6 or 8.  However, the most powerful rolls are 12, followed by 11, then 10. 

All the Possible Combos in High Rollers

Total	Combinations that can be Cleared
2	2
3	3, 1-2
4	4, 1-3
5	5, 1-4, 2-3
6	6, 1-5, 2-4, 1-2-3
7	7, 1-6, 2-5, 3-4, 1-2-4
8	8, 1-7, 2-6, 3-5, 1-2-5, 1-3-4
9	9, 1-8, 2-7, 3-6, 4-5, 1-2-6, 1-3-5, 2-3-4
10	1-9, 2-8, 3-7, 4-6, 1-2-7, 1-3-6, 1-4-5, 2-3-5, 1-2-3-4
11	2-9, 3-8, 4-7, 5-6, 1-2-8, 1-3-7, 1-4-6, 2-3-6, 2-4-5, 1-2-3-5
12	3-9, 4-8, 5-7, 1-2-9, 1-3-8, 1-4-7, 1-5-6, 2-3-7, 2-4-6, 3-4-5, 1-2-3-6

Let’s have some fun,

Eddie

This blog is property of Edward Shore, 2017