Dice Probablity

Nakata RyoheiOtani RyotaSakano Mikiyasu

BackgroundWe wondered whether the probability of each roll will be equal to 0.16.

Prof. Izumori advised that I should roll dice thirty-thousand times to investigate dice probability. So I decided to make automatic dice roller.　

Commercially Available Dice shaker

Fault:Dice come from wrong placeDice doesn’t always roll well

Result

300 600 9000.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0.2

0.21

roll 1roll 2roll 3roll 4roll 5roll 6

Self-made Dice Roller 1

Fault ：It isn’t suited for rolling many dices at the same time.

Result

300 600 9000.14

0.15

0.16

0.17

0.18

0.19

0.2

roll 1roll 2roll 3roll 4roll 5 roll 6

Observations I

• It is essential to roll dice many more times.• It is necessary to make a new automatic dice

roller.

Experiment III Saikoronwheel for dice rotation

ＷＥＢ camera

CPU boardSmall direct-current motor

The breadboard for electronic circuits

Switching AC/AD adaptor

Result

1500 3000 4500 6000 7500 9000 105000.14

0.15

0.16

0.17

0.18

0.19

Observations II

　 I considered the dots as hemispheres and define their radius as r…

　 The weight of each side is… 1>2>3>4>5>6 … in this order.

Observations II

　 Thus, it can be expected that the more dots, the higher the frequency of rolling that side, and the less dots, the lower the frequency.

Assignment

• finish rolling dice 30,000 times and collecting data.

• improve Saikoron machine as a continuous experimental tool.

• verify the probability of those dice.• examine the variation in the probability after

changing the center of gravity of the dice.

Gratitude

• Norifumi YAMADA (Professor, Fukui University),

• Hitoshi IZUMORI (Professor, Kanagawa University)

• Naoki KOBAYASHI (IRISO SEIMITSU Co., Ltd)

Bibliography

　• "my Arduino work note“(Tetsuya Suzuki work,

latosol publication, 2013)• "Arduino will be begun" (Massimo Banzi work,

O`REILLY publication, 2012)

Thank you for listening!

Preparation

1. CPU board 　　　 Arduino 　 UNO 　 R32. micro-relay switch 　 (Made in OMRON) 　 G6E-134P3. electronic circuits bread board4. small DC motor (Mabuti motor RE140RA) attached to a

two-step pulley5. dice rotating wheel6. Switching AC adapter (1.5V 　 600mA)7. ＷＥＢ camera 　　 ( 3.2million pixel web camera

made in Melco)8. pulley and rubber ring