Dice Probablity Nakata Ryohei Otani Ryota Sakano Mikiyasu

Background We 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 place Dice doesn’t always roll well

Result 0,21 0,2 0,19 0,14 0,13 0,12 0,11 0,18 0,17 0,16 0,15 300 600 900 roll 1 roll 2 roll 3 roll 4 roll 5 roll 6

Self-made Dice Roller 1 Fault ： It isn’t suited for rolling many dices at the same time.

Result 0,17 0,16 0,15 0,14 0,2 0,19 0,18 300 600 900 roll 1 roll 2 roll 3 roll 4 roll 5 roll 6

Observations I • • It is essential to roll dice many more times.

It is necessary to make a new automatic dice roller.

ＷＥＢ camera Experiment III Saikoron wheel for dice rotation CPU board Small direct-current motor The breadboard for electronic circuits Switching AC/AD adaptor

Result 0,19 0,18 0,17 0,16 0,15 0,14 1500 3000 4500 6000 7500 9000 10500

Observations II I considered the dots as hemispheres and define their radius as r… 𝟒 𝛑𝒓 𝟑 × 𝟏 𝟑 = × 𝒕𝒉𝒆 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒅𝒐𝒕𝒔 𝟐 𝒔𝒉𝒂𝒗𝒆𝒅 𝒔𝒒𝒖𝒂𝒓𝒆 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 R3 2. micro-relay switch (Made in OMRON) G6E-134P 3. electronic circuits bread board 4. small DC motor (Mabuti motor RE140RA) attached to a two-step pulley 5. dice rotating wheel 6. Switching AC adapter (1.5V 600mA) 7.

ＷＥＢ Melco) camera ( 3.2million pixel web camera made in 8. pulley and rubber ring