Playing with dice
April 14th, 2009
Computerized dice, to be exact. And I’ve made an animation of it!
For want of useful work I’ve made a Processing application roll 6 dice 10,000 times, and have it keep track of the scores. In the dice game that I’ve sometimes played with Aleksandra the score of six dice is as follows: for each group of 3 dice with the same value, you get the value times ten (for instance, 3 4 6 2 3 3 would give 30). Except when it concerns the value 1, that group of 3 counts as 100. Every other additional value to that group doubles the score, so that 3 3 3 3 2 4 would give 60 and 1 1 1 1 2 3 would give 200.
Remove the groups from the dice. After that, count all the remaining 1’s and 5’s, where each 5 counts as 5 and each 1 as 10. Complicated? Here’s an example: 1 1 2 5 5 6 would give 2 x 10 + 2 x 5 = 30. Another example: 4 4 4 4 5 6 would give 40 x 2 + 1 x 5 = 85. The last example: 1 1 1 4 5 6 would give 100 + 1 x 5 = 105.
I kept count of each score from 0 to 120, and plotted it after each dice. The animation consists of the first 2000 rolls (compressed in 1000 screenshots), where you can see how variations are big at first but diminish when the number of dice-rolls increases. The animation can be downloaded by clicking here or on the preview image, and it is also available in the rest of this story. Be aware that the animation is 5.17MB.
After throwing six dice 10,000 times, the counts have come up like this:
| Score | # | % | Score | # | % | |
| 0 | 297 | 3.0 | 65 | 159 | 1.6 | |
| 5 | 803 | 8.0 | 70 | 240 | 2.4 | |
| 10 | 1342 | 13.4 | 75 | 76 | 0.8 | |
| 15 | 1289 | 12.9 | 80 | 105 | 1.1 | |
| 20 | 1541 | 15.4 | 85 | 25 | 0.3 | |
| 25 | 888 | 8.9 | 90 | 33 | 0.3 | |
| 30 | 552 | 5.5 | 95 | 41 | 0.4 | |
| 35 | 201 | 2.0 | 100 | 356 | 3.6 | |
| 40 | 366 | 3.7 | 105 | 212 | 2.1 | |
| 45 | 228 | 2.3 | 110 | 75 | 0.8 | |
| 50 | 490 | 4.9 | 115 | 0 | 0 | |
| 55 | 100 | 1.0 | 120+ | 215 | 2.2 | |
| 60 | 403 | 4.0 |
And finally, the animation is here:
My name is Marco Hokke. My blog is about the things that interest me and things I might forget if I would not blog them.
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