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→‎Improved Game?: -> Improved Dice? Replaced erroneous content, replaced with different dice table.
imported>Cuc
imported>Cuc
(→‎Improved Game?: -> Improved Dice? Replaced erroneous content, replaced with different dice table.)
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[[User:Cuc|Cuc]] ([[User talk:Cuc|talk]]) 03:25, 3 November 2020 (PST). Revised [[User:Cuc|Cuc]] ([[User talk:Cuc|talk]]) 23:55, 3 November 2020 (PST). Revised (added point 4.) [[User:Cuc|Cuc]] ([[User talk:Cuc|talk]]) 22:03, 3 December 2020 (PST)
 
== Improved GameDice? ==
Previously, I made an error in counting and thought that some combos have a different probability to appear. But it's clear that any combo (say Red or Green) has a probability of 5/6 to appear, because only ONE combo doesn't have either color (in this case, Yellow and Blue). We do not need a different dice. But some probabilities may be lower by removing some colors (but which one?). I had a design of a dice that featured the probability of 4/6 for the combos (R or G) and (G or B). We can remove G from the Y/G combo to achieve this.
In the probability table above, we get the following probabilities for Combos:
 
A dice that provides these probabilities is:
{| class="wikitable"
|-
! ComboN !! ProbabilityColor !! DesiredCombo
|-
| R or Y1 || 5/6 || 5R/6B
|-
| R or G || 6/62 || 4/6Y
|-
| R or B3 || 4/6 || 5R/6G
|-
| Y or G || 4/6 || 5Y/6B
|-
| Y or B5 || 6R/6 || 5/6Y
|-
| G or B || 5/6 || 4G/6B
|}
'''Table.''' Improved Dice?
'''Table.''' Probabilities and Desired Probabilities with earlier distribution.
 
Note that one throw has ONLY Yellow.
I will playtest this and report back.
Perhaps, additionally, you should be allowed to throw again until you get another number, if you throw G/B and the Bank is empty.
 
--
 
I considered that two combos that do not share a color, should be on opposite sides of the dice, and perhaps that there isn't a color that adds to 6 (1+2+3) or 15 (4+5+6), but this is impossible. However, we'd like the combos Y+R and G+B to be as close to the expected 5 x 3.5 = 17.5 as possible. The following dice delivers:
 
A dice that provides these probabilities is:
{| class="wikitable"
|-
Line 123 ⟶ 131:
| 1 || R/B
|-
| 2 || Y/B
|-
| 3 || R/G/B
|-
| 4 || YR/BY
|-
| 5 || R/YG
|-
| 6 || GY/BG
|}
'''Table.''' Improved Dice.?
 
I'm sure that in practice, this dice performs equal to any other dice that has the combos distributed in a different way, but this design appeals to my sense of aesthetics.
Note that one throw has ONLY Yellow.
[[User:Cuc|Cuc]] ([[User talk:Cuc|talk]]) 15:58, 16 May 2021 (PDT)
I will playtest this and report back.
Perhaps, additionally, you should be allowed to throw again until you get another number, if you throw G/B and the Bank is empty.
Anonymous user
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