Dave Myers
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I don't know if that thread was just petering out, or if the question was too hard (that should elicit some responses!) but here is my question that went uncharacteristically unanswered:


Roll 24 d6 dice, four each of six different colors. I know, fun already.

To clarify: four red d6, four yellow d6, four blue d6, etc. for a total of six colors, 24 dice.
What are the probabilities of:

a) three of a kind, each a different color (ie a blue one, a red one, and a yellow one)

b) four of a kind, each different color

c) five of a kind, each a different color

d) six of a kind, each a different color

e) a run of three, each a different color

f) a run of four, each a different color

g) a run of five, each a different color

h) a run of six, each a different color

I) a run of three, all the same color

J) a run of four, all the same color

K) three of kind, all the same color

L) four of a kind, all the same color
 
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Eisen Montalvo
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Have you tried http://anydice.com? I think you should be able to get the answers without too much hassle.
 
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Steve Zagieboylo
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I don't see how anydice is going to help with a-h. For I-L, it can do it, since those chances are the same as if you had only four dice and rolled them six times.

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Andreas Pelikan
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Can you tell us more about the game. Is it a reaction game with players racing to find the longest runs / most of a kind, etc.? Have you playtested and are now trying to balance VP values? Do you seriously find it fun to roll a bucket of dice?

It's disappointing to answer questions that are going to lead nowhere, so tell us why and how our answers will be helpful. Will you know what certain percentages mean if someone gives them to you, and will you be able to utilize them? E.g.
myersd37 wrote:
What are the probabilities of:
b) four of a kind, each different color

37.29% - at most 4 of any kind,
84.18% - exactly 4 of any kind, possibly more of a different kind
98.57% - 4 or more of any kind
(+-0.005% each)
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Sturv Tafvherd
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The thing that stops me is 24 dice.

Success rates are going to be relatively high with that many dice. It's like asking for 5 card poker hand probabilities given 3 decks and drawing 50 cards.

And even going past the probability questions, I start asking myself if I want to play a game involving rolling 24 dice all at once, and sorting / looking for combinations.

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Dave Myers
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Good questions, all.

The game is in the very initial design stage. I am trying to establish the hierarchy of the "hands" and also see if some are too easy to count as a "score" and how the sequences compare with the -of a kinds.

The gist of the game is this:

Players are all scientists (each with his/her own color that corresponds to the six dice colors) looking for discoveries (a, b, c, etc from original post). The first player rolls all the dice (yes, all 24; it is just barely possible...) and looks what he/she wants to discover, then passes the remaining dice to the next player. The second player may choose to re-roll all the dice of ONE color, then choose a combination to discover. Then pass the next player, re-roll one color, choose, pass, Etc until there are no viable combos. At that point, the player with the "best" discovery (dice combination) wins the round, scores, etc. and the player with the lowest loess points. There are bonuses if your color was included in the "winning" combo.

The scoring is a little more complicated than just a point track, but you get the use of dice, hopefully.

Again, it is in very early stages.
 
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Jim Hansen
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I am bored/nauseated by the thought of trying to look at 24 dice of 6 different colors and determining if any of the above scenarios apply. I imagine each roll will take a good 30 seconds just to determine what the outcome was.
 
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Sturv Tafvherd
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myersd37 wrote:
Good questions, all.

The game is in the very initial design stage. I am trying to establish the hierarchy of the "hands" and also see if some are too easy to count as a "score" and how the sequences compare with the -of a kinds.

The gist of the game is this:

Players are all scientists (each with his/her own color that corresponds to the six dice colors) looking for discoveries (a, b, c, etc from original post). The first player rolls all the dice (yes, all 24; it is just barely possible...) and looks what he/she wants to discover, then passes the remaining dice to the next player. The second player may choose to re-roll all the dice of ONE color, then choose a combination to discover. Then pass the next player, re-roll one color, choose, pass, Etc until there are no viable combos. At that point, the player with the "best" discovery (dice combination) wins the round, scores, etc. and the player with the lowest loess points. There are bonuses if your color was included in the "winning" combo.

The scoring is a little more complicated than just a point track, but you get the use of dice, hopefully.

Again, it is in very early stages.


First, a clarification: every time someone "makes a discovery," the dice involved are removed from the pool.

Next, an observation: therefore, the probabilities of each type of combination changes ... thus, those "ranks" change. I don't have a big problem with that, since the same could be said of Blackjack ("21").

Next, yet another observation: assuming you still use a fixed ranking, the "skill" involved in this game is detecting the highest ranked combination. And I can imagine that smart players will simply go down that ranked list and see if they can find that combination.

That said, you might want to restrict the amount of time a player has to take their turn.... a 10 second timer sounds challenging to me.


Now ... on a different note: Tenzi
Quote:
Every player gets 10 dice.

The object of the game is to roll the dice as fast as possible, the player who gets all dice on the same number and yells "Tenzi!" is the winner.


Now, imagine that idea applied to your game...
Quote:
Every player gets 24 dice. Four dice each of six different colors.

The object of the game is to roll the dice, set dice aside into as many different combinations as fast as possible. At some point, someone yells "Eureka!", everyone stops rolling and gets a few seconds to group their dice into as many combinations as possible. The player with the most combinations wins.


And in that game I described, you don't necessarily have to figure out the probabilities at all. Indeed, having a "run of 3" and a "3 of a kind" would be worth more than a single "run of 6" or a single "6 of 6 diff colors"

 
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Dave Myers
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Thanks for the discussion, Stormtower. I appreciate the thoughts. My family enjoys Tenzi, but I would see this game as something different.

What if 24 dice, four of each in six different colors, are being rolled, but each player is rolling his/her own color in secret. If you have fewer than six players,the remaining dice are publicly rolled. Now, on your turn you still want to make the same combinations, but there is bargaining among players since there will be a bonus if your color is involved in the best combination.

I guess my point is the game is still progressing in my mind, but I wanted the hierarchy of the combinations in order to start testing different rules and scoring mechanisms. One player doesn't have to roll all 24 dice, but I still think the results should be taken as one result, even if the dice are controlled by individual players and even if there are re-roll opportunities. It comes down to where does the sequence of 3 and 4 of the same color fit among the likelihoods of 3, 4, 5, and 6 of a kind of all different colors? I do not have the probability skills to handle this question.

My prediction is that the order from easiest (most probable) to hardest (least probable) would be this:

3 of a kind (all different colors)
4 of a kind (all different colors)
Sequence of 3 (all same color)
5 of a kind (all different colors)
6 of a kind (all different colors)
Sequence of 4 (all same color)

That's just my gut, but my gut is the worst way to figure probability questions. That's why I came here. Can anyone make a more educated guess than I?

 
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