GM Needs Math Genius!

[Water Bob]

I need some help with math. I'm working on something (that I'll post) for a game, but it's been decades since I took Finite Math.


Probability: Permutations and Combinations.


I have three six sided (fair) dice. One is red. One is white. One is blue.


Order matters.*


I want to roll all six dice, matching any two of them.






*I think order matters. What I'm trying to simulate is a card game, like poker. I'm imagining six-sided, octagonal cards. Each of the six sides on a card is imprinted with a character and a suit. I want to be dealt three cards, and a hand is made by discarding one card and matching one sides with the remaining two cards.






So, how many combinations are possible?


Is this correct--


6 x 6 x 6 = 216 possible pairs.




216! / 214! = 46,440 possible hands.


Is that correct?

 

[ExploderWizard]

I am not a math genius but you mention that you have 3 dice, then go on to reference all 6 dice. So which is it 6 dice or 3?

Also 6 sided cards would be cubical not octagonal.

With six sided dice and four suits you will need to decide which colored dice replicate which suits and on what numbers. D8's or D12's might work better for this if you are using the traditional four suits.

 

[Water Bob]

You can see why I need help!

I am not a math genius but you mention that you have 3 dice, then go on to reference all 6 dice. So which is it 6 dice or 3?

3 dice, each with 6 outcomes. A six sided die.

Really, I'm trying to simulate the six sided cards.

Also 6 sided cards would be cubical not octagonal.

I think you're thinking of the dice. Cubical. No, I'm trying to simulate outcomes on playing cards, like a deck of poker cards. These cards would be hex shaped. Six sided hexes.

This is a rough pic, but it's what I could find at Google Images. Imagine the below was a playing card.

Each playing card has six sides. Imagine that, along the flat edges of each side, were printed a symbol and suit.

You'be dealt three cards, but you can only play two. You have to discard one card. What I'm tryning to figure is: How many possible outcomes in a hand if you are dealt three cards and can only use two.

You play the cards--make your hand--by matching sides on two of the cards. You'd lay them on the table so that they look like this....

See how the two flat sides fit together. Whatever matching suit and symbol that you've matched on those two sides is ranked--that's the hand you play.

 

[ExploderWizard]

I think you're thinking of the dice. Cubical. No, I'm trying to simulate outcomes on playing cards, like a deck of poker cards. These cards would be hex shaped. Six sided hexes.

Ah, ok. Hexagonal rather than octagonal. Got it.

This is a rough pic, but it's what I could find at Google Images. Imagine the below was a playing card.

Each playing card has six sides. Imagine that, along the flat edges of each side, were printed a symbol and suit.

You'be dealt three cards, but you can only play two. You have to discard one card. What I'm tryning to figure is: How many possible outcomes in a hand if you are dealt three cards and can only use two.

You play the cards--make your hand--by matching sides on two of the cards. You'd lay them on the table so that they look like this....

See how the two flat sides fit together. Whatever matching suit and symbol that you've matched on those two sides is ranked--that's the hand you play.

I think making mock up cards will help. Each card has six sides so the numerical distribution will be even. The tricky part will be the suits if you are using the traditional four. I think model cards can help with this.

You can find free hex paper online. Blow up the hex size to a decent card size, print and cut them out. Divide the hexes into 6 sections. Then you can see the layout and decide how you want to assign the suits.

 

[GMMichael]

42?

 

[Water Bob]

42?

I dropped trying to figure the problem. I realized that I didn't need the probability for what I was doing.

If you want to see the finished product, look at THIS THREAD FOR THE STAR WARS D6 RPG.