SFR, Inc.

[goldbh]

How many different combinations of armies are there which a player could present at the start of a 36 health point standard Dragon Dice game?

Rules:

1. Unlimited supply of Dragon Dice as available in any marketplace as of 1st Jan 2007.

2. Start of the game definition - Immediately after setup and before the first roll.
a) Standard game definition - Magic Items (including Artifacts and Medallions) are allowed and a 50% Magic restriction applies.

3. Army definition - The armies on the board plus Dragons, Terrains and Kings Die. IE no Dragonkin or Minor Terrains.

4. Dice variants are not included (IE a pink Pelter is a Pelter)

5. Rules are subject to change in the interests of vagueness and imprecision (This rule will be removed as soon as all competitors agree the parameters).

6. Entries can be in any form (mathematical, equation or notation) but must show the logic behind the answer.

7. The possessor of the prize dice will judge the best entries and the forum members will vote on the outright winner.
a) In the event of a draw the winner will be decided by an on line game.

8. The Prize - One Mint TSR UK GOLD CHAMPION

9. The prize die will be shipped free of charge to the winner but the winner must agree to send the possessor a Birthday Card for 2 years.

10. Closing date for entries 13th March 2007.
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[chuckpint]

By standard game, do you mean 36 health?

Are only legal armies allowed? By that I mean, all normal army construction rules, including no more than 50% mages.
_________________
You can never have too many dice.
First Place at the first ever Daemon Dice sealed starter tournament.
Battlefest tied for first GenCon 2012
Single Race Champion GenCon 2008-2009, Sealed Box Champion GenCon 2007,2009,
My collection is 21,500 Dragon Dice, 20,000 Daemon Dice, and others (too many to count).

[piMaster]

Does that mean each army must use at least one die from each of the twelve races?

Do you mean each army must have all 12 Eldarim in it?

The way its worded makes it a little ambiguous.

Are magical items/artifacts/medallions allowed/not allowed?

[DEEPBLUEB2]

The way I see it.....
you are asking...
"Using the entire Dragon Dice Universe"...
How many possible tournament armies can be made?(36 health)

[piMaster]

What about the Kings' Die?

Are dragons/dragonkin/terrains/minor terrains to be taken into consideration?

---

Well Jim, he didn't say whether or not MIAM are allowed, so we don't know if its all possible 36 health armies.

So goldbh, we need some clarification.

[DEEPBLUEB2]

The Vampire is 2 points of magic even though it is a 3 health unit.
This factor allows for more army construction combinations.
Likewise, there are other dice that have
different magic points versus health. ie flying carpet.....

[Pelter_Boy]

The way I read this, you're looking for every possible tournament legal army; am I correct?

I haven't finished the calculation, but I found that there are 104 tournament legal 2-health armies (assuming a 2-health tournament) using only 2 races (no magic items). I once made a problem trying to find different combinations of a 12-scoop sundae, and it turned out to be over one septillion combinations. I would expect this would produce a larger answer.

Also, how will it be proven if the person who gets the answer is right or wrong?
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2006 World Champion of Dragon Dice
AKA Roburk the Insane Winged Demon Undead Pelter, Champion of S&JW
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First person banished south of S&JW
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[chuckpint]

Ok, then I have the correct answer: "A really really huge number."
_________________
You can never have too many dice.
First Place at the first ever Daemon Dice sealed starter tournament.
Battlefest tied for first GenCon 2012
Single Race Champion GenCon 2008-2009, Sealed Box Champion GenCon 2007,2009,
My collection is 21,500 Dragon Dice, 20,000 Daemon Dice, and others (too many to count).

[DEEPBLUEB2]

If anyone can solve this equation.....it is.....
Bruce Parrello
Inventor of the Dragon Dice Assistant


I think Brad could too!!!!!! (If the parameters were defined)

[DEEPBLUEB2]

And then you would have to consider.....
that minor terrains are optional.....
Just ask Robert
and Dragonkin too would be optional...I think
(if Magestorm is even equated)
and also....
the amount of minor terrains and Dragonkin could vary
for example...
a player could bring only 1 minor terrain and 1 health of Dragonkin

with those variables applied to every army,
the number would be like Chuck said.....
"A really really huge number."

[cliffwiggs]

[DEEPBLUEB2]

[cliffwiggs]

[piMaster]

If magical items are involved, it will become more than an equation. For each army that meets the health/magic point value requirements, you have to check to see if that army can carry all of their items. There is no equation that can check that (or at least I can't imagine one).

And yes, the answer is going to be really, really big.

[DScottOBrien]

N= ((a*X)(b*X/1/2x)(c*x/1/3x)(d*x/1/4x))20*12 + (a*y)(b*y/1/2y)(c*y/1/3y)(d*y/1/4y)5 + (a*z)(b*z/1/2z)(c*z/1/3z)(d*z/1/4z)5 + (d*x/1/4x)*10
..................................................x............................................ y.................................................................... z..............................................x

Where a=1, b=2, c=3, d=4
X=Army size
y=# of MIA
z=dragonkin

Don't know how close this is, but above is my equation on the problem, giving a final total result of 4,083,548,483. This is figured using 36 points as the total health of the army
_________________
D Scott O'Brien
Dice Junkie
Anal-retentive rules scrutinizer

[DScottOBrien]

The equation I posted does not take into consideration terrains or dragons, because they are not really considered and army. As far as the MIA, I used a figure of 1/2 the army size as a max, because if you start with all 1 point units, each unit can carry 1 item.
_________________
D Scott O'Brien
Dice Junkie
Anal-retentive rules scrutinizer

[Pelter_Boy]

The answer is:

1,826,194,576,382,643,498,056,970,234,654,980,324 (about 2 11-illion)different armies.

Anybody care to prove/disprove me?
_________________
Former Destroyer, son of Ddice
2006 World Champion of Dragon Dice
AKA Roburk the Insane Winged Demon Undead Pelter, Champion of S&JW
First person banished North
First person banished south of S&JW
First person with posts banished from the forum

[DEEPBLUEB2]

[ddicerc]

[ddicerc]

Here's what I understand the question to be:

"Using only tournament-legal units, magic items, and the King's Die, what is the number of tournament-legal starting armies that can be made from the existing pool of Dragon Dice?"

This includes all racial units and Eldarim, excludes misprints and prototype runs, and assumes all units count the same regardless of release (so a TSR and SFR Gold DKC are the same unit, a Scalder original and promo are the same unit, a TSR and SFR DM is the same unit, etc.) It also excludes dragonkin, dragons, and minor terrains, since they do not begin (or even belong) in the army. I also include the Kings' Die, since it does begin in the starting army, but I don't believe it is defined as a unit.

This would create a pool of:

235 racial unit dice (19 each for the first five races, 20 each for the last 7)
103 magic items (20 of each color, plus the medallions)
12 Eldarim (DH/DS/DM/DL)
King's Die

That would be a pool of 351 dice.

Is this a fair statement of the problem?

[And with the magic items, just think-before the latest rules came out, you had army requirements for carrying each level of medallion. That would create a need to sieve out even more combinations.]

I can say with some degree of certainty that the answer is a positive integer of less than infinite quantity.
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Steve "DDice" Braun
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