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so i calculated the chance the tervigon has to lose his ability each turn and that is: 4/9... four out of nine times, or almost 50%, your tervigon will roll doubles. but these are just numbers and i apologize to anyone who is a mathhammer hater hehe.
despite this fact i am definitely using the tervigon because i still like them odds. even if you do roll doubles on your first turn you have a good chance to get a large squad of termagaunts
anyway i thought i wouuld put this magic number out there for the nid community
I assure you that statistically speaking it's 66 times out of 216 possibilities, so roughly 30% chance and not that whopping 45%!
Math explanation
If you roll two dice you have 6 chances on 36 to roll doubles.
If you add a dice to that you have the original 6 + another 6 due to the extra dice , but one has to be subtracted as it's already counted for in the first 6 possibilities (i.e. the 1 1 1 combination). That means 11 double combinations per 2 die group. Multiply that by 6 times for the third die and you get 66. The sum of all combinations rolling 3 dice is 6x6x6= 216.
So 66/216 = ~0.30 -> 30% chance of rolling doubles! =)
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Kheldar, did you count for the times you roll triples too? I think you didn't and that's what makes your odds look better.
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Tervigon Conversion
The possible ways to roll doubles are:
x, x, x
x, x, y
x, y, x
y, x, x
Where x is a duplicate of any other number rolled, and y is some other number.
For each triplicate, there are six possible results.
For each combination of duplicates, there are six possible results, for each of 5 possible other numbers.
Every other possible result will yield a unique combination of numbers.
For each three dice rolled, there are 216 possible results.
( 3 * ( 5 * 6 ) ) + 6 = 96 / 216 = 4 / 9 = 0.4444 = 44.44%
Roughly translated, each Tervigon will spawn Termigaunts for an average of 2.25 turns.
A note to the math hammer haters: Statistical information is always accurate within a small margin of error. With fewer trials, this margin is greater. Conversely, with more trials, this margin is lesser. Indeed, your Tervigons may only spawn a single turn, when at other times they will spawn for the entire game. Consider this data as being accurate when averaged across your entire career as a Tyranid player, and not during a single game. This information is relevant only if you seek to understand how a unit will perform the majority of the time, and is only useful if you acknowledge that there will be variance within individual instances.
Cheers!
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I am pretty sure you are double counting when you roll triples. Kheldar is correct, each time you roll you have 11/36 chance of rolling doubles.
Let's say you roll a 1 on the first die. How many ways are there to get at least one more 1 on two dice? Look at this table:You'll find there are 11 ways. So the chances are 11/36. Do the same exercise for 2 through 5 and keep counting and you'll see that the chances are 11/36 for each of the 6 numbers. Which brings you to Kheldar's ~30% number.Code:1 2 3 4 5 6 1 X X X X X X 2 X 3 X 4 X 5 X 6 X
I don't quite understand what you are trying to state.
How did I double count triples, when there are exactly 6 / 216 ways to yield three identical numbers when rolling three six-sided dice? My breakdown counted each individual combination that could yield doubles (or in the case of a triplicate, a combination of doubles).
I'll even write a quick java program to simulate this process.Code:// Simulates every possible combination of results when // rolling three DICE_SIZE-sided dice, and counts every possible // combination which results in at least two of the number // being identical. public class DoublesProbability { public static void main( String[] args ) { // Change value of DICE_SIZE to change the number of sides on each dice to be simulated. int DICE_SIZE = 6; int diceOne, diceTwo, diceThr; int isDouble = 0; for( diceOne = 1; diceOne <= DICE_SIZE; diceOne++ ) { for( diceTwo = 1; diceTwo <= DICE_SIZE; diceTwo++ ) { for( diceThr = 1; diceThr <= DICE_SIZE; diceThr++ ) { if( diceOne == diceTwo || diceOne == diceThr || diceTwo == diceThr ) isDouble ++; } } } System.out.println( "Number of duplicates and triplicates: " + isDouble ); } }Please pardon my lack of documentation.. if you're familiar with java, it should be simple enough to figure out, otherwise it's a rather moot point to explain.Code:----jGRASP exec: java DoublesProbability Number of duplicates and triplicates: 96 ----jGRASP: operation complete.
The program computes every possible combination of results when rolling 3d6, beginning with
1, 1, 1
1, 1, 2
...
1, 1, 6
1, 2, 1
1, 2, 2
...
1, 2, 6
...
etc... until
6, 6, 6
Every time two or more of the results are equal to each other, isDouble is incremented by 1, counting every possible combination of doubles and triples. The total is 96, and there are 6 * 6 * 6 ( or 216) possible combination of dice. 96 / 216 = 4 / 9.
EDIT:
Ah, I see what you are trying to say. Your table does not provide accurate statistics for a 3d6, only a 2d6 (each dice would require it's own dimension on the table, which would require a 6x6x6 table). Also, you are not counting the combinations but the individual dice. For a 2d6, there are 6 possible ways to roll a double. For a 3d6 there are 16 different ways to roll a double for each number
1, 1, 1
1, 1, 2
1, 1, 3
1, 1, 4
1, 1, 5
1, 1, 6
1, 2, 1
1, 3, 1
1, 4, 1
1, 5, 1
1, 6, 1
2, 1, 1
3, 1, 1
4, 1, 1
5, 1, 1
6, 1, 1
and there are 6 possible numbers.
2, 2, 2
2, 2, 1
2, 2, 3
2, 2, 4
... etc.
3, 3, 3
3, 3, 1
3, 3, 2
3, 3, 4
... etc.
and so on.
6 * 16 = 96.
You have to count every possible combination of dice which would yield a double, out of the total possible combination of dice rolled. This includes counting each double 1 on the first two dice, for each other number of the third dice... and so on.
Last edited by BossGorestompa; January 22nd, 2010 at 19:21.
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I've gone ahead and broken the entire thing down into individual results. The following will display the dice result ( 3 to 18 ), the number of possible combinations that will produce that result (and the % chance of it occurring), and the number of possible doubles each result can produce (and the % chance of it occurring).Code:# of pos. # of pos. Combination Doubles Result ( 3 ) = 1 / 216 ( 0.46 % ) :: 1 Doubles ( 0.46 % ) Result ( 4 ) = 3 / 216 ( 1.39 % ) :: 3 Doubles ( 1.39 % ) Result ( 5 ) = 6 / 216 ( 2.78 % ) :: 6 Doubles ( 2.78 % ) Result ( 6 ) = 10 / 216 ( 4.63 % ) :: 4 Doubles ( 1.85 % ) Result ( 7 ) = 15 / 216 ( 6.94 % ) :: 9 Doubles ( 4.17 % ) Result ( 8 ) = 21 / 216 ( 9.72 % ) :: 9 Doubles ( 4.17 % ) Result ( 9 ) = 25 / 216 ( 11.57 % ) :: 7 Doubles ( 3.24 % ) Result (10) = 27 / 216 ( 12.50 % ) :: 9 Doubles ( 4.17 % ) Result (11) = 27 / 216 ( 12.50 % ) :: 9 Doubles ( 4.17 % ) Result (12) = 25 / 216 ( 11.57 % ) :: 7 Doubles ( 3.24 % ) Result (13) = 21 / 216 ( 9.72 % ) :: 9 Doubles ( 4.17 % ) Result (14) = 15 / 216 ( 6.94 % ) :: 9 Doubles ( 4.17 % ) Result (15) = 10 / 216 ( 4.63 % ) :: 4 Doubles ( 1.85 % ) Result (16) = 6 / 216 ( 2.78 % ) :: 6 Doubles ( 2.78 % ) Result (17) = 3 / 216 ( 1.39 % ) :: 3 Doubles ( 1.39 % ) Result (18) = 1 / 216 ( 0.46 % ) :: 1 Doubles ( 0.46 % )
I've recently become a fan of this thing called Dubstep. And you should too.
Datsik & Flux Pavillion - Crunch (Youtube)
Da Moo Kowz is da drinkinest Orks of dem all!