Can any math whizzes tell me the odds of the following after rolling five dice one time?

-All odd numbers

-All even numbers

-Total sum less than 10

-Total sum greater than 25.

Thanks!

Thu, 02/07/2013 - 14:37

NewbieDesigner

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Joined: 01/20/2011

Can any math whizzes tell me the odds of the following after rolling five dice one time?

-All odd numbers

-All even numbers

-Total sum less than 10

-Total sum greater than 25.

Thanks!

Thu, 02/07/2013 - 14:46

#1
TwentyPercent

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Joined: 12/25/2012

Assuming all 6-sided

Assuming all 6-sided dice:

All Odd = 3.125% chance (0.5^5)

All Even = Same as above

Sum < 10 = 0.2058% chance (1/3)^4 * (1/6)

Sum > 25 = Same as above

Hope this helps.

Thu, 02/07/2013 - 19:39

#3
NASG

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Joined: 10/15/2012

I think your % for <10 and

[edit: re-read your numbers, re-checked my maths, re-posted!]

I think your 0.2% for <10 and >25 look on the low side..

I'm not the greatest at maths so I found these diagrams of the standard distribution using 5d6 on some math guys blogs:

http://photos1.blogger.com/blogger/6863/540/1600/dice5.png

http://dinodini.files.wordpress.com/2011/03/msp86419f157hhi439i1c100002b...

It's not all that clear, but the chances of rolling 10 are 0.02 (2%) and 9 is about 0.01 (1%) and then 8 is 0.005 (0.5%).. adding all these up, I'd estimate your chances are ~3.5%.

This would of course, be the same for >25.

I'm mediocre at Maths and so await being corrected! ;-)

HTH

Fri, 02/08/2013 - 06:03

#4
Dulkal

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Joined: 02/07/2012

TwentyPercent wrote:Sum < 10

Sum > 25 = Same as above

As far as I can see, that would be the chance of rolling no higher than a two on the first four dice, plus the final die must be exactly 1.

However, it is also possible to roll less than ten with other permutations, such as 33111 or 21222, so the actual chance should be higher.

Fri, 02/08/2013 - 08:37

#5
TwentyPercent

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Joined: 12/25/2012

Dulkal wrote:TwentyPercent

Sum > 25 = Same as above

As far as I can see, that would be the chance of rolling no higher than a two on the first four dice, plus the final die must be exactly 1.

However, it is also possible to roll less than ten with other permutations, such as 33111 or 21222, so the actual chance should be higher.

You are correct; I was only looking at a single scenario. Below are the all the scenarios I see that would give Sum<10. This chance definitely seems lower than that probability chart, but I'd like to know why below wouldn't be correct.

Dice1 1 1 1 1 1

Dice2 1 1 1 2 1

Dice3 1 1 2 2 1

Dice4 1 2 2 2 3

Dice5 5 4 3 2 3

Scenario % 0.00429% 0.10288% 0.15432% 0.20576% 0.11574%

Total % 0.58299%

Fri, 02/08/2013 - 10:11

#6
NewbieDesigner

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Joined: 01/20/2011

Know of any online dice

Know of any online dice simulators that allows you to freeze dice?

Fri, 02/08/2013 - 10:49

#7
NASG

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Joined: 10/15/2012

But there are five

But there are five permutations for:

4 x 1 and 1 x 2, i.e. 11112 11121 11211 12111 21111 (Dice 2 above)

There are ten for Dice 3:

11122 11212 11221 12112 12121 12211 21112 21121 21211 22111

There's another 5 each for 11113, 11114, 11115, 11116.

Plus permutations for 11123, 11133, 11134...

Have to stop now, my head is spinning :)

Fri, 02/08/2013 - 11:23

#8
NewbieDesigner

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Joined: 01/20/2011

I want to have three stacks

I want to have three stacks of cards with easy, medium and hard difficulties (basically strength of the bull players are riding). The cards will have mostly poker hand combinations on them to accomplish. Players will have 5 dice to roll (one roll probabilities listed below in parenthesis). They can freeze dice and reroll until the goal has been completed. Players will draw any six cards they want so they can choose their own difficulty.

-Hard-

Five of a Kind (.08%)

Sum total <10 (?)

Sum total >25 (?)

-Medium-

Four of a Kind (1.9%)

Full House (3.8%)

Straight (3.0%)

All evens (?)

All odds (?)

-Easy-

Three of a Kind (15%)

Two pair (23%)

One pair (46%)

Does this seem about right? I can adjust the sum totals to make them more difficult if necessary and would like to get them close to the odds of 5 of a kind.

So if players can complete these six cards before other players knock them off (other players have to roll and freeze their own dice), they will score points with each card having points based on difficulty in addition to the base 50 points for not gettting knocked off.

Fri, 02/08/2013 - 16:51

#9
NewbieDesigner

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Joined: 01/20/2011

I ditched the >25 or <10

I ditched the >25 or <10 since I think counting dice will be too cumbersome for a real time turn.

Instead I went with "all one's and two's", "all three's and fours", and "all fives and sixes" for a few more choices in the hard stack.

Fri, 02/08/2013 - 18:44

#10
NomadArtisan

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Joined: 12/12/2011

Dice Probabilities

This seems like a good thread to post this on.

Fri, 02/08/2013 - 19:30

#11
nand

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Joined: 07/27/2008

This is a script for nanDECK

This is a script for nanDECK for calculating permutations:

PR[dice]5=1|2|3|4|5|6

[less10]=FILTER(+[dice],5,6,7,8,9)

[more25]=FILTER(+[dice],26,27,28,29,30)

FONT=Arial,16,,#000000

TEXT=1,"Total={(dice)}",0,0,100%,10%

TEXT=1,"Less than 10={(less10)}",0,10%,100%,10%

TEXT=1,"More than 25={(more25)}",0,20%,100%,10%

The result is:

Total=7776

Less than 10=126

More than 25=126

And nanDECK can print (or save into a file) all the sequences of results. For example, these are the 126 rolls < 10:

11111

11112

11113

11114

11115

11121

11122

11123

11124

11131

11132

11133

11141

11142

11151

11211

11212

11213

11214

11221

11222

11223

11231

11232

11241

11311

11312

11313

11321

11322

11331

11411

11412

11421

11511

12111

12112

12113

12114

12121

12122

12123

12131

12132

12141

12211

12212

12213

12221

12222

12231

12311

12312

12321

12411

13111

13112

13113

13121

13122

13131

13211

13212

13221

13311

14111

14112

14121

14211

15111

21111

21112

21113

21114

21121

21122

21123

21131

21132

21141

21211

21212

21213

21221

21222

21231

21311

21312

21321

21411

22111

22112

22113

22121

22122

22131

22211

22212

22221

22311

23111

23112

23121

23211

24111

31111

31112

31113

31121

31122

31131

31211

31212

31221

31311

32111

32112

32121

32211

33111

41111

41112

41121

41211

42111

51111

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