help with probabilities (rolling 5 dice)

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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!

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.

NewbieDesigner
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Joined: 01/20/2011
awesome!

awesome!

NASG
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Joined: 10/15/2012
I think your % for <10 and

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

Dulkal
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Joined: 02/07/2012
TwentyPercent wrote:Sum < 10

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

TwentyPercent
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Joined: 12/25/2012
Dulkal wrote:TwentyPercent

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

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?

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 :)

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.

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.

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Joined: 12/12/2011
Dice Probabilities

http://anydice.com/

This seems like a good thread to post this on.

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