View Full Version : 6 Dice Full House - Probability Check

Cracked a power scroll today with 6 dice and rolled a 1, 2, 3, 4, 5 and 6 together - no double. I'm still dumbfounded that I could have made this roll under pressure, allowing my opponent to dispel that critical play.

Can someone please calculate the % odds of that happening, and show your working? Surely it is very, very low - if it isn't, maybe i'll re-think my gameplay a little.

cybercaine

15-08-2010, 06:53

So the odds of rolling a 123456 with 6 dice are as follows I believe: (6!)/(6^6). That is that the first die rolled could be any number, the second could be any number but the first, the third any number but the first two, and so on. This approx. = .0154 or 1.54%.

Don Zeko

15-08-2010, 06:54

That math sounds right to me.

Clobbersaurus

15-08-2010, 06:55

I believe it's 1 in 6 to the 6th power, or 1:46,656.

You have a 1 in 6 chance of getting a given number on a dice, 6 to the 6th power is 46,656 (total combination of rolls). You have one chance of rolling 1-6.

knightime98

15-08-2010, 07:05

Both are somewhat correct.

One is IF order of rolling a specific number is needed.

The other is IF any number but a doubles is needed to be rolled.

Your chance to roll specifically in order

a 1 - first

a 2 - second

...

to 6.. in order

would be the 1 in 46,656 chance.

Essentially 6 to the 6th power.

Provided that Order is NOT important Cybercaine is providing the answer you need.

Getting a straight on 6 dice is not any easy feat but not impossible and should happen about 1 to 2 percent of the time.

Play yahtzee about 100 times a year and you'll understand the way that I do. Getting a natural straight does happen somewhat frequently but yet infrequently...

So there you have it.

Hope this helps.

A long way of doing it would be this way..

Roll one die..

the number is irrelevant..

say a 5..

Now roll a 2nd die..

Your chance of NOT rolling a 5 is a 5 in 6 chance (83.33 percent)

say it is a 4..

Now roll a 3rd die..

Your chance of NOT rolling a 4 or a 5 is (66.66 percent)

say a 1.

Now roll a 4th die.. and shows a (50/50 percent)

Now roll a 5th die and shows (33.33 percent)

Now roll a 6th die and you must roll what you need exactly and yields a 1 in 6 or (16.66 percent).

Now take all these numbers and multiply them out to give your chance.

.8333 x .6666 x .50 x .3333 x .1666

will yield your chance of rolling a straight on 6 dice where ORDER is NOT important.

Yields your chance of .015422 percent...

multiply by 100 for to get actual chance out of 100..

1.54 out of 100 times you will have have your straight.

cybercaine

15-08-2010, 07:23

Both are somewhat correct.

One is IF order of rolling a specific number is needed.

The other is IF any number but a doubles is needed to be rolled.

Your chance to roll specifically in order

a 1 - first

a 2 - second

...

to 6.. in order

would be the 1 in 46,656 chance.

Essentially 6 to the 6th power.

Provided that Order is NOT important Cybercaine is providing the answer you need.

Getting a straight on 6 dice is not any easy feat but not impossible and should happen about 1 to 2 percent of the time.

Ummm. . . somewhat correct? I believe he wanted to know the odds of rolling 6 dice and not getting a double. Those were the odds that I provided. If he wanted to know the odds of getting 123456 in exact sequence, then I would have stated 1/(6^6). The other guy might have been somewhat correct, but I was spot on. Though I do appreciate the care with which you explained the lack of order (which I admit was a better explanation than mine for someone who didn't know what was going on).

knightime98

15-08-2010, 07:27

Can't we just all get along :)

I went to 6 decimal places you only went to 4 :P~

LOL..

I had to write it out. I figured it out to match your response the long way. In the end we both came up with the same answer... You just did it first before I saw the post.

Well done !

chamelion 6

15-08-2010, 09:48

Ha! I think you're both wrong! Trying to distract us with all yer fancy math stuff...

I got my 6 dice and I'm gonna sit here and roll 'em till I PROVE y'all wrong!!!!

(Yeah... right...)

8 )

cybercaine

15-08-2010, 10:14

Ha! I think you're both wrong! Trying to distract us with all yer fancy math stuff...

I got my 6 dice and I'm gonna sit here and roll 'em till I PROVE y'all wrong!!!!

(Yeah... right...)

8 )

You just might at that if you use the GW Dice. . . :P

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