4 or 5 dice - no 1 or 5 probability

Can someone please tell me what the probability is of rolling 5 six sided dice (all at once) and not getting a least one 1 or 5? What about when rolling 4?
How is this different than the odds given the same scenario?

Thank you in advance for your kind consideration of this newbie.

Darrin

Hi Darrin,

When rolling five dice, the probability of NOT getting at least one 1 or one 5 is small... .13168 (About 13.17%)
(4/6)^5

In other words, if you are playing "Oh Shit" or "Farkle" or whatever name that dice game is going under these days, there is about an 87% chance you will roll that much needed 1 or 5, when rolling five dice.

When rolling just four dice, obviously not rolling at least one 1 or one 5 will happen more often. The probability jumps up to .19753.... about 19.75%.

(4/6)^4


If you want to know the odds, it's easy. A 20% chance, for example, will happen 1 time in 5. So the odds are 4 to 1 in your favor. (Or against you, depending upon how you look at it.)

A 13% chance will happen about 1 time in about 7.6 attempts. So the odds are 6.6 to 1 in your favor. (Or against you, depending upon what you want.)

Hope this helps.

Why does Farkle make it '1' or '5' instead of '1' or '6'?

There are lots of variants of this game out there, including branded ones like "Farkle", "Risk and Roll 2000", "Cosmic Wimpout", and surely others.

In general, starting a turn with 5 (or 6) dice, you must roll a 1 (worth 100 points), a 5 (worth 50 points), or a three of a kind (worth 100 x value, except 1's are 1000). Some versions allow for other special combos (1-6 straight; 3 pair). You also must set aside the dice you wish to score, and then decide if you want to roll again. Scoring with all 6 dice usually allows you to reroll all 6 dice again to increase score.

Also depending on the version, you may have to score a certain amount of points before being allowed to stop.

So while the odds of getting a 1 or 5 are nice to know offhand, when you have 3 or more dice, getting triplets can increase the odds of scoring.