Posted by gunnsatbeach
Mar 21, 2015

## Dice at Farkel

When rolling three dice, what are the odds of either a five or one coming up?

mustangsally Mar 21, 2015

i would do this by figuring the ways each die could NOT be a 1 or a 5

for 3d6

4*4*4=64 = ways NOT getting a 1 or a 5

there are 6*6*6 ways 3d6 can land = 216

216-64=152 ways they could land

there is also a math method called inclusion/exclusion

http://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle

that takes more time (for some) but can easily solve more difficult type problems

for 3 sets

(2/6 + 2/6 + 2/6) = 1

-

(2/6 * 2/6)

-

(2/6 * 2/6)

-

(2/6 * 2/6)

+

(2/6 * 2/6 * 2/6) = 0.703703704

same results but different method used

you must have a reason to know this?

Sally

beachbumbabs Mar 21, 2015

Sally,

Farkle is a bar game, where 5's are worth 500 points, and 1's worth 1000. The other dice are worth nothing. Each successive roll, you keep the 5's and 1's towards your points, and must roll another 5 or 1 to continue your turn or stop and take your score; if you don't improve, you lose your bank. I think they usually start with 5 dice, and the OP is trying to decide whether to keep his total with 3 dice left to roll, or stop there.

JMO of what he really wants to know - his odds on continuing.

tringlomane Mar 21, 2015

Yeah, in farkel, you must make a scoring combination to continue in the game.

The easiest way to continue is to roll at least one "1" (100 points) or one "5" (50 points)

But also with three dice remaining, you can also score by getting 3 of kind of any number (dice rank x 100 points; 3 1s sometimes are 1000 points).

So on top of making at least one 1 or 5, but you may also continue with 222, 333, 444, and 666.

So the overall probabilty of being able to continue...

Chances of at least one 1 or one 5:

1 - (4/6)^3 = 152/216 = 0.7037037037037037037037037037037

plus 222, 333, 444, and 666

4/216 + 152/216 = 156/216 = 13/18 = 72.22%

Gabes22 Mar 28, 2015

I have played Farkel on numerous occasions, from my experience you have a mathematical edge in getting a scoring hand when only having 2 dice in your hand rather than passing it. However, there is a point in which it might be too risky to press it, for instance if the roll gets up to a comfort threshold, like maybe 1500 points to risk getting nothing by rolling it.