Math Question for Farkle

Farkle is a game played with 6 dice. You roll all 6 dice. If you have any scoring die, you can set them to the side, and elect to record the points you have scored up to that point, or choose to roll the remaining dice. However, if you fail to get any more scoring die on the next roll, you lose all the points you have not yet recorded up to that point. If you manage to score points with all 6 dice, then you get to roll all 6 dice again, and keep accumulating a score, until you decide to freeze and record your accumulated score. Once you freeze, your score is recorded and the dice pass to the next person. A game consists of 10 scoring rounds.

1 is worth 100 points
5 is worth 50 points
3 of a kind (in one throw of the dice) is the value of the number x 100 (5-5-5 is 500), except for 1s which is 1,000.
for more than 3 of a kind, each succeeding die is worth the whole amount (5-5-5-5 is 500+500) (5-5-5-5-5 is 500+500+500)
If you throw a straight with all 6 dice, (on one throw), it is 1,500
If you throw 3 pairs with all 6 dice, (on one throw), that is worth 750 points

If on any roll, you do not have at least 1 of the above scoring, you Farkle and lose any points not yet recorded.

For all you math gurus, my feeble attempt at this math will be hilarious, but as I am faceless, I will risk the laughter....

I will stick with just the scoring probability of the 1 and 5.

I have 2/6 chance of rolling a 1 or 5 with one die = 33% (I am pretty sure I have this one right.)
I have a 2/6 + 2/6 chance of rolling a 1 or 5 with two dice = 66% ?
I have a 2/6 + 2/6 + 2/6 chance of rolling a 1 or 5 with 3 dice = 100% ?

Are the odds of rolling the 1 or 5 really additive, or should I be calculating the odds of rolling the 4 other numbers, and then subtracting that from 1 ?

Any one care to demonstrate the best way to play the game going by the odds of success on each succeeding throw?

Quote: RaleighCraps

I have a 2/6 + 2/6 chance of rolling a 1 or 5 with two dice = 66% ?
I have a 2/6 + 2/6 + 2/6 chance of rolling a 1 or 5 with 3 dice = 100% ?

The probability of getting a 1 or 5 on one or more of N dice is 1 - (2/3)^N.

N = 1: 33.3%
N = 2: 55.6%
N = 3: 70.4%

--Dorothy

Wow, I was wrong. Turns out I could be embarrassed by my attempt to calculate the odds.

Just to rub it in a little, Raleigh, using your method, what would have been your estimate of the probability of rolling a 1 or a 5 using four dice?

Quote: Doc

Just to rub it in a little, Raleigh, using your method, what would have been your estimate of the probability of rolling a 1 or a 5 using four dice?

When I got over 100% chance, yet I knew I had thrown farkles with all 6 dice, I decided I was in outer space with my reasoning. I'll take partial credit for realizing I was going to subtract something from 1 though. ;-)