Statistically when to stop rolling in Greed
Greed (a.k.a. Farkle) has an extensive amount of statistical analysis done on the game.

Now that you have updated your question, here is my updated answer.

If you want to maximize your score, what you need to figure out is what is your expected score if you risk rolling, compared to your score if you choose not to roll. So, the first thing you need to know, is what is your expected number of points you will earn for rolling 6-dice. Below is a chart of the different possible Patterns (6-of-a-Kind, 5-of-a-Kind, etc.), the possible ways of ORD 'ering those particular patterns (which are all the same combination), the number of DIF 'erent patterns that can be made with other numbers from 1-6, and the Total permutations (which should add up to 6^6=46656).

+-----------+----+---+-----+
|Pattern    |ORD |DIF|Total|
+-----------+----+---+-----+
|a,a,a,a,a,a|   1|  6|    6| 6-Kind
|a,a,a,a,a,b|   6| 30|  180| 5-Kind (possible '1' or '5' score singles)
|a,a,a,a,b,b|  15| 30|  450| 4-Kind (possible '1' or '5' score singles) 
|a,a,a,a,b,c|  30| 60| 1800| 4-Kind (possible '1' or '5' score singles)
|a,a,a,b,b,b|  20| 15|  300| 2 * 3-Kind
|a,a,a,b,b,c|  60|120| 7200| 3-Kind (possible '1' or '5' score singles)
|a,a,a,b,c,d| 120| 60| 7200| 3-Kind (possible '1' or '5' score singles)
|a,a,b,b,c,c|  90| 20| 1800| 3 Pair
|a,a,b,b,c,d| 180| 90|16200| (possible farkle, possible '1' or '5' score)
|a,a,b,c,d,e| 360| 30|10800| (possible '1' or '5' score)
|a,b,c,d,e,f| 720|  1|  720| straight
+-----------+----+---+-----+
|      Total|1602|462|46656|
+-----------+----+---+-----+


I didn't separate these individual patterns by how much they actually score, because it would be way to big of a table. The table would have to differentiate from each different kind of 3-of-a-Kind, and possible '1' and '5' single die scores. I did separate them when running a calculation of the average (total points/permutations). The only important information from that computer analysis is:


1080/46656 : The odds that when you roll 6 dice, you cannot score anything. (Farkle)
388.033 : The average number of points that you make on your first roll of 6 dice, if you score.


You can use the above information, you can examine all possible outcomes of rolling a single die, and look at the risk (how many points you will lose if you fail to score) versus the amount of points that you will gain. You can think of this as you would any sort of gambling question. 


Question: Imagine a game where you pay $X, and you roll a die. If you roll a '1' you win $100 plus your original bet ($X), if you roll a '5' you win $50+$X, if you roll anything else you lose your bet ($X). How much would you pay to play this game? 
Answer: Anything up to $37.50. Until that point, you expect to win more money than you lose. The sum of your losses multiplied by their probability of happening (-37.5 * (4/6) = 25 = ((100*(1/6)+(50*(1/6)) is equal to the sum of your winnings multiplied by their probability of happening.

1) +$100

2) -$37.5

3) -$37.5

4) -$37.5

5) +$50

6) -$37.5


Now, lets add up all the possibilities for Greed assuming you have X points already, and you intend to roll six dice if you win the single die roll.

|Outcome              |Odds the Outcome Occurs | Points *Odds |
+---------------------+------------------------+--------------+
|Lose rolling one die |4/6                     | -4/6*(X)     |
|Win  50 +Avg six dice|(1/6)*(46656-1080)/46656|(AVG+50)*Odds |
|Win 100 +Avg six dice|(1/6)*(46656-1080)/46656|(AVG+100)*Odds|
|Lose rolling six dice|(2/6)*(1080/46656)      | -(5/648)*(X) |
+---------------------+------------------------+--------------+
                Total | 1.0                    |              |


Time for Some Algebra

Solve for the sum of all the above outcomes equals zero.


(add each line above together)


0 = -(4/6) * X - (5/648) * X + (2*AVG+50+100)*(1/6) * (46656-1080)/46656)


(multiply the first X term by 108 to get the same denominator for both X terms)


0 = -(432/648) * X - (5/648) * X + 150.771547


(Add X term to both sides, simplify two added terms)


(437/648) * X = 150.771547


(Solve for X)

X = (648/437) * (150.771547) = 223.6 (approximately)


Since scores are always a multiple of 50, you should stop rolling when you hit 250 points. I leave the the 2 dice question as an exercise for the OP. You should have all the tools necessary to calculate it (I will check your work if you attempt to answer it. If you do attempt to answer it, post the question in a new thread linking back to this thread, and explain your work).

Optimal Strategy for Multiplayer

Another more difficult question to answer is what is the optimal strategy to win. The calculations for this are more complicated, because you have to take into account how likely the opponent is to win before you (their likely score before your next turn, etc.) I have no doubt that a nearly optimal Greed computer program can be created for (two players). As you increase the number of players though, the problem gets exponentially more difficult. You might want to check the links in this post that talks about how optimal Yathzee for one player was created, and how the two player version is pretty close to optimal.