There are 6^2 = 36 possible outcomes when we re-roll the 1 and the 4. We first calculate the number of different outcomes that result in a particular hand and use this to determine the probability of each hand. For example, the probability of rolling a 2 and a 6 is 2/36 since we could roll the 2 and then the 6, or the 6 and then the 2. The probabilities of each of the hands are:
| Hand | Number of Outcomes | Probability | Straight |
| 6 - 2 | 2 | 2/36 = 1/18 | Large |
| 1 - 2 | 2 | 2/36 = 1/18 | Large |
| 6 - (not 2) | 4 · 2 + 1 = 9 | 9/36 = 1/4 | Small |
| 2 - (not 1 or 6) | 3 · 2 + 1 = 7 | 7/36 | Small |
| no 2 or 6 | 4^2 = 16 | 16/36 = 4/9 | None |
Note that a six paired with any other number can occur two ways, but a pair of sixes occurs in only one way. This is why the third and fourth rows have a plus one in the number of outcomes column.
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Next, for each of the possible first roll outcomes we calculate the probability of getting a large straight or a small straight on the third roll. For the 6-2 and 1-2 hands we already have our large straight so we are done. For the 6 - (not 2) hand we re-roll the non-2 die. We have a 1/6 chance of getting a two and a large straight, and a 5/6 chance of not getting a 2 and having only a small straight. For the 2 - (not 1 or 6 hand) we will keep the 2,3,4,5 and re-roll one die, giving us a 1/3 chance at rolling a large straight and a 2/3 chance of having only a small straight. In the case where we rolled no 2 or 6 on the second roll, the situation for our third roll is the same as the situation for our second roll, so the above table gives the probabilities of each outcome.
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Combining these results we see that the probability of a large straight is
1/18 + 1/18 + (1/4) · (1/6) + (7/36) · (1/3) + (4/9) · (1/18 + 1/18) &asymp 0.267.
The probability of a small straight (but not a large straight) is
(1/4) · (5/6) + (7/36) · (2/3) + (4/9) · (1/4 + 7/36) &asymp 0.535.
The probability of getting no straight at all is (4/9)2 &asymp 0.198.
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If we re-roll only one die, then on our second roll we have a 1/6 chance of rolling a 2 and getting a large straight. We also have a 1/6 chance of getting a 6 and a small straight. In this case, on our third roll we have a 1/6 chance of rolling a 2 and getting a large straight. However, 2/3 of the time we get neither a 2 or a 6 on our first roll in which case our situation does not change. Therefore our chance of getting a large straight is
1/6 + (1/6) · (1/6) + (2/3) · (1/6) &asymp 0.306
The probability of getting only a small straight is
(1/6) · (5/6) + (2/3) · (1/6) = 0.25.
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The chance of getting no straight is (2/3)2 = 4/9 &asymp 0.444. So re-rolling only the 4 gives you a slightly higher chance of getting the large straight, but a much lower probability of at least ending up with a small straight. If you only need a large straight then re-rolling just the four is the better strategy, but if a small straight would also be valuable then re-rolling the 1 and the 4 might be a better move.