In some CRPGs, you start by creating a party, or sometimes just a single character. In some of those, there is some randomness involved in character creation; in particular, it's not unusual for stats to be determined randomly. The question, of course, is "when do you stop re-rolling"?

For a specific example, let's consider a game that handles stats similar to classic Wizardry:
* On character creation, each character has fixed base stats determined by race (which has already been chosen).
* The character gets a random number of bonus points, which can be distributed to stats as the player chooses. Of course, more bonus points are better.
* There is no way to save the roll and still keep re-rolling; the player must either accept the current roll or discard it and hope for a better roll.
* The maximum bonus point roll is not known to the player.

Now, the question is:
* When should I stop rolling for stats?

One possible strategy is to roll n times, keep track of the highest number of bonus points, then re-roll until that result or better comes up again. For this strategy, what should the value of n be?

Or, can you think of a better approach?

To be fair you shouldn't stop until you get the desired stat you aimed for ! it took me 8 hours straight rerolling once in BG until i was happy.

Just be patient.

But maybe I would like to spend those 8 hours actually enjoying the game?

Also, in many of the games I think of (Wizardry and Bard's Tale, for exmaple), the roll doesn't actually matter in the long run, as your stats will max out anyway if you level up enough. (I actually prefer it when the roll doesn't matter in the long run; having stats be nearly immutable is one of the things I don't like about Baldur's Gate, though it isn't a dealbreaker; there's other aspects of that game that are worse.)

Do you want to be haunted with doubt and shame every time you lose a close battle? lol

Re-roll as fast as you can. Stop when you see exceptionally high stats. Shouldn´t take long.

Losing is fine, particularly since it *is* a game mechanic.

(I dislike it when games punish you harshly when this happens, incidentally.)

Also, some games are not that hard at the start and instead get harder as you progress; in fact, really all (sufficiently long) single player games should be like that, but unfortunately many games (particularly games where the player gets stronger as the game progresses) fail that criterion.

I could also mention the speedrun perspective, where (if character creation is factored into the time) one only rerolls until the stats needed for the speedrun are obtained (and sometimes you *want* a stat low for this purpose!). What does "exceptionally high stats" mean, particularly when it's your first time playing the game and you don't know what's typical and what's good?

I mean stats, that are higher than the first few rolls. It´s the way, I do it. But if I should choose a more mathematical approach: I would roll ten times, write all numbers down, keep the highest result, and re-roll again until I get a higher result.

Of course, is 10 a good number, or is there a better number to choose? (Remember that the time it takes increases with the value of "n" (which you chose to be 10), and the increase is non-linear.)

A more specific statement of the problem is, suppose you are limited to k rolls, and if you run out, you *have* to take the last one, even if it's sub-optimal. What should the strategy be here, and if using the strategy you mentioned, what should the value of n be?

In this case it depends on the time you are willing to invest in the character creation, I think. Of course you can roll 20, 50 or 100 times. But I think, you can get a good overview of the possible values with around 20 rolls. Of course you need more rolls, if you assume, that the developers made really rare "high drops". In this case, let´s say you have five rolls. I would roll four times. If I am happy with the fourth roll, I would keep it. If I´m not, then I would roll a last time and live with the result.

Use loaded dice!

You mean, "manipulate the RNG!", right?

Before you ask, this is actually possible in some games. Pokemon players have used RNG manipulation to, among other things, get Pokemon with good IVs (which is the Pokemon equivalent of getting good stat rolls).

(Also possible to great effect in Dragon Warrior 1, but that game has no randomness in starting stats and stat games. Dragon Warrior 3 might be a better example, and speedrunners do use RNG manipulation there as well.)

Roll once and stick to your results. That's how true roleplayers do it.

Well with rolls in Wizardry I always go for a minimum of 18 points, the class I'm trying to achieve may factor in as well but 18 is always my starting point.

And if the result is not viable?

(Incidentally, this can happen in Advanced Dungeons & Dragons (2e and earlier). Every class has a stat reqirement, and every character needs to have a class, so (especially rolling 3d6 for each stat in order) there's the possibility of rolling a combination of stats that do not qualify for any class, and being unable to finish character creation as a result. I believe 3e did away with stat requirements for classes, so this problem won't happen there, but such a character might not be fun to play (and spellcasting classes can't cast spells if the stat is too low).)

1) Look up the maximum roll.
2) Use any kind of cheat to simulate getting a reasonably good roll, such as 75 to 85 out of 100 possible points.
3) Enjoy the actual game.

Rolling for stats in video games bothers me, I don't find it enjoyable. If I can skip it with any kind of cheat, be it through console commands, file editing or a simple save game editor, I definitely prefer that over spending an hour rolling for stats until I get something I'm content with.
Likewise, there have been games in which I liked the gameplay a lot and, due to having no modern difficulty slider, decided to cheat myself stats equivalent to a particularly bad roll.

It's different when I get to play with people, though. There it's the first roll and you try to get the most out of it, since the greatest share of fun is in the player-player interaction and having sub-par stats can add a lot of spice to a game.