Honest Rolls Character
Honest Rolls Character is a tabletop games trope, which on /tg/ is usually referred to as some variant of "3d6 in order". It refers to a method of character generation popularized, if not created by, Dungeons & Dragons, where the player rolls dice to generate Ability Scores and sticks with the first result rolled for each Ability Score.
This method of generating character stats isn't popular these days (indeed, even back then House Rules frequently circumvented this) because, since the rolls are honest, they are also completely random. You will get average or below-average stats more than half the time, and stats well below average on occasion, especially if you forgot to pay homage to the Random Number God before you rolled; and if you had your heart set on a pre-conceived character concept, the dice were more than happy to mess up your plans, usually by placing a low number into a score that you really needed a high number in.
Just looking at D&D in particular, just one stat below 8 - and remember that for any given stat, there is approximately a 16.2% chance that it will be 7 or less in the 3d6 scenario - will severely limit your character abilities; two or three stats below 8 can render it unplayable as a PC. And that's before you actually try to play the character and have to deal with the penalties for below-average stats, which was anything from a -1 penalty to hit and damage for a low Strength for the earliest versions, to a big penalty to AC if your Dexterity was the stat that took the hit in the later versions. Prior to 3rd edition, this problem was even more pronounced, as you needed a bare minimum in certain ability scores to qualify for certain classes AND for certain races (which were one and the same, in the original D&D). Which meant that if you had your heart set on playing a Paladin, you were almost certainly screwed over if the DM insisted on this method of score generation, as its extremely high stat requirements in multiple ability scores meant your odds of randomly qualifying for it were practically on par with winning the lottery.
Some Game Masters live for the chance to run a campaign where someone is brave enough to run such a character, up to the point where they'll require honest rolls characters so they can have a campaign supposedly focused on personalities and role play rather than a munchkin-fest. (The possibility that one or more players might then just happen to honestly roll up "munchkin" characters anyway is rarely addressed.) This tends to clash with the sort of player who comes to the table with a firm idea of what sort of character they'd like to play in their head already, as well as with most notions of 'party balance' since some player characters are apt to be just plain randomly better than others in the same group; but it can work if all the players are on board with it and willing to roll with whatever the dice hand them.
Despite its association with the Old School Roleplaying crowd, even they don't always agree on whether or not the original 3d6 in order method is really the best method for character generation - the stereotypical grognard will argue that it's essential to ensuring a "real" RPG experience, but there are just as many fans of retroclones who think that it just screws over the players and turns them off.
In fact, ironically, Gygax himself was no great fan of this system! Whilst he created it for the OD&D game, he wasn't happy with it. When he went on to make his "improved" version, Advanced Dungeons & Dragons, he initially left this method of character generation out entirely! In the 1st edition PHB/DMG, "Roll 4d6 and drop the lowest, rearrange as desired" is Method 1 of the four recommended methods for determining character attributes. The other three are "Roll 3d6 twelve times and retain the highest six scores", "roll 3d6 six times for each ability score and retain the highest result" and "generate twelve sets of ability scores, each time rolling a 3d6 for each ability score, and retain the single set the player prefers". He explicitly warned players and DMs against using the 3d6 in order method to generate PCs, and even recommended a variant of it for generic NPCs.
It wasn't until AD&D 2nd edition that he reluctantly brought it back as one of the six methods of character generation. The other five methods he recommended consisted of "Roll 3d6 twice for each ability score, and then keep which result you prefer for that score", "Roll 3d6 and arrange the results to whichever ability scores you want", "roll 3d6 twice, keep the results you want and arrange to taste", "roll 4d6, drop lowest, arrange as desired", and "start with an 8 in all stats, then roll 7d6 and add the results from each dice to each ability score as you prefer".