Similar to the Hoarder is the player who recognizes that we're getting close to leveling up, and this seems likely to be the climactic encounter for Level X, so I'll nova out all my bennies now since they recover immediately after anyway. Recovery per session makes this tactic much easier to implement.
If I have a low STR or a low INT, do I build a character who needs that stat for key activities of the character? Low INT wizards and low INT Bards seem less than likely. 8 WIS wizards will be pretty happy about their Will saves, I suppose. Maybe I'll drop a low stat even lower (a -1 penalty with 1 reroll or a -3 penalty with 3 re-rolls, on a stat I rarely use so the rerolls will be available for a lot of rolls, seems like a mechanics, rather than flavour, choice).
Seems like some stats are more suited than others to this system. My CHA or INT affects rolls. My DEX or CON affect AC and HP, and I get no benefit offsetting those drawbacks.
A couple of posters have suggested a "flaw that gives you a benefit when you suffer a drawback" model. What if you earned a reroll when your low stat negatively impacted you? You miss that Knowledge Check by your INT penalty, or get hit because of your DEX penalty, so you get a benefit which can be used on a future action involving that stat. This would have to be monitored for "useless roll abuse" ("I try to remember the name of that town - oh, failed by one, I get an INT reroll"), but would link benefits received with frequency of impediment from the low stat. As a deterrent to hording, perhaps you can only have a maximum number of unused re-rolls equal to the negative stat modifier.
If I have a low STR or a low INT, do I build a character who needs that stat for key activities of the character? Low INT wizards and low INT Bards seem less than likely. 8 WIS wizards will be pretty happy about their Will saves, I suppose. Maybe I'll drop a low stat even lower (a -1 penalty with 1 reroll or a -3 penalty with 3 re-rolls, on a stat I rarely use so the rerolls will be available for a lot of rolls, seems like a mechanics, rather than flavour, choice).
Seems like some stats are more suited than others to this system. My CHA or INT affects rolls. My DEX or CON affect AC and HP, and I get no benefit offsetting those drawbacks.
A couple of posters have suggested a "flaw that gives you a benefit when you suffer a drawback" model. What if you earned a reroll when your low stat negatively impacted you? You miss that Knowledge Check by your INT penalty, or get hit because of your DEX penalty, so you get a benefit which can be used on a future action involving that stat. This would have to be monitored for "useless roll abuse" ("I try to remember the name of that town - oh, failed by one, I get an INT reroll"), but would link benefits received with frequency of impediment from the low stat. As a deterrent to hording, perhaps you can only have a maximum number of unused re-rolls equal to the negative stat modifier.