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ShadowRanger
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If she's rolling the former type of die (poorly distributed), and has a weak "roll" (more drop than roll), and always rolls from a given starting point (I know a few folks who always put the 1 on top before the roll as some sort of anti-1 juju; I've done it myself on occasion), the amount of actual "rolling" that occurs would be fairly limited, and the "half" of the die can become pretty predictable (Update: Based on your comments, she uses metal dice; compared to plastic dice, they don't bounce or tumble readily without significantly more lateral force [they roll like bricks in my experience], which makes it much easier for predictable results like this to happen). Compare to how the Wheel of Fortune wheel always seems to stop only a few spaces after the last space spun (people aren't strong enough to spin it much further, so every spin is "weak", making one full rotation and stopping shortly thereafter), or how toast "always lands butter side down" when it's just knocked off the table by a tap, because the usual forces and heights involved produce a predictable number of flips (there was a Mythbusters on this that demonstrates it under controlled conditions).

If she's rolling the former type of die (poorly distributed), and has a weak "roll" (more drop than roll), and always rolls from a given starting point (I know a few folks who always put the 1 on top before the roll as some sort of anti-1 juju; I've done it myself on occasion), the amount of actual "rolling" that occurs would be fairly limited, and the "half" of the die can become pretty predictable. Compare to how the Wheel of Fortune wheel always seems to stop only a few spaces after the last space spun (people aren't strong enough to spin it much further, so every spin is "weak", making one full rotation and stopping shortly thereafter), or how toast "always lands butter side down" when it's just knocked off the table by a tap, because the usual forces and heights involved produce a predictable number of flips (there was a Mythbusters on this that demonstrates it under controlled conditions).

If she's rolling the former type of die (poorly distributed), and has a weak "roll" (more drop than roll), and always rolls from a given starting point (I know a few folks who always put the 1 on top before the roll as some sort of anti-1 juju; I've done it myself on occasion), the amount of actual "rolling" that occurs would be fairly limited, and the "half" of the die can become pretty predictable (Update: Based on your comments, she uses metal dice; compared to plastic dice, they don't bounce or tumble readily without significantly more lateral force [they roll like bricks in my experience], which makes it much easier for predictable results like this to happen). Compare to how the Wheel of Fortune wheel always seems to stop only a few spaces after the last space spun (people aren't strong enough to spin it much further, so every spin is "weak", making one full rotation and stopping shortly thereafter), or how toast "always lands butter side down" when it's just knocked off the table by a tap, because the usual forces and heights involved produce a predictable number of flips (there was a Mythbusters on this that demonstrates it under controlled conditions).

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ShadowRanger
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  1. You've accurately recorded every d20 roll for a number of sessions, and they're wildly disproportionately high (e.g. after 50 rolls, she's rolled fewer than 5 rolls below 10, which is effectively impossible, statistically), and
  2. You've rolled the same die yourself, on the same surface, several times, and accurately recorded the results, to rule out weighted dice or a magnetic die rolled on a ferrous surface (or vice versa)

There's one last possibility that could be influencing this: What type of d20 she has, and how she rolls the die. Some d20s don't evenly distribute their values; they almost always make opposing sides sum to 21, but some d20s put all the high values on one side (a single vertex is surrounded by 16-20, with all values above 11 on one "half" of the die). Others mix and match to distribute the values around the surface more evenly; the 20 might share a vertex with 2, 18, 4, and 16 (with that half comprising all the even numbers), with the opposing vertex having 1, 19, 3, 17, and 5 (with that half comprising all the odd numbers. AndAn image search for "d20" will show you both types.

  1. Have her use d20s with better numerical distribution; she may still only get results from half the die (maybe mostly just around one vertex, as your example indicates the vast majority of rolls being in the 16-20 range, matching the first d20 design I described), and only getting even results is still a slight benefit (she'll crit twice as often, and average half a number higher than everyone else), but it'll be a lot less disruptive if she's just slightly luckier, not insanely so. If she's really rolling to just one vertex most of the time (e.g. on a well balanced die, all rolls might be 2, 4, 16, 18 or 20), that's probably still too good (those are basically two failures and three successes, with one fifth of all rolls being crits), and you'll have to move to #2.
  2. Get her a dice tower. A good one should remove the human component by ensuring the die's final state depends not on the force or angle with which it was deposited, but on microscopic differences in angle, location of first bounce, etc., differences too small to control with human levels of precision. A more expensive solution, but one that ensures her results are as uniform as possible.
  1. You've accurately recorded every d20 roll for a number of sessions, and they're wildly disproportionately high (e.g. after 50 rolls, she's rolled fewer than 5 rolls below 10, which is effectively impossible, statistically), and
  2. You've rolled the same die yourself, on the same surface several times, and accurately recorded the results, to rule out weighted dice or a magnetic die rolled on a ferrous surface (or vice versa)

There's one last possibility that could be influencing this: What type of d20 she has, and how she rolls the die. Some d20s don't evenly distribute their values; they almost always make opposing sides sum to 21, but some d20s put all the high values on one side (a single vertex is surrounded by 16-20, with all values above 11 on one "half" of the die). Others mix and match to distribute the values around the surface more evenly; the 20 might share a vertex with 2, 18, 4, and 16 (with that half comprising all the even numbers), with the opposing vertex having 1, 19, 3, 17, and 5 (with that half comprising all the odd numbers. And image search for "d20" will show you both types.

  1. Have her use d20s with better numerical distribution; she may still only get results from half the die (maybe mostly just around one vertex, as your example indicates the vast majority of rolls being in the 16-20 range, matching the first d20 design I described), and only getting even results is still a slight benefit (she'll crit twice as often, and average half a number higher than everyone else), but it'll be a lot less disruptive if she's just slightly luckier, not insanely so.
  2. Get her a dice tower. A good one should remove the human component by ensuring the die's final state depends not on the force or angle with which it was deposited, but on microscopic differences in angle, location of first bounce, etc., differences too small to control with human levels of precision. A more expensive solution, but one that ensures her results are as uniform as possible.
  1. You've accurately recorded every d20 roll for a number of sessions, and they're wildly disproportionately high (e.g. after 50 rolls, she's rolled fewer than 5 rolls below 10, which is effectively impossible, statistically), and
  2. You've rolled the same die yourself, on the same surface, several times, and accurately recorded the results, to rule out weighted dice or a magnetic die rolled on a ferrous surface (or vice versa)

There's one last possibility that could be influencing this: What type of d20 she has, and how she rolls the die. Some d20s don't evenly distribute their values; they almost always make opposing sides sum to 21, but some d20s put all the high values on one side (a single vertex is surrounded by 16-20, with all values above 11 on one "half" of the die). Others mix and match to distribute the values around the surface more evenly; the 20 might share a vertex with 2, 18, 4, and 16 (with that half comprising all the even numbers), with the opposing vertex having 1, 19, 3, 17, and 5 (with that half comprising all the odd numbers. An image search for "d20" will show you both types.

  1. Have her use d20s with better numerical distribution; she may still only get results from half the die (maybe mostly just around one vertex, as your example indicates the vast majority of rolls being in the 16-20 range, matching the first d20 design I described), and only getting even results is still a slight benefit (she'll crit twice as often, and average half a number higher than everyone else), but it'll be a lot less disruptive if she's just slightly luckier, not insanely so. If she's really rolling to just one vertex most of the time (e.g. on a well balanced die, all rolls might be 2, 4, 16, 18 or 20), that's probably still too good (those are basically two failures and three successes, with one fifth of all rolls being crits), and you'll have to move to #2.
  2. Get her a dice tower. A good one should remove the human component by ensuring the die's final state depends not on the force or angle with which it was deposited, but on microscopic differences in angle, location of first bounce, etc., differences too small to control with human levels of precision. A more expensive solution, but one that ensures her results are as uniform as possible.
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ShadowRanger
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For this answer, I'm assuming:

  1. You've accurately recorded every d20 roll for a number of sessions, and they're wildly disproportionately high (e.g. after 50 rolls, she's rolled fewer than 5 rolls below 10, which is effectively impossible, statistically), and
  2. You've rolled the same die yourself, on the same surface several times, and accurately recorded the results, to rule out weighted dice or a magnetic die rolled on a ferrous surface (or vice versa)

There's one last possibility that could be influencing this: What type of d20 she has, and how she rolls the die. Some d20s don't evenly distribute their values; they almost always make opposing sides sum to 21, but some d20s put all the high values on one side (a single vertex is surrounded by 16-20, with all values above 11 on one "half" of the die). Others mix and match to distribute the values around the surface more evenly; the 20 might share a vertex with 2, 18, 4, and 16 (with that half comprising all the even numbers), with the opposing vertex having 1, 19, 3, 17, and 5 (with that half comprising all the odd numbers. And image search for "d20" will show you both types.

If she's rolling the former type of die (poorly distributed), and has a weak "roll" (more drop than roll), and always rolls from a given starting point (I know a few folks who always put the 1 on top before the roll as some sort of anti-1 juju; I've done it myself on occasion), the amount of actual "rolling" that occurs would be fairly limited, and the "half" of the die can become pretty predictable. Compare to how the Wheel of Fortune wheel always seems to stop only a few spaces after the last space spun (people aren't strong enough to spin it much further, so every spin is "weak", making one full rotation and stopping shortly thereafter), or how toast "always lands butter side down" when it's just knocked off the table by a tap, because the usual forces and heights involved produce a predictable number of flips (there was a Mythbusters on this that demonstrates it under controlled conditions).

In all of those cases, you have what you think of as many equally probable options, but the lack of entropy (in this case, sufficient lateral movement and bouncing to trigger tumbling and spin in the die) being injected into the system means that only some of the options are likely.

If this is a possibility, you have a couple options:

  1. Have her use d20s with better numerical distribution; she may still only get results from half the die (maybe mostly just around one vertex, as your example indicates the vast majority of rolls being in the 16-20 range, matching the first d20 design I described), and only getting even results is still a slight benefit (she'll crit twice as often, and average half a number higher than everyone else), but it'll be a lot less disruptive if she's just slightly luckier, not insanely so.
  2. Get her a dice tower. A good one should remove the human component by ensuring the die's final state depends not on the force or angle with which it was deposited, but on microscopic differences in angle, location of first bounce, etc., differences too small to control with human levels of precision. A more expensive solution, but one that ensures her results are as uniform as possible.