What are the odds?

By Shamus
on Jul 5, 2007
Filed under:
Nerd Culture

A roundup of serveral people who had interesting responses to my Seesaw probability theory:

Darkenna sets a non-believer straight in this thread.

Everyone knows that anecdotal evidence is the most convincing.

The science behind seesaw probability.

More analysis here.

EDIT: Also, never mistake superstition for science! Or is that the other way around?

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1818 comments. (18 is the only non-zero number that equals twice the sum of its decimal digits.)

From the Archives:

  1. Bruce says:

    So if a die rolls a twenty and no-one sees it, does it still count? What constitutes a roll? Landing on a flat surface or pausing in a face up state.

    Perhaps it is wise for all die should be kept secure from rolling (in an unloaded 1 state) while being transported, as you may inadvertently be dropping twenties behind you as you move from A to B.

  2. Bruce says:

    Gah, my first First and I mess up on the grammar…

    Damn the lack of an edit function…

  3. Nanja Kang says:

    I have cited this rule for the last year and a half with my gaming posse. I have a mage player who is a d6 freak, he may have a doll house for his dice, he may play with them at home when we don’t play D&D, I don’t know. However I do know that since I am the DM, I am not allowed to touch my players dice AT ALL. (They claim the opposing forces with change the juju of the dice.) And of course I personally have my own DM dice and my player dice… I learned the hard way that my DM dice do not like it when I use them when not DM’ing… scary.

  4. Anon says:

    Bruce: Quantum physics experiments show that electrons will act like waves that interfere with each other, even when individual electrons are fired, unless they are observed, in which case they will act like matter.
    See this video on the “double-slit” experiment, and prepare to have your mind blown.
    If one applies this to dice, one could deduce that a die will only effect future rolls if you observe the rolling.

  5. H8R says:

    There’s this guy who wrote this Mac software called “Lottery Wizard” or something, and he actually charges money for it, claiming by implication that it’ll help a regular lottery player by tracking prior numbers and so on, which is utter bunk. It’s so much utter bunk that every time the guy posts an update to his software in VersionTracker, the comments section under it gets slammed by a dozen people all decrying what utter bunk the software is, followed by a handful of posts about how anyone stupid enough to not understand the Gambler’s Fallacy deserves to lose $17 and a great deal of time on software that has no possible way of actually increasing anyone’s chances of winning anything, so leave the guy alone.

    There’s this neat book out there called “Innumeracy, Mathematical Illiteracy and its Consequences,” and it should be required reading for everyone in the world, especially gamers.

  6. Dan says:

    I’ve found that you can completely reset a d20 by rolling it 20 times inside a completely enclosed box, so that there is no possibility that the resulting rolls can be observed. I’m sure a lead box would be preferable, so that neither angels nor Superman could inadvertently see the results, but I’ve found that cardboard does the trick.

    Be very careful, however, to roll the die exactly 20 times. If you go over that, you’ll need to roll it at total of 40 times. If you accidentally roll it 21 times, and the last roll happens to be a 20, you’ve wasted the unobserved 20 while also poisoning the die’s future rolls.

  7. Romanadvoratrelundar says:

    So, this is a box fitted with those bubble gloves like doctors have? I mean, if it’s completely enclosed?

  8. Dan says:

    Looks like gamers have the same delusion gamblers have.

  9. Space Ace says:

    Reminds me of a drinking game.

    It involves two six-siders and the numbers thrown combine to form a number. A 4 and 3 are 43, a 5 and a 1 are 51, etc. Doubles make for numbers in the hundreds (a 1 and a 1 are 100, for instance). It’s quite simple, if your throw is the lowest, you have to drain a glass. But there is more! A 2 and a 1 don’t make 21, but something called a “mex”, which doubles the amount of alcohol involved and is a perfect way to either make your friends suffer or drink all the beer they payed for.

    The thing is, I could swear the probability of throwing another mex increases astronomically once one has already been thrown.

  10. Cenobite says:

    Nanja Kang @ #3:

    That’s because there is a social hierarchy among dice, just like among us humans. Being the dice of the DM is a PRIVILEGE. It marks the dice as being superior probability determinants over all of the other dice, who belong to mere players. The DM’s dice drive the course of the game — the players’ dice can only be rolled in response to the the DM’s dice, not the other way around. The class divide grants (or denies) dice an ego boost and a corresponding work ethic, depending on which side of the divide they fall under. This is why the DM’s dice will always perform better than players’ dice. One class is oppressing the other.

  11. wumpus says:


    More evidence for the possible non-randomness of dice throwing, in an actual scientific context, can be found in the work of the recently deceased Princeton Engineering Anomalies Reseach (PEAR) lab:


    Why do I know about this? Because one of the members of the lab’s staff, York Dobyns, was my favorite GM (mostly for Champions/Hero based games) when I was in college…


  12. Thad says:

    Just remember: a roll only counts if the GM catches you at it.

    (Oh, and PEAR won’t let anyone skeptical examine their results, so most people don’t have much truck with there results. Go over to http://www.randi.org and search for PEAR.)

  13. Miral says:

    I’ve always thought that this was one of the failings of d20: the rolls are unidirectional (higher is always better). It’d be fairer (though also a bit more confusing) if some rolls you needed to get as low as possible while others you wanted as high as possible — and you had to use the same dies for both kinds. Otherwise the game is vulnerable to people with loaded dies (even if the loading was not intentional — it could have been a manufacturing flaw).

  14. David says:

    “It’d be fairer . . . if some rolls you needed to get as low as possible while others you wanted as high as possible”
    That’s when you get into the world of d%’s. On a standard d10 roll, the highest you can roll is a 10, which reads as 0. The lowest is a 1. However, when you combine 2 d10s to make a d%, rolling both 1’s is an 11. A bad roll by itself, but not the worst. Rolling both 0’s DOES get you the best roll (unless you’re playing CoC), but oddly enough, the worst roll comes when you combine a high roll with a low roll. (Or in Cthulhu, that gets you the best roll.) A 0 followed by a 1 gets you a roll of 1, which is a critical failure in d&d and other d20 games. However, a roll of 1 followed by 0 ends up as a 10, which makes one case where the high roll after the low roll made it less than two low rolls in a row. Very confusing in the long run.

  15. Luke says:

    Let’s not forget about the other important factors here:

    A die can only be recharged a finite number of times. This means that some dice will become permanently depleted. When that happens you need to retire the d20.

    Also if any currently depleted d20 touches a “charged” d20 it will instantly knock-off it’s remaining charges. This is especially evident when you throw a depleted die into a pool of “fresh” dice – it will start a chain reaction that will “poison” the whole pool.

    This is called dice poisoning and in the past it actually lead to big arguments in my gaming group – especially when we were playing d6 version of Star Wars. In that game you would sometimes make rolls with 10-15 or more dice, so we had strict rules about which dice are “off limits” for the big rolls. Swiping a single depleted dice into your dice pool to make that 20d6 roll was considered criminal, because it would poison almost all the available dice ruining the game for everyone.

  16. wumpus says:

    Howdy Thad,

    I don’t want to rehash the threads on the Randi site, but I’d have to say that they don’t really seem to add much light to the subject, so much as heat. There do appear to be people there asserting that PEAR didn’t/wouldn’t publish its procedures (and that they couldn’t find anyone to review their results), but even that assertion seems unsupported.

    Knowing one of the principal staff members, as I did, I find the assumption that PEAR was all some sort of scam to be difficult to believe. Most of the Randi people are treating them as if they were a carnival sideshow or parlor tricksters – out to perpetrate fraud/put on a show for profit. Is it so hard to believe that they were honestly doing their best to scientifically test (which means attempt to _disprove_, as science cannot prove anything) some ‘paranormal’ hypotheses?

    Of course, it does seem possible that the statistical tools they used to do their analysis may, in the end, be inappropriate or insufficient to the task. I don’t have enough background in statistics to tell. The reluctance of those who do have that background to even look at their work, though, while perhaps understandable (Who wants to be associated with research that has already been tarred as ‘research’?), is hardly proof that their methods are unsound.

    All of which is moot, anyway, because ever since I became aware of PEAR’s work, my personal improbability field has been altering their results in whatever way is most harmful to me, which probably means making the world more boring, i.e. dampening their results to demonstrate that there is no such thing as an improbability field.


  17. gedece says:

    This could be very simple to bypass: calculate the ammount of times you roll your dice over the course of one RPG session, then multiply it by 2 to be on the safe side. Get as many D20s, and get two big dice bags.

    You get a fresh D20 and roll it normally for game purposes, untill it hits a 20, then you get it into the other bag. you pick a fresh D20 and start again.

    now comes the tricky part: you have to find a gaming group that plays something where a 1 is the most desirable result, and repeat the process but changing the bag you draw from to the receiving end and the one you put things on to the getting end.

  18. Phil says:

    I’m going to get to work on coding dice that actually have a finite number of 20s for my IRC games.

    I figure there will be ’rounds’ of 50 rolls. The software will roll the die 50 times and count the number of 20s rolled. This is the number of 20’s you’ve got saved up for the next 50 rolls. Every time you don’t roll a 20, the chances of rolling one increase until you run out of 20s. When you reach the 50th roll or when you roll a 1, the system resets. Any 20s you hadn’t rolled yet are gone if you rolled a 1.

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