Percentile Dice Probability

I have a probability question I was hoping someone could help me out with. We've started a Call of Cthulhu campaign. In our gaming group, one of the members reads percentile dice strangely:

My interpretation of results:

His interpretation of results:

Basically he always treats a 0 on the ones column die as ten. So if you roll a 90 on the tens, and a 0 on the ones that becomes 90+10=100.

I can't find fault with the method as it also produces a result of 1-100, but it is adverse to every rule system I've seen. My question is, does this change the curve of probability based on the number positioning on the die. With the traditional method, 99% of the time the ones digit die represents and resides between the 8 and 4 sides of the dice. With this alternate method it is 100% of the time counted as a 10. I believe that the difference is negligible, but I am unsure as how to prove it.

Thoughts?

Seems fine to me from a cursory glance.

It would make things slightly easier if he would do the same rolls as everybody else but if he insists then who cares?

Your friend is mental and he's using his weird way to increase his score on his roles. If you role a 20 and a 0 you've rolled a 20 but if they do it, they've rolled a 30. If you both roll a 20 and a 7 then you've both rolled a 27. There's no negative to him rolling a 0 on the "ones" dice because he's just adding 10 to what he rolled, and assuming higher numbers mean a greater chance of success, he's increasing his chance of success. So as long as they don't roll 00 the worst score they can get is 11. As long as you don't roll 00, the worst you can get is 10.

Their method seems like cheating though possibly being doing unintentionally.

Instead of addition which is what he's doing, you use the dice to represent the ten's and one's (which is what you're doing). The X0 represents the Tens and the X represents the Ones. Only when you roll 00-0 do you change that to mean 100

@jesus_phish: He's not cheating. He still has the same odds as anyone else to roll any particular number between 1 and 100: exactly 1 in 100. It's definitely a bit odd and counter-intuitive, but whatever floats his boat. As long as he's up front about it.

the only difference I can see is changing the range of values from 0-99 to 1-100.

They have the same odds yes, but they're also getting to some of the higher numbers quicker by the method they're using. The way the OP rolls and tots up the result means he goes 100, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ........ 98, 99.

The way his friend tops up the score he goes 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 20,11........100, 91... 99. That's all I meant by cheating. In a game where getting high numbers matters (I assume for CoC you want to roll above your skill score), those method results in getting higher numbers sooner in the sequence.

So the 0 becomes more powerful. I suppose it's sort of a Aces High/Low thing, but you're never going to play poker with people who are playing different rules than you without establishing if an Ace is better than a King or worse than a 2, though I realize CoC is probably a co-op game.

@jesus_phish:

The only effect I can see on the probability are the relative positioning of the numbers on the die face. Assuming the die were perfectly shaped, and the rolls forceful enough I don't believe that the odds are different with either method. I certainly see validity in is method as far as constancy of mechanics go. It makes rolling a 100 more consistant, 90+10 = 100 whereas 00+0 = 100 in the traditional method.

@erickmartins: The value are 1-100 in either system.

@sir_gunblade: Yeah the odds are of course they same, I just think it makes the 0 more powerful. It turns the dice from 0-9 into 1-10, which is fine, but it means that if they roll a 0, it's a ten, and if you roll it, it's a 0, that's all. The only time for you a 0 is not a 0, is if you roll all 0's.

I can see where he is coming from but in the history of dice based games with percentile dice his reading of them is incorrect.

@sir_gunblade: wasn't aware that rolling 0-0 was 100. If that's the case, they're exactly the same thing.

Your friend is crazy, thats not how you use a D100.

For the sake of "ease of use", you really should agree that the dice are used at "face value" instead of "added". The only quibble thing is "what does '00' mean?" where you need to agree that it is either 0 or 100.

At the end of the day either method works and it's just whatever convention you want to use. Assuming the two dice are fair, the probability isn't affected, but it's needlessly confusing for your playgroup to use two different conventions on how to interpret the symbols on the percentile dice.

I mean, when your friend rolls a D6, your friend could say that the number of his roll is actually 7-x, where x is the number of dots that came up on the die roll. The probabilities are the same, BUT WHY WOULD YOU DO THAT?

Tell your friend to stop being an idiot and stop using his system where you add the two dice together. It's standard convention everywhere that one die is the tens column, the other die is the ones column, and 00 is read as 100. His method isn't consistent, in that a zero on one die doesn't really mean the same thing on each die. On one die a zero means zero, then on the other die a zero means 10. His method technically works, but it's not intuitive at all and pretty much defies common sense.

His method doesn't need a special case for 100 (in that a 9 then a 0 means 90+10), compare to the usual method where you need a special case where 0 and 0 means 100 (normally the formula would be 10x +1y where x and y are the two dice, but if they both come up zero then you don't use that formula). But that's the only real advantage. And to a normal person, looking at two dice that say 2 and 0, and saying that's obviously 30, you'd look like a crazy person.

There are rules for dice I'm pretty sure. Percentile rolls are handled by rolling two ten-sided dice together, using one as the "tens" and the other as the "units". A roll of ten or zero on either die is taken as a zero, unless both are zeros or tens, in which case this is 100. Some sets of percentile dice explicitly mark one die in tens and the other in units to avoid ambiguity.

The dice I have always seen are used together.

10, 20, 30, 40, 50, 60, 70, 80, 90, 00

1, 2, 3, 5, 5, 6, 7, 8, 9, 0

If you ask me I see little point in making a special rule for 0 & 00 =100. Why not just have the percentage be from 0% (you missed) to 99% (you hit). There is not much need for changing a rule...who the fucking cares if you can only get a max of 99%

It makes no difference at all. There still is exactly one way to roll each value 1-100, you're just changing 10 of the 100 mappings.

So assuming his dice aren't loaded and he is consistent about his interpretation it's not an issue.

Your friend is strange and needs to learn that his way of counting dice is almost counter-intuitive to practically every pen and paper game there is. I DM and this is behavior I would not encourage, since I often have new players and this would confuse the heck out of them.

I've asked another game playing friend of mine, he uses the same method as your friend. So either we have the same friend or there are a group of people out there who need to learn dice.

Thanks for all of the opinions. I can't find a difference in the probability so I'm letting him use his method, but he has to be consistent. We'll all veteran gamers so no one will get confused, and I'm running Beyond the Mountains of Madness so I might as well give the players some semblance of control ;)