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I suspect my players may be fudging their rolls in an online IRC and Skype game. While I can't confirm this (for obvious reasons), I'm highly suspicious.

I logged all their rolls over the course of the night. The system uses D6 die pools, where a 4 or higher is a success (typically); 50% chance. They had a 73.68% success rate with their rolls. 84/118 rolls were successes. Additionally, not a single roll was less than half successes, over the course of 24 rolls.

I am fairly certain I have reason to be suspicious here. I briefly raised the point at the end of the session, in some manner like:

Here is a quick thing: I was keeping track of the rolls, and around 75% of them were successes. With over 120 rolls, it's kind of significant, and bothers me, but we shall see how it goes.

I'm trying not to openly accuse them of fudging rolls; that wouldn't get me anywhere. How do I tell, though? And how do I discourage this? Is simply pointing it out enough?

It's possible for me to simply declare that I'll do rolls myself, but that becomes unwieldy, and often introduces problems in and of itself. Additionally, if I do that, it will probably come across as treating them like kids.

In lieu of moving to a service which does synchronized dice rolls, what can I do?

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You have two basic choices for how to have your players roll their dice:

  • Ask them to make their rolls in secret, and trust the results they tell you.
  • Ask them to roll their dice in the open, so that there's no question they're telling the truth.

If you take the first option you must trust your players and accept what they tell you!

You need to be able to trust them and work with them, and they need to be able to trust you and work with you. The game experience is going to be quite toxic otherwise - I'll talk about that later. You've chosen a method which requires trust, so provide that trust.

If they are fudging, accept it for the fun value. You can't tell if they're doing it anyway. This is exactly the same as DMs who roll behind the screen: the players may suspect that sometimes the DM went easy on the nearly-dead target and fudged a miss, but the players should be able to trust the DM to make the game fun for them. That doesn't mean you need to pretend it isn't happening - just accept it and be okay with it, and continue playing.

Higher than average results are entirely possible.

They're improbable, yes, but not impossible, and doesn't suggest cheating.

Today, I played my first Pokemon TCG game with a friend. We did a lot of things that called for coin flips, and out of ~25 flips, only four were tails. It's highly improbable, but it happened.

Some players somehow roll quite well on average. I recently rolled several sixes on a series of challenges, some of which only a six would beat. We have a member here who's the opposite: he consistently rolls improbably low, with any set of dice, even with a dice tower. (It's incredible, but it's been happening for years; here's the records from one session which was played in person - no fudging occurred.)

Some don't have precision cut dice, and the common types of dice manufacturing can make vulnerable dice by accident. Ilmari explains at the beginning of his answer here. This isn't conscious cheating, it's just a flaw of the manufacturing process. You probably have slightly weighted dice!

Bottom line: If you want to use a dice rolling method requiring trust, extend that trust, or don't use that dice rolling method.

What if you can't provide that trust and accept their rolls?

If you keep going like this and can't trust your players, you'll end up relating to them as cheaters and you'll probably be irritated by their cheating - whether or not they really are. That's going to be really fun for them being treated like cheaters, and I say that with massive amounts of sarcasm. They won't be able to trust you to be impartial with them because you won't trust them. The experience will be very toxic and toxic experiences destroy groups and any fun value in games.

So, if you cannot trust them, tell them you want to switch dice rolling method.

Be straightforward and honest in telling them why: the results they're getting bugs you, and you have no way of knowing they're cheating or not, and you'd prefer to trust them but you'd rather just find a rolling method that eliminates any reason to be suspicious to begin with - that way, you can all have fun without you needing to be concerned.

Find a dice roller that lets you view each others' rolls and use it.

If you do this and the average results change, don't use that as a reason to suspect they were cheating. The success rates they were having were entirely possible, however improbable, and they may not have been cheating at all.

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In two 5d20 rolls I score eight 1s - 5 in the first roll and three in the other one. Improbable but possible. – Maurycy Jun 30 '13 at 11:20
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+1 for likening it to a DM screen and the question being trust, not dice. Also for simply accepting fudging (as long as it's not horribly disruptive) – LitheOhm Jun 30 '13 at 15:56
    
This is an interesting response, and almost comes across as "dice don't really matter, except in edge cases." That, though, is a good point, and could very well be true. I'll bear that in mind for the next session! Thank you! – Emrakul Jun 30 '13 at 16:23

You mentioned this at the end of the session. If they were honest they'd not have fudged in the first place, so the problem is now that either they'll ignore that, or if they are clever, just get more subtle and fudge unimportant rolls down so that the important rolls can be pushed up without suspicion.

Suspecting your players can poison a game. You've said you don't want to use a service that does synchronized dice rolls - why not?

Without that, your choices boil down to living with it, or counter-fudging the dice. The former you've already found out that you're not happy to do, and the latter will, if they are fudging rolls, will just encourage them to fudge more.

If you do decide to go with synchronized rolls in the end, for my online games I've used MapTool which is a free Java based shared map and text chat, with built in dice rolling.

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If you don't want your players to feel like you don't trust them, don't tell them you're moving for the dice - say it's for 'greater utility' or you've heard good things about MapTool, which is true based on the answer above. – Dakeyras Jun 30 '13 at 9:25
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Another great solution is the CatchYourHare.com die roller. It's ONLY a shared die-roller, implemented in Javascript/AJAX, it allows dragging dice around, multiple colors, and several other nifty elements. I find it ideal when playing with VOIP players. – aramis Jun 30 '13 at 9:46
    
+1 maptools is cool – LitheOhm Jun 30 '13 at 15:57
    
@aramis That is an awesome utility; I may use that. – Emrakul Jun 30 '13 at 16:08
    
@EmrakultheAeonsTorn Yes, it sure is. It's wonderful. I only wish I could pick a different font so I could do the symbolic dice for Edge of the Empire and The One Ring. – aramis Jul 1 '13 at 19:59

http://math.stackexchange.com/a/432850/83542

The chance of 84 successes out of 118 rolls when the chance of success is 50% is:

0.00000236224

Which is unlikely, yes, but not impossible - What you have to realize is that there are a lot of roleplayers out there and when we all roll, one of us is going to have that lucky streak.

To give you a bit more feel, that number up there is approximately 1 to half a million. That means, every time you have 500.000 roleplayers in a game session (Or every 100.000 times you have a session with 5 players), one of the players should have a streak like that.

Let's assume that in the whole world, only one person in a hundred is a roleplayer often enough to play once a month (I think there are more of us but for the ease of math and all that). That gives us 7 billion/100 = 70 mio played sessions (Counting a session with X players as X sessions) each month.

Those 70 million sessions should give us 70 million over half a million = 140 people who roll that lucky every month.

Does that mean it is likely that your player rolled that lucky? No, he probably cheated - the probabilities work both ways - the chance that out of 70 million sessions, he was in one of those 140 sessions that rolled lucky are... 1:500.000 (It's the same number from before)

But every month, there are 140 people who do roll that lucky, and if you're the DM for one of those guys, you don't want to falsely accuse them of cheating.

Now if they roll that lucky again NEXT month...

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I logged all their rolls over the course of the night. The system uses D6 die pools, where a 4 or higher is a success (typically); 50% chance. They had a 73.68% success rate with their rolls. 84/118 rolls were successes. Additionally, not a single roll was less than half successes, over the course of 24 rolls.

I am fairly certain I have reason to be suspicious here.

Not quite. Granted, the odds of what you describe are very slim in a single session. However, that is keeping in mind only that single session. That's not the relevant figure here: in computing dice odds we need to consider each and every instance when dice are rolled. As Medivh calculated out and explained, this will happen. It's a lot like thinking about a friend and them calling - eventually coincidence prevails.

This is the law of small numbers. While it may be unlikely given just the sample size of your group's rolls for a session, it's improbability lessens when it's thrown into the pool of all dice rolled everywhere.

I'm trying not to openly accuse them of fudging rolls; that wouldn't get me anywhere. How do I tell, though? And how do I discourage this? Is simply pointing it out enough?

It definitely wouldn't get you anywhere. Track more sessions, I suppose, if you want to tell. Save for catching them and calling them out (a bold move to be sure), it all boils down to just the odds. Be sure you've got math on your side in that case. In order to discourage dice roll fudging you can switch to an area where it's much harder to pull off, like dicelog.com.

But, if you want to believe they're skewing rolls, even that might not be enough. A friend and I were using that one night and he rolled five ones in a row on a d20. 20^5=3.2 million. Highly improbable but not impossible - though I still doubt he wanted to perish in that dungeon.

It's possible for me to simply declare that I'll do rolls myself, but that becomes unwieldy, and often introduces problems in and of itself. Additionally, if I do that, it will probably come across as treating them like kids.

Too much of a pain, IMO. Many people like to roll dice. Don't take that away from them on mathematical suspicion, especially when not all the math backs you. It would come across as treating them like kids because that's exactly what it is - "I'm going to do this so that we can all be sure to play fair."

In lieu of moving to a service which does synchronized dice rolls, what can I do?

TL:DR

Don't take dice numbers so seriously, unless they're disrupting your campaign. Did you prepare that session for them to overcome or for it to destroy them?

On a practical note, you could simple randomize in other ways. Once I ran a combat with a friend over the phone who is notorious for fudging dice. Knowing his to-hit, crit range and AC, I reduced the numbers from a twenty-sided die to say one through ten or one through five, depending on the foe. If he had a fifty percent chance of hitting then I'd require that he guess which portion (high or low) of 1-10 I was thinking of, and if he guessed exactly then it was a crit. We went with average damage. He didn't mind, your experience may vary.

The solution above is made easier/more fun with some love of math but I'm guessing from your statistical analysis of your gaming session it might be up your alley.

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The system I normally use with my friends when we play online is that the GM rolls all the dice (actual physical dice) and reads out the result. Since you are already trusting the GM for everything else, and rolling behind a screen is a common practice, this method doesn't offer a lot of friction.

Now, some people may consider the change of system to be offensive. It does show a certain lack of trust. But if you think it's necessary for your enjoyment of the game, then it's an important thing to do. Be diplomatic about it, explain your concerns, and don't blame anyone in particular.

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I would use a tool for playing online. I'm sure there are some available, but I wrote my own. It was a basic chat client that allowed private messages to the DM / group, and dice rolls - including players/DM rolling hidden dice that only the DM can see.

Players like to roll their dice even if they can't see the result. So we used the app and everyone can see what people rolled, and if it was a secret roll such as a player making a perception check, they'd hit secret roll and then the DM would indicate what happened.

The DM could also roll in secret from the players (used to press it randomly now and then to spook them:).

Sometimes you just gotta force them to do this. I had a guy in an actual session keep rolling natural 20s by not rolling the dice properly or outright cheating. It was like a compulsion. Once forced not to be able to do it he had much more fun when he did roll a nat 20. Not sure how he thought nobody noticed. Never called him out on it though, just made everyone roll onto a surface in the middle of the table so he couldn't 'drop' the dice onto a 20.

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