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Drache64
2019-03-12, 05:23 PM
So I tested my dice and found a few cheesex dice that were significantly weighed, the most prominent one seems so weighted it has a significantly higher chance of getting 2/18/20 but it still rolls pretty average out of 100 rolls. (Just rolled and got: 2,3,9,16,19,18,2,2,3,18)

Is it immoral to use this dice? What are your thoughts on checking your dice weights?

Mr Beer
2019-03-12, 05:41 PM
If you examine your dice, locate ones that offer you a statistically significant advantage and then secretly use them in order to gain that advantage, yes it's cheating.

The Kool
2019-03-12, 05:49 PM
You won't get a meaningful result if you roll a sample size as small as the one you presented. You mention it still rolls pretty average out of 100, and that's the point where it starts to matter. I forget the exact statistically significant number, but I wouldn't feel comfortable basing my result off of fewer than 100 rolls.

MoiMagnus
2019-03-12, 06:00 PM
I suggest you to follow this simple statistical proceedure to check the fairness of your dice: https://rpg.stackexchange.com/questions/70802/how-can-i-test-whether-a-die-is-fair (if you didn't already do it)

Anyway, answering your question, and assuming you're right, I would probably not care at all as long as the biais isn't too strong, and unless the weak biais is has 20 or a 1 is part of the faces.
Because rolling more 20 and/or 1 than the average in a consistant way can be pretty frustrating for the other players.

Otherwise, I would stop using it as a PC, because that's cheating. (Though I still might keep it around in case any player lack dice)

LibraryOgre
2019-03-12, 06:07 PM
Nope. Now, if you're going out to acquire weighted dice, or weighting them yourself, that's immoral. I don't see anything wrong with owning dice that are slightly imbalanced, unless they're obviously "broken".

Folks have had "lucky" dice since the beginning of the game. I still have "Old Blue", a 30 year old ten-sider that we loved for initiative in 2e because it always rolled low.

King of Nowhere
2019-03-12, 06:40 PM
what do you mean by "significant"?

because in common language, "significant" means "important, big, meaningful". so a dice with a significantly altered distribution is a problem.

but in scientific language, "significant" means "we crunched the data, and we are more than 95% sure that it's not due to random fluctuations". So your favored faces could have a channce of 5,0001% instead of their exact 5%, and if you could prove that's because they are slightly unbalanced, then it's a significant deviation. But as far as affecting the game, it's meaningless.

So, try to get some hard data. how did you find out such dice are loaded (no offence intended, but you sound like you don't know much statistics, so you may even have misinterpreted the results)? what's the confidence range of the procedure? What kind of a difference do they actually make in the game?

personally, i would trust dice vendors to give sell dice that are fair enough for the purposes of the game. I could see a casino dealing in millions wanting to make super sure the percentages are exactly right, but for a game of D&D? not worth the hassle.

As far as cheating, if you tested alll your dices and learned where they give best odds and then were careful to always use the best dice for the situation, yes, that would be cheating. in intent, because on the practical side nobody would really notice unless they kept track of hundreds of rolls and had a good understanding of statistics.

Drache64
2019-03-12, 07:14 PM
By tested, I meant I filled a cup with water and salt until the dice floated, then I saw if it rolled and came to rest on a random number when dropped in the solution.

The dice in question floats and rests on the Apex between the 2/18/20

I then rolled the dice quite a bit to see if I noticed any difference, now being aware of the flaw I noticed it did tend to result in 2 and 18 slightly more than other numbers.

Statically I'm not sure what that would result in.

To note, this isn't my go-to dice, I use a full metal set, but when I have to roll multiples I'm not sure I should be allowed to use this dice anymore.

I've set it aside for now, but discuss it openly with my group and we roll it for fun in between games so I can show them the weight. It's so slight that not everyone believes me until I break out the salt and water to show them.

Pauly
2019-03-12, 07:30 PM
To test a dice properly you need to do the tests linked earlier. Although I prefer to do 10 tests per face not 5.

You also have to remember 2 things:-
1) Random distribution is not even distribution. For example if you roll a d6 six times an even distribution would be a result of 1,2,3,4,5,6. However the odds of that coming up on a random distribution is something like 1.4% iirc.
2) Dice are like the male appendage - they have no memory and no conscience. What is the chance that a perfectly weighted dice that has just rolled three natural 20s in a row will roll another natural 20 with the next roll? Some people would say 1 in 160,000 (1/20 x 1/20 x 1/20 x 1/20). The real answer is 5% (1/20) because previous dice rolls do not affect future dice rolls. The universe does not owe you anything, it does not need to bring your luck back to average.

The Kool
2019-03-12, 09:05 PM
The short version of the test is this: Roll the die a couple hundred times (I'm not kidding, 100-200 minimum). Record every single result. Count how many times each face was rolled. If the numbers are basically even, you have a fair die. The various methods you've been linked to are just fancy ways of determining if the count of each number is what you expect or not.

Drache64
2019-03-12, 11:42 PM
No offense to everyone, but most of those are terrible ways to test your dice. Testing the weight is literally the best and only way to tell if a dice is literally weighted. If your dice is not weighted and it's not rolling correctly then you'd want to check the mold to make sure there is no warp or other deformity on the edging.

As someone said above, every time you roll your dice it's going to be a random result. Getting a result is a 1/20 chance every time you roll. You'd not only need to roll the dice thousands of times, but ensure you are rolling the dice on the same type of surface the same way without any significant changes in how you drop, roll, etc the die.

But if you drop the die in a buoyant solution so it floats, you should see the die spin easily and come to rest on a different result, if it always comes to rest quickly and in the same orientation, then you have a bubble or other deficiency in the mold. This is very common in cheesex dice. I found 5 out of 40 of my d20 had significant weights on one side.

This question wasn't about how to test your dice, I can help with that if people are curious. The question was what to do with the dice when you find them, and the morality of having the knowledge.

IE: it's okay to use dice you feel are lucky because you see them roll higher, but once you test it and find it's not lucky but weighted, then what do you do with that knowledge?

I feel the right thing to do is discard the defective die, even though the defect provides you with a "benefit".

All in all it seems the moral of the story is don't test your "lucky" dice. Ignorance is bliss.

Kaptin Keen
2019-03-13, 12:36 AM
Actually, rolling a nice big sample size is every bit as accurate as dropping the dice into water - and closer to an actual use scenario. If you want to nitpick, you should do both to confirm results.

Obviously, the moral high ground would be to throw away the dice.

But the really dastardly thing to do would be to only use those tested dice for tournaments and the like. Come, join the Dark Side. We have cookies - and weighted dice, too =)

JoeJ
2019-03-13, 12:49 AM
Actually, rolling a nice big sample size is every bit as accurate as dropping the dice into water - and closer to an actual use scenario. If you want to nitpick, you should do both to confirm results.

If you're going to do that much work, you should follow up with a chi-squared test to determine exactly how likely it is that your results actually mean the die is biased.

Pauly
2019-03-13, 01:43 AM
No offense to everyone, but most of those are terrible ways to test your dice. Testing the weight is literally the best and only way to tell if a dice is literally weighted. If your dice is not weighted and it's not rolling correctly then you'd want to check the mold to make sure there is no warp or other deformity on the edging.

As someone said above, every time you roll your dice it's going to be a random result. Getting a result is a 1/20 chance every time you roll. You'd not only need to roll the dice thousands of times, but ensure you are rolling the dice on the same type of surface the same way without any significant changes in how you drop, roll, etc the die.

But if you drop the die in a buoyant solution so it floats, you should see the die spin easily and come to rest on a different result, if it always comes to rest quickly and in the same orientation, then you have a bubble or other deficiency in the mold. This is very common in cheesex dice. I found 5 out of 40 of my d20 had significant weights on one side.

This question wasn't about how to test your dice, I can help with that if people are curious. The question was what to do with the dice when you find them, and the morality of having the knowledge.

IE: it's okay to use dice you feel are lucky because you see them roll higher, but once you test it and find it's not lucky but weighted, then what do you do with that knowledge?

I feel the right thing to do is discard the defective die, even though the defect provides you with a "benefit".

All in all it seems the moral of the story is don't test your "lucky" dice. Ignorance is bliss.

The bucket test only tells you if the center of balance is off. There can be other reasons as to why a dice is not rolling true, such as being irregularly shaped.

Kaptin Keen
2019-03-13, 03:08 AM
If you're going to do that much work, you should follow up with a chi-squared test to determine exactly how likely it is that your results actually mean the die is biased.

That seems ... somewhat superfluous. I'd consider it more valuable to calculate the exact, expected effect on actual games - like, with this die, I should expect a 5% increase in winningness .. but with this other die, it could be as high as 7%.

Then I'd consider calculating the value gain. Like, if I buy 1000 dice, and 10% of them turn out to be weighted, can I then sell them on with a profit? Which of course leads me to think: www.weighteddice.com is not taken. Obvious webshop idea right there. 'Here at Weighted Dice, we deliver only carefully tested and confirmed biased dice, day-to-day!'

Weighted dice aren't illegal or anything, right? Using them for actual gambling obviously would be, but selling them shouldn't be. I'm by no means advocating crime here, just joking =)

(It occurs to me that you could maybe even take money from the dice makers - 'hi, we'd like to offer you our cheap, cheap service to test your dice for bias, so you can go out and sell them at higher price. We just take a very low price .. and we'll get rid of the bad dice for you, at no additional cost!'

www.luckydice.com also isn't taken.)

Grek
2019-03-13, 03:29 AM
Ethically, if you test your dice and find them to be unfair, you should stop using them during games. It doesn't matter how you find out (although the rolling them a bunch and counting thing IS better statistical practice), it just matters whether they are fair or not.

King of Nowhere
2019-03-13, 07:00 AM
By tested, I meant I filled a cup with water and salt until the dice floated, then I saw if it rolled and came to rest on a random number when dropped in the solution.

The dice in question floats and rests on the Apex between the 2/18/20


Ok, so the test is accurate in telling that there is a slight imbalance. It does not determine, however, how much that affects the roll.

So you have 3 possibilities

1) throw away the dice and buy a new one. they are cheap enough, and probably not worth all the trouble.

2) keep the dice. The imbalance is likely small enough that it doesn't really matter for the game.

3) run a full statistical test to determine how skewed is the statistical distribution.
That requires hundreds of rolls, as statistics tend to even out only in the long run.
Depending on how big is the deviation, decide whether to keep or throw the dice.

Oh, of course you also have the evil option of keeping the dice and using it when you want more chances of 20 or 18 (they outweight the greater chances of 2).

Personally, I think 3) is too much hassle to be worth. I'd pick 1) if you have a heaplod of dice you don't really care about, or 2) if it's some kind of beautiful artistic dice that you'd hate to lose.

The Kool
2019-03-13, 07:23 AM
You've determined with your saltwater test that there is a physical imbalance in the die. That's great, but it tells you nothing about the statistical imbalance of the die. Does it affect the randomness of the result? Well thanks to a variety of factors, we can't say for certain. We can test the randomness by subjecting it to a rigorous use-test though. If we put it through several hundred rolls, we'll get to directly observe if a number comes up more frequently then another. If it doesn't, then there's your answer: The die is still fair. Regardless of weight.


IE: it's okay to use dice you feel are lucky because you see them roll higher, but once you test it and find it's not lucky but weighted, then what do you do with that knowledge?

I feel the right thing to do is discard the defective die, even though the defect provides you with a "benefit".

I'll be perfectly honest with you, if you're asking this question, then you already know the answer. You will feel guilty if you keep using it, so don't. Keep it, toss it, give it away, but you've already made your decision. You said yourself that you stopped using it.

Willie the Duck
2019-03-13, 07:41 AM
Leaving aside the accuracy of the test, as well as whether the difference in results is particularly meaningful or significant, is the original questions of 'Is it immoral to use this dice? What are your thoughts on checking your dice weights?'

To the later question, I'd say my thoughts on checking ones dice is that it may well be a Pandora's box and you're better off not knowing. No one is playing with the Platonic ideal of a perfect die, and it may well be that all dice you own would each be roughly equally biased towards one result or the other (mind you, this specific result is relatively favored for a high-roll situation, a lot of other dice might be biased towards more innocuous results).

To the question of cheating, I'd say it's certainly straining your social contract with your peers. There's an expectation that you are using a form of random determination when you are rolling dice in most games (else why are you bothering with dice in the first place?). If your random determination is knowingly less random than the ones your peers have (because you are actively and knowingly using one with specific biases), then you are playing with a specific leg up compared to them, in an portion of the game that is expected to be impartial (you might have a leg up on your peers based on things like system mastery, but that's one everyone knows about and agreed to ahead of time).

Imbalance
2019-03-13, 07:53 AM
I have nothing to do with your dice!

Willie the Duck
2019-03-13, 08:40 AM
I have nothing to do with your dice!

HA! I think of doing the same thing whenever someone throws out a 'if it walks like a duck...' reference. :smallbiggrin:

Kardwill
2019-03-13, 08:59 AM
Is it immoral to use this dice? What are your thoughts on checking your dice weights?

If you really, honestly think a dice gives you a real, physical advantage, then using it secretly would be cheating, as you've probably concluded since you're asking the question. When everyone is supposed to play on a level field, then hiding an unfair advantage would actually mean you're betraying that expectation and are lying to them.

If you've said to your group "Hey, guys, you know that "lucky" 20 sider I had since middle school. Well, turns out it might actually be inbalanced", and they don't care/don't mind or are actually amused by the idea, then roll away! :smallsmile:

One of my players has a "lucky" d10 since high school that we never actually tested but we think it has been a huge advantage for any kind of % systems (it rolls a lot of 0), but we don't mind as everyone knows it and this dice is part of the player's legend (He tends not to use it much nowadays, but we didn't pressure him into it)
The player that we suspect was a secret cheater (tons of very good rolls every time nobody checked his "black-on-dark-green d20 rolled behind the bottle of Coke"), though? He's not invited anymore.

Tabletop RPGs are a social hobby. Trust and honesty are important.

Hackulator
2019-03-13, 10:35 AM
If you examine your dice, locate ones that offer you a statistically significant advantage and then secretly use them in order to gain that advantage, yes it's cheating.

What this guy said.

LibraryOgre
2019-03-13, 11:38 AM
How does the bucket test work with traditional d10s and d4s?

The Kool
2019-03-13, 11:46 AM
Tabletop RPGs are a social hobby. Trust and honesty are important.

Very much this. Our group has one player with "the blue dice" that often get requested. He's willing to roll them on behalf of other people, but usually leaves them locked in his box. I think it has rolled more 20s than other dice, but that could be confirmation bias.

Sometimes you just get lucky. Same player gifted me a set of dice, first time I crack it open... Needed a 20 to hit the paladin? Two hits and a crit in round 1. Of three attacks. Every single round following, the die landed at least one hit on him. It seems to roll fair the rest of the time, but the entire group has acknowledged that it wants that paladin dead, and we all have a good laugh over it.

JoeJ
2019-03-13, 12:23 PM
That seems ... somewhat superfluous. I'd consider it more valuable to calculate the exact, expected effect on actual games - like, with this die, I should expect a 5% increase in winningness .. but with this other die, it could be as high as 7%.

That calculation would not be meaningful if you don't first determine whether the die is genuinely biased. The chi-squared test will let you determine whether the distribution you got from rolling over and over is the result of a biased die or just random chance.

Kaptin Keen
2019-03-13, 01:11 PM
That calculation would not be meaningful if you don't first determine whether the die is genuinely biased. The chi-squared test will let you determine whether the distribution you got from rolling over and over is the result of a biased die or just random chance.

Which would be totally relevant if I planned on using the dice myself - but less so if I just plan to sell them on. It's marketing =)

Quertus
2019-03-13, 03:07 PM
If, when rolled by someone else, the dice produces results which deviate from the norm to a statistically significant degree, then it is weighted.

If you knowingly use a weighted die, you are cheating.

Some people can control or influence the outcome of a die roll. If you knowingly influence the results of a roll, you are cheating.

Lunali
2019-03-13, 05:51 PM
How does the bucket test work with traditional d10s and d4s?

The test works just as well, but small imbalances are less likely to have an effect on dice with fewer faces.

dps
2019-03-14, 11:14 PM
Leaving aside the accuracy of the test, as well as whether the difference in results is particularly meaningful or significant, is the original questions of 'Is it immoral to use this dice? What are your thoughts on checking your dice weights?'

To the later question, I'd say my thoughts on checking ones dice is that it may well be a Pandora's box and you're better off not knowing. No one is playing with the Platonic ideal of a perfect die, and it may well be that all dice you own would each be roughly equally biased towards one result or the other (mind you, this specific result is relatively favored for a high-roll situation, a lot of other dice might be biased towards more innocuous results).

To the question of cheating, I'd say it's certainly straining your social contract with your peers. There's an expectation that you are using a form of random determination when you are rolling dice in most games (else why are you bothering with dice in the first place?). If your random determination is knowingly less random than the ones your peers have (because you are actively and knowingly using one with specific biases), then you are playing with a specific leg up compared to them, in an portion of the game that is expected to be impartial (you might have a leg up on your peers based on things like system mastery, but that's one everyone knows about and agreed to ahead of time).

Yeah, I have to agree with this.

Amano666
2019-03-17, 07:32 AM
2) Dice are like the male appendage - they have no memory and no conscience.

This is a really messed up statement and I expected better on this forum. SHAME on you.

Jay R
2019-03-17, 06:22 PM
The purpose of a die is to generate a random number, in which every number has an equal chance of coming up.

If you use a die for which you know this is not true, then yes, you are trying to break the rules, and get an unfair advantage. It makes no difference if you found a die with an air pocket that rolls too many 18s and 20s, or if you chose to buy a weighted die or a die with two 20s and no 1s.

Trying to get more 20s than you have a right to is violating the spirit of the game.

If you are mistaken, and the die is fair, but you think it isn't, and so you roll it to get too many 20s, then you are still breaking the rules; you're just not doing it very well.

The game assumes a random number. Any attempt to get an unfair number of good rolls is ... well ... unfair.

D+1
2019-03-17, 11:01 PM
So I tested my dice and found a few cheesex dice that were significantly weighed, the most prominent one seems so weighted it has a significantly higher chance of getting 2/18/20 but it still rolls pretty average out of 100 rolls. (Just rolled and got: 2,3,9,16,19,18,2,2,3,18)

Is it immoral to use this dice? What are your thoughts on checking your dice weights?
I firmly believe that short of using dice DESIGNED to cheat, any decently manufactured dice will roll randomly enough for ALL RPG purposes. Even if they ARE weighted by accident of manufacture to roll some numbers over others, I have yet to hear more than WILD, UNSUPPORTED tales of people that can roll dice with such skill as to get the number they want, or who can even detect a trend in normal play to prove any die is so biased as to be genuinely unfair.

Bias in dice is a sales pitch to get you to buy more dice (and probably pay more for them) and your DM and fellow players will NEVER detect a difference. For RPG purposes it's a lot of hooey. Take your set of sample rolls. Lots of very good, very bad, and nothing in the middle. Maybe it IS imbalanced that way. But will you know which you'll get? When you roll high will it be for a to-hit roll or a skill check? Can't predict that? Then the die is random enough IMO.

Also, if anyone feels that this is an edge they NEED/WANT in D&D they have far bigger issues than dice.

kyoryu
2019-03-18, 09:04 AM
(Just rolled and got: 2,3,9,16,19,18,2,2,3,18)

That is highly skewed. Highly.

Your three 'weighted' numbers should come up 15% of the time, on average. In this case, of 10 rolls, HALF of them were in the 'weighted' range. Now, those were actually more 2s than 18s, but since the weight appears to favor both 18 and 20, if you find that the bias is towards them all relatively equally even (which it doesn't appear in this small sample set), then you'd have a significant advantage.

If you KNOW that your dice are imbalanced in your favor, and continue to use them, then yes, it is cheating.

Weighing your dice is not cheating inherently. But what you do with the information may be - if you weigh your dice and only use the least-imbalanced ones, then that would not be cheating at all. If you weigh your dice with the intent of finding the ones that are best biased towards you, then it would be.

JoeJ
2019-03-18, 12:24 PM
That is highly skewed. Highly.

The chi square value for those numbers is 30, which is significant at the 0.1 level, but not at 0.05.

The results are highly questionable, however, because the sample size is so small. The rule of thumb is that you should have a number of rolls at least equal to 5 times the number of sides, or in this case at least 100 rolls.

Jay R
2019-03-18, 01:29 PM
The chi square value for those numbers is 30, which is significant at the 0.1 level, but not at 0.05.

The results are highly questionable, however, because the sample size is so small. The rule of thumb is that you should have a number of rolls at least equal to 5 times the number of sides, or in this case at least 100 rolls.

I wouldn't use a chi-squared test with so few rolls, for the reason you just gave. The test has so little power with a small sample size.

Willie the Duck
2019-03-18, 02:38 PM
Ten rolls, we should probably limit ourselves to non-parametric tests, along with limiting ourselves to drawing the kind of conclusions one makes with such analysis. Or we can ask the OP to roll it more.:smalltongue:

Jay R
2019-03-19, 09:14 AM
Having said that the test is low power with a small sample size, we can still do better by testing the specific question in front of us. [The more specific the test to the exact question you are interested in, the better the results.]

If we only test whether 2, 18, and 20 come up 15% of the time as expected, we get a χ2 value of 9.61, with one degree of freedom.

That yields a p-value of 0.00194, so yes, even with this small sample size, we can reject the null hypothesis and conclude that those three values will continue to come up too often.

That conclusion is justified at an alpha level of 0.05, or 0.01, or even 0.002.

Elysiume
2019-03-20, 12:59 AM
Is testing your dice weight cheating? Not necessarily.
Is testing your dice weight and then selecting dice that are biased towards high numbers cheating? Yes. You may not have purchased weighted dice, but you found out which dice of yours were weighted and chose to use them. If you know that something gives you an unfair advantage (with the caveat that in a cooperative game, "unfair advantage" is a term I've seen hotly debated) and choose to use it, you're cheating.

Would you sit down to play and tell the table "hey, I tested my dice and this one is disproportionately weighted towards high rolls so I'm going to use it"? If this feels like something you'd need to hide, you probably already know it's cheating.

Ravens_cry
2019-03-20, 01:46 AM
Would you sit down to play and tell the table "hey, I tested my dice and this one is disproportionately weighted towards high rolls so I'm going to use it"? If this feels like something you'd need to hide, you probably already know it's cheating.
A fairly good rule of thumb in a relationship as well, on a side note.

darkrose50
2019-03-20, 08:17 AM
So I tested my dice and found a few cheesex dice that were significantly weighed, the most prominent one seems so weighted it has a significantly higher chance of getting 2/18/20 but it still rolls pretty average out of 100 rolls. (Just rolled and got: 2,3,9,16,19,18,2,2,3,18)

Is it immoral to use this dice? What are your thoughts on checking your dice weights?

Just about all dice are weighted. They are tossed into a rock polisher and all the edges and corners are worn off to different degrees. Basically just about all of our dice suck, but some are more horrible than others.

Measuring something should just about never be considered negatively. We had one of those personality tests at work (though a third party that supposedly specializes in this sort of thing). Several of the questions were poorly written. One basically could be summarized as "do you look for loopholes" . . . with the assumption built in that anyone looking for loopholes is unethical. A company should STRONGLY want people that look for loopholes, and point them out. I wrote the company about a bunch of there questions, and was offered a job interview (I never took it, but it was flattering).

If the dice are swingy one way or the other, then you might want to replace them.

Someone has a service where they connect a Bobble-like-device to roll the dice, have a camera recording the results, and then a computer tallies the results.

enderlord99
2019-03-20, 08:59 AM
This is a really messed up statement and I expected better on this forum. SHAME on you.

I mean, I'm a guy and I can confirm none of my appendages have memory (based on how awful my handwriting is) but I'm sure there are men with consistent, practiced penmanship and-

That's not what was meant by "male appendage" was it?

kyoryu
2019-03-20, 09:31 AM
Measuring something should just about never be considered negatively.

Measuring is not negative.

What you do with that information can be.

Rhedyn
2019-03-20, 09:42 AM
So I tested my dice and found a few cheesex dice that were significantly weighed, the most prominent one seems so weighted it has a significantly higher chance of getting 2/18/20 but it still rolls pretty average out of 100 rolls. (Just rolled and got: 2,3,9,16,19,18,2,2,3,18)

Is it immoral to use this dice? What are your thoughts on checking your dice weights?
If you are using empirical evidence to determine the best dice you have and then use those, then yeah you are cheating. You are effectively "weighing" your dice.

Now just using dice that you feel roll higher or using a bad empirical method, then no that isn't cheating.

kyoryu
2019-03-20, 12:18 PM
If you are using empirical evidence to determine the best dice you have and then use those, then yeah you are cheating. You are effectively "weighing" your dice.

Now just using dice that you feel roll higher or using a bad empirical method, then no that isn't cheating.

100%.

Peoples' judgement of how random things are is usually pretty terrible, especially for short sequences.