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With how much time/money we spend on our armies, should we spend a bit on dice? I did something yesterday and it was such an useful experience for a 40k Hobbyist like me (and perhaps you), I thought it'd be worth sharing not just the results, but also process I used in case you want to set aside 30 minutes and try this yourself. I took 16 of GW's white dice from GW starter sets (i.e. Black Reach, Armageddon, etc.), rolled them 50 times as I would in a game, and just Excel'd the results. That's basically like 800 rolls, just to have some idea how bad my rolls were. INB4 it's not scientific enough - I agree, but the goal is to answer, "Do I want to buy (better) dice for my 40k games?" For example, I didn't use a zero-variance robotic arm to throw these because I don't use a robotic arm during 40k games (although as an Iron Hands player that would be totally sweet). I didn't separate out the different types of GW white dice, which I'm sure got mixed with my friends' sets over years of playing, but that's what happens to many of us. TL;DR - this was not a lab environment, but it is representative of what I do in-game, because I don't play 40k in a lab environment, therefore those imperfections are more relevant to my question because they would appear in actual 40k games. +++ QUESTION(S) +++ Do I need to buy decent dice? Are the stories of GW dice rolling ones a third of the time true? How bad are cheap GW dice? +++ BACKGROUND +++ My friend told me about this article: https://www.dakkadakka.com/wiki/en/That's_How_I_Roll_-_A_Scientific_Analysis_of_Dice and I noticed it was referenced here on B&C 10 years ago, but didn't want to necro the thread, plus I want to share the process, because it was valuable. Long story short - on a six-sided die, any given result should come up one-sixth of the time. But the authour of the above article found, with most boardgame (non-casino) dice, Ones came up almost a third of the time! He attributed the problem to the imbalance of pips on dice and rounded edges (as compared to hard square casino dice), because dice-makers can save money on materials. That sounded very logical to me, so I wanted to test it out for myself. +++ HYPOTHESIS +++ Cheap six-sided dice give worse results, in that they'll give more statistically skewed, irregular, unevenly distributed results. Instead of giving any normal given result one-sixth or 16.6 repeating% chance, can be all over the place and rolls Ones about 30% of the time, like in the dakka article. The authour suggested, "Economics wins," meaning those problems were caused by cheap dice. +++ METHOD +++ So I chose the cheapest dice I had! I used GW's starter set white dice, the ones they begrudgingly give you with your big box purchases, because it's not a draw/selling point. You buy sets for the minis, even the rules, but no one ever says they want the dice! I scooped 16 readily available dice (I have more, but in different bags and I was lazy) in both hands, like I would in a 40k game. I'd shake at a random amount of time while listening to a television news program...because that's what happens. Sometimes you roll fast, sometimes you're listening to your friend/opponent explain a rule while you're still shaking them bones; it's not a lab environment but it's representative of what we actually do. Then I'd arrange the dice from ones to sixes in order, look at them and record the results on an Excel spreadsheet. I did that 50 times, equivalent to 800 rolls, then looked at the results at the very end, to avoid any additional biases. The table I used was my painting/computer table, a wooden one. It MAY have a different result with a softer mat surface, like a game mat. (For those that want a "control group" to compare the dice rolls with, the "control group" is actually the Mathhammer. On a six-sided dice, each side should come out on average once in six times, so 1/6=16.6% repeating, etc. That's the baseline we're testing against.) +++ RESULTS +++ Imma post the spreadsheet first, then explain, easier to show then tell: To quickly explain the table in case it's not organised well: Ones to Sixes: these columns show how much of each result was rolled Total: this is just an Autosum of all the previous columns to check, "Did I record all my dice?" Can ignore, but useful during data entry Average: the mean average should be 3.5 on a six-sided die. That's why Leadership checks, on 2d6, were usually 7, as it's by far the most common combination you'll roll. It was just a quick way to eyeball variance while I entered each roll of data. EDIT - though I initially added this out of curiosity, this turned out to be an useful reference to see if your rolls skewed on the high or low side. Bottom Blue LIne: this is basically the final results, an Autosum of how much each result came up, then the average of that sum Percentages: this is the real bottom line, the end goal of this exercise, to see how the rolls were distributed. I just divided the sum of each roll result by the number of times I rolled (800 altogether). +++ CONCLUSIONS +++ I mentioned 2 averages before: an average roll should have a mean of 3.5 and a number should come up 16.6% repeating of rolls. Welp, after 50 rolls of sixteen dice, the average roll was around 3.50...that's pretty much as close as one can hope for to the expected. As for the percent of times any face comes up varies between 15.63% to 17.88%...which is roughly within the plus-or-minus. I set out to test this theory the authour of the dakka article suggested, that ones come up almost twice as much as they should. That's obviously bad, as that's what causes plasmaguns to blow up, but my data do NOT suggest this is the case (for my dice at least). Despite that initial assumption, my numbers came out pretty even-stevens, disproving the theory that Ones come up most often! While there WAS a slight skew towards ones (17.63%), but are even sixes (17.88%), directly contradicting that article. I didn't mean to, as I wasn't out to embarrass the guy, if anything I wanted to match his findings so I can blame everything on my dice. Turns out nope, the dice were fine...the problem's probably me. +++ 3 TAKEAWAYS +++ I want to note three key takeaways, just odd things I observed, during this process. First, this was a small sample size and the results will be even better if we rolled more. 50 rolls of two handfuls of dice? As that number increases, i'm guessing the spread will even out more because of the law of large numbers. That band of 15.63% to 17.88% will get narrower with more rolls...which really brings them close to the 1/6 chance any face should come up on a 6-sided die. Second, the most impressive thing was how neat the average roll of 3.50 (almost matching exactly the expected Mathhammer average), but it's also worth noting how that might be because the probabilities of "opposite faces" really seem to match up. In other words, ones and sixes seem to come up about the same number of times, while twos and fives also match each other in how often them come up, then threes and fours have about the same percentage with each other. (That probably is by design, so each pair of opposite sides all have 7 pips, holes drilled in them, which causes the imbalance...but at least the dice roll results will then balance out. In fact, I remember when I first played boardgames, I noticed opposite sides always added up to seven...this was a strong reminder.) Third, rolling and recording, THEN looking at your overall results at the end, is the biggest benefit of this exercise; it forces us to look at the total trends, NOT a snapshot view. At some points, I absolutely convinced myself I was rolling more ones i.e. "observer bias". Note my 4th test, where I rolled 7 ones. I really fixated on that at the time, thinking it validated every complaint I had about my dice. It was only by forcing myself to enter all the data 50 times in an Excel that I could see the overall picture, which surprised me. +++ RECOMMENDATIONS +++ Try rolling your dice yourself while implementing your own system. It doesn't matter what method you use, as long as you have a method you stick with! Having an Excel in front of me kept me honest. The data entry process and looking at the total results at the end makes you look at things objectively. (Seriously give it a shot with your own dice. It literally took me 30 minutes waiting for a TV show to come on. It took me far longer to share this info here than it did for me to actually roll the dice and do the data entry). No need to buy fancy casino dice...el cheapo GW starter set white dice work out fine. In fact, I reckon they're way more evenly distributed (i.e. "good) then the fancy ones they're selling with Ultramarine symbols printed on their yin-yangs. Reason for editing - really appreciated our fellow Fraters reading and commenting. Turns out, this might be an useful post for future reference, so I cleaned it up for easier reading/user-friendliness. Thanks a lot, Brethren.