tag:blogger.com,1999:blog-4519319818452068646.post1052913535379425176..comments2024-02-16T18:32:38.635-05:00Comments on The Back 40K: Serial Vs. Parallel Dice RollingFarmpunkhttp://www.blogger.com/profile/09622091234212120598noreply@blogger.comBlogger27125tag:blogger.com,1999:blog-4519319818452068646.post-63107230866356895212011-08-12T05:42:12.489-04:002011-08-12T05:42:12.489-04:00Much thanks SW!Much thanks SW!L Witha Zhttps://www.blogger.com/profile/16089402505678172242noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-40455499647322308772011-08-02T20:48:26.019-04:002011-08-02T20:48:26.019-04:00Ah. I found where you made the "Lucky Shot&q...Ah. I found where you made the "Lucky Shot" comment. It got lost somewhere in the middle of the other Dice topic. I also somehow missed the couple of references to it in earlier comments on this topic. Apologies for that.TheNeverTherehttps://www.blogger.com/profile/00546704663653589055noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-2168000870412238362011-08-02T18:34:27.821-04:002011-08-02T18:34:27.821-04:00A major thing with reducing the number of consecut...A major thing with reducing the number of consecutive rolls is it makes the odds much easier to calculate. One or two dependent rolls is doable in your head whereas the chains of 4+ odds get fiendish to work out very fast!Koronahttps://www.blogger.com/profile/08250234754318025124noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-70249285649271039042011-08-02T17:33:32.192-04:002011-08-02T17:33:32.192-04:00@Flekkzo
You've said it better than me. :)@Flekkzo<br /><br />You've said it better than me. :)SandWyrmhttps://www.blogger.com/profile/02265244938930651317noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-3668528627424235232011-08-02T16:03:47.059-04:002011-08-02T16:03:47.059-04:00@Sandwyrm
Sounds to me like the math behind this ...@Sandwyrm<br /><br />Sounds to me like the math behind this is far less important than the intent of what you suggest. A simpler system using other means to achieve certain aspects of a unit. GW generally add dice to "improve" a units chance of doing something. More attacks, a better chance for a die to "advance" to the next roll, etc. While you suggest fewer rolls and other mechanics.<br /><br />For instance the 10 lasguns. Why not say that for each time you half the number of shots you can up the strength by 1? Go from 10 shots to 5 shots but you can do more damage. It would simplify the game rather than complicate it (rolling 45+ dice is *not* simple).<br /><br />For the math inclined, I didn't even remotely do any math on my lasgun example. I'm sure it isn't fair, it's just an idea of how you can use a different design principle than "roll more dice".Flekkzohttps://www.blogger.com/profile/14508641232973488303noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-24547186426355350172011-08-02T14:44:37.052-04:002011-08-02T14:44:37.052-04:00@TheNeverThere
I keep repeating this idea, but no...@TheNeverThere<br /><br />I keep repeating this idea, but nobody seems to be noticing.<br /><br />If your 10 lasguns can't possibly wound the target, then you get a weight-of-fire roll. Roll a single D6 for X number of models. On a 6 you cause a wound or a critical hit on a vehicle.<br /><br />If Draigo walks into your Grot squad and you can't hurt him, roll a D6 for that round of combat for X number of surviving models. On a 6 he takes a wound.<br /><br />It's a different mechanic that would produce similar results to now without all the extra rolling.SandWyrmhttps://www.blogger.com/profile/02265244938930651317noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-51282174143345484592011-08-02T14:26:23.360-04:002011-08-02T14:26:23.360-04:00idk. i kinda think doing graphs on dice rolling i...idk. i kinda think doing graphs on dice rolling is taking the fun out of the game and moving it to an extreme. while i understand both points of view, i just dont know. why not just play some more games and increase your chances of winning by rolling more dice. loluberdarkhttps://www.blogger.com/profile/13352343779774789871noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-22954615969942043582011-08-02T14:12:21.293-04:002011-08-02T14:12:21.293-04:00@TheNeverThere: Well, that only works as long as y...@TheNeverThere: Well, that only works as long as you assume that there is no re-balancing of the army books. <br /><br />Can't remember it clearly, but I don't think Sandwyrm indicated to just throw in a different matrix and then go and change all the statlines in the game w/o overhauling the force allowance and point costs too. ^^<br /><br />@auto-hit/fail: I don't have a problem with a auto-hit/fail mechanism per se, but I don't think it works that well with a system thats build around single d6 checks, with a tendency of dependent strings of 3-4 dice rolls. I think the "chance to fail" is way too high and as long as the system keeps using the d6 core mechanism, I would rather see some 1000+ years old chapter master just waltz over 10 guardsmen in CC, than end with a system where a avatar of a war god with WS10 has a 45% chance to end up not hurting a grot or guardsmen. That's just plain silly...Karnsteinhttps://www.blogger.com/profile/13889090422057767719noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-44983609662112659762011-08-02T14:02:26.131-04:002011-08-02T14:02:26.131-04:00We are arguing two separate points.
You're sa...We are arguing two separate points.<br /><br />You're saying that you can roll fewer dice and come up with the same probability.<br /><br />I agree. That is a fact.<br /><br />What I'm sating is that if you roll fewer dice you will see more variance in your results. You won't see the most likely outcome as much because you are taking from a smaller sample set.CaulynDarrhttps://www.blogger.com/profile/14556761303500891267noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-78589710389859292132011-08-02T13:53:09.289-04:002011-08-02T13:53:09.289-04:00There is no distribution curve on a d6. It's ...There is no distribution curve on a d6. It's flat.<br /><br />I do know that determining the probability of dependent events is different from the probability of independent events. <br /><br />What I'm saying is that a series of dependent events is made up of discrete independent events.<br /><br />The odds of rolling a six after rolling a six is still 1/6. The odds of forming a set of two rolls and having both of those rolls yield a six is 1/36. That still doesn't change the fact that each six was still a 1/6 chance. Rolling one die does not magically change the probability of the next roll.<br /><br />If you want a game that effectively manages random chance, you have to do one of two things. Roll enough dice(either in parallel or sequence) to average out the complete set of rolls, or use a dice mechanic that maps to a normal distribution(i.e. Warmachine).<br /><br />I'm not against games that use fewer die rolls if you can come up with a reasonably predictable dice mechanic. But if you reduce the number of die rolls with a dice mechanic that uses a flat distribution curve, you make random chance a more important factor in the results.<br /><br />You can manage probabilities all you want, but those are just estimations of possible results. Estimations that are less accurate over smaller sample sets.CaulynDarrhttps://www.blogger.com/profile/14556761303500891267noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-50590267135469249642011-08-02T13:37:22.498-04:002011-08-02T13:37:22.498-04:00I get what you're saying about how we roll too...I get what you're saying about how we roll too many dice as things are written right now (glance at Green Tide), and I don't really have a problem with that. The only thing I really have a problem with is that stat chart from your previous article with Terminators being T7. This would mean that nothing that's S4 or lower (on your other chart) could hurt it. Period. Which would make armies that can take Termies as Troops (you know who you are) nearly impossible to kill, since (most) base weapons are S4. This would, more than likely, break the game. Now, I'm not saying it's wrong to want the game to reflect the fluff, I'm just saying that you have to be careful when doing so, and draw a line in the sand somewhere. Because if the game accurately reflected the fluff perfectly, Draigo would be a single-model army.<br />(Braces for rebukes)TheNeverTherehttps://www.blogger.com/profile/00546704663653589055noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-92156737565316559982011-08-02T12:56:28.665-04:002011-08-02T12:56:28.665-04:00@CaulynDarr
You aren't following what I'm...@CaulynDarr<br /><br />You aren't following what I'm trying to say.<br /><br />Yes, rolling a bucket of dice, say 200, for your to-hit rolls (one throw) will even out your luck such that it approaches a distribution that looks like a bell curve. This is statistics 101. I don't dispute that.<br /><br />What I'm disputing is the taking of this principle and trying to say that it applies to dice rolled in a sequence (one after the other). It doesn't. That's lazy thinking. <br /><br />Different principles apply to dice rolled in a sequence/series than to dice rolled in parallel. You get a different sort of distribution curve and an overall lowering of your granularity at the success end the longer the sequence. Which is what I'm trying to show in this post.SandWyrmhttps://www.blogger.com/profile/02265244938930651317noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-53191784338900520402011-08-02T11:02:05.317-04:002011-08-02T11:02:05.317-04:00One more example to make it clear.
Lets say tha...One more example to make it clear. <br /><br />Lets say that instead of rolling dice for a game of 40K we used a random number generator to generate n random values between 1 and 6. Every time we need a die result we just pop the top value from the list. Notice that if you pop 4 results in a row versus 4 dice at one time, you still get the same results.<br /><br />Say we also played a really short game that used only 10 die rolls under the current system, and then 6 die rolls under your system. Here's the random set of 10 dice: [6,6,6,3,5,2,4,1,1,1] That's a average distribution over the ten dice, but if you only look at the first 6, you rolled one hell of a game.<br /><br />So if you total sample size of random events is smaller, there's a higher chance of having a un-average sample set.CaulynDarrhttps://www.blogger.com/profile/14556761303500891267noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-23940093152339480502011-08-02T10:36:10.702-04:002011-08-02T10:36:10.702-04:00The alternative is to use 2d6 together and get you...The alternative is to use 2d6 together and get yourself a nice Gaussian normal distribution. Then you can effectively get a way with fewer overall dice rolls because those rolls are more predictable.CaulynDarrhttps://www.blogger.com/profile/14556761303500891267noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-79741406078644017782011-08-02T10:31:03.319-04:002011-08-02T10:31:03.319-04:00When you roll dice in sequence you do generate a p...When you roll dice in sequence you do generate a probability for that sequence, but each individual die roll is still an independent result on its own.<br /><br />So if you roll 10 dice at one time, or 10 dice in a row, the given probability of seeing any one result on any one die is still 1/6.<br /><br />What Mike is saying, and I agree with, Is that, if you have 2 events or 3 events that work out to the same average probability, 3 is the better choice. It's better because 3 independent events that are interpreted together in a sequence are slightly less susceptible to random chance than two.<br /><br />You can't predict the results of a single d6, but if your roll enough dice you will get an even distribution of all the results. Whether I roll dice in row or at the same time, that doesn't effect the distributions of all the results. If you reduce the total number of dice you roll in a game from 200 to 100, you are that much more likely to see a total distribution of results that skews to one subset of results. So while your method controls the probabilities for single events within the game, it would effect the overall game because less dice means you are less likely to see an average distribution of results.CaulynDarrhttps://www.blogger.com/profile/14556761303500891267noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-91959773608511269182011-08-02T10:06:00.227-04:002011-08-02T10:06:00.227-04:00Korona has it.
@Mike
If we could design a game t...Korona has it.<br /><br />@Mike<br /><br />If we could design a game that did away with the bucket-o-dice (anything over 20) and yet still felt less random than 40K, while reflecting the fluff better; would you be interested in playing? How about all of that in a 1 hour game?<br /><br />That's what I think that we can accomplish here with a series-of-2 mechanic (instead of 40K's series of 3/4) and a few "hero" rolls to give us those shining moments of valor without all the tedium.SandWyrmhttps://www.blogger.com/profile/02265244938930651317noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-87680135166292933932011-08-02T09:46:13.329-04:002011-08-02T09:46:13.329-04:00@Lantz
I've added some more explanation just ...@Lantz<br /><br />I've added some more explanation just after that chart.SandWyrmhttps://www.blogger.com/profile/02265244938930651317noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-26593220440755193152011-08-02T09:34:22.318-04:002011-08-02T09:34:22.318-04:00@Flekkzo
There are other ways to ensure Hero mome...@Flekkzo<br /><br />There are other ways to ensure Hero moments that don't gimp the game. The weight of fire idea, for example. If your 10 lasguns can't wound that Terminator (because the chart doesn't allow it) you can roll a single die per 10 guys and wound a single Terminator on a 6.SandWyrmhttps://www.blogger.com/profile/02265244938930651317noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-3659532664794247122011-08-02T09:31:26.249-04:002011-08-02T09:31:26.249-04:00@Ahrimaneus
"…Or, the more dice you roll, th...@Ahrimaneus<br /><br />"…Or, the more dice you roll, the better =)…"<br /><br />I understood Mike's point (and yours) just fine. What I'm saying is that both of you are incorectly applying a general truism to a case where it doesn't work. <br /><br />Rolling dice in parallel? YES, more is better. Up to a point.<br /><br />Rolling dice in Series? More doesn't increase reliability. Because the sample size is still one. You DO get more finely grained results, but those results are not linearly distributed. You get extremely fine-grained results at the low-end (failure), and extremely coarse results at the high end (success).<br /><br />Lastly, the statistical abberations you mention are mostly a product of the auto-pass-on-6 and auto-fail-on-1 system that we play with. Going with a auto-pass/auto-fail system (no 1 or 6 charity) on 2 series dice would expand the range of results we play in, save time, and still allow us to have our hero moments by using a different mechanic such as a single "Weight of Fire" roll for an otherwise useless unit's firing that always wounds on a 6.SandWyrmhttps://www.blogger.com/profile/02265244938930651317noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-76379949936210171522011-08-02T09:29:07.311-04:002011-08-02T09:29:07.311-04:00@ Ahrimaneus I think you're falling into the s...@ Ahrimaneus I think you're falling into the same trap Mike did.<br /><br />Rather than use the terms "series" and "parallel" I would use "dependent" and "independent".<br /><br />If you make multiple independent rolls then you will smooth your results thanks to averages. An Ork's "bucket-o-dice" is a great example of this. Because none of the rolls affect each other the goofy outliers are essentially drowned out and made irrelevant by the sea of average rolls.<br /><br />If you roll the same number of dice but have them all dependent on each other then you're basically just making one "super" roll. Those goofy outliers can't be ignored because a single whiff will scupper the whole result.<br /><br />A chain of dependent rolls adds nothing for the stability of the final outcome.Koronahttps://www.blogger.com/profile/08250234754318025124noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-30327060277863742892011-08-02T08:41:23.554-04:002011-08-02T08:41:23.554-04:00PS - Anything is "bad" if taken to an ex...PS - Anything is "bad" if taken to an extreme, which is why a single roll to determine the entirety of hit/damage/save/etc. is bad, and why tons and tons of rolls to get there is bad. You have to find a sweet spot, where both players are involved in the rolling, and where follow-up rolls have an opportunity to better balance "streaky" rolls.<br /><br />Also, 40k is not a skirmish sized heroic game really ... heroic scale, but it's not about Mephiston auto-ganking entire squads ... at all. It's about grunts and tanks and guns and swords and all of them coming together in big ole full scale conflicts.Mike Brandt; mvbrandt@gmailhttps://www.blogger.com/profile/00818846784767602047noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-34037393249353866842011-08-02T08:25:36.091-04:002011-08-02T08:25:36.091-04:00Ahrimaneus hit the point on the head.
I get what ...Ahrimaneus hit the point on the head.<br /><br />I get what you're saying, I just don't think I was as clear in a brief comment with what I'm saying.<br /><br />The enjoyment of a game decreases (For me), and the "feel" of random increases when there are fewer sets of rolls between targeted outcome and outcome. Again, Ahr hit it well.Mike Brandt; mvbrandt@gmailhttps://www.blogger.com/profile/00818846784767602047noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-81971355495821967762011-08-02T07:11:50.348-04:002011-08-02T07:11:50.348-04:00God I love these posts. Though I didn't unders...God I love these posts. Though I didn't understand the first unlabeled chart in the least. Can you clarify what it represents?L Witha Zhttps://www.blogger.com/profile/16089402505678172242noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-83920581771365209032011-08-02T05:06:03.322-04:002011-08-02T05:06:03.322-04:00I've got big hands, always shake well for a fe...I've got big hands, always shake well for a few seconds before dropping with a built in roll just so no matter how many dice I've got (up to a point, dont play IG or Nids!), I'll give them a good random roll. Large number of dice are not an issue.<br />Small number of dice (Deathwing) always get a good in-air spin.<br />I would ALWAYS prefer to roll more dice to achieve the same probability than fewer dice, mainly due to... Technical wurds like wot Ahrimaneus sed.<br />Just went back to your 'reinventing 40k' post, and quite like the new X vs Y table. What I don't like is the Mephiston waltzes through combats auto killing. This game is about thinking and working the odds. As a DW player, I can roll an incredible number of invul saves, then roll three 1's in five wounds from a flamer. If you're trying to remove this sort of thing from hapenning, fine, but Ol'glittery vampire lord has, can, and will roll six 1's.Farmer Geddonhttps://www.blogger.com/profile/08317142137061920849noreply@blogger.comtag:blogger.com,1999:blog-4519319818452068646.post-78954544796351174562011-08-02T04:29:48.572-04:002011-08-02T04:29:48.572-04:00I agree with Sandwyrm
1. The amount of dice rolle...I agree with Sandwyrm<br /><br />1. The amount of dice rolled in a game of 40k, esp. with special/heavy weapons, elite armies or powerful&costly HQ models is still far far away from anything that pleases the "law of large numbers". At least that's what I remember from my 2weeks course on statistical analyse back in my first semester of at the U. <br /><br />I'm mean just take a look at a squad of Longfangs: with 4 ML/LC and 6 rounds you end up rolling something between 2(hit, wound, no save( and 4 dice per model. That's 8-16 dice per round, 48-96 dice per game. Assuming that you manage to play 6 rounds, keep the whole squad alive and not run out of targets. <br /><br />And don't get me started on the numbers you roll with a single gun tank. <br /><br />So I don't think cutting down the number of dice you roll in a serie and moving towards a "to hit/wound"-chart that allows stuff like a carnifex wound&kill a grot w/o the player having to roll and hoping that no 1 shows up, won't screw the game...because it is far far away from producing reliable numbers anyway.<br /><br />2. The "other games are worse" argument is also wrong, because WM for example uses a 2d5+value and you need 2 tests to hit&remove a model. Sure, WM also has a auto.fail mechanism but the chances to roll snake eyes are 1/36 for a normal check and 1/216 for a boosted 3dice attack.Karnsteinhttps://www.blogger.com/profile/13889090422057767719noreply@blogger.com