Beams, dice and maths

[Da Boss]

Hi a quick question for you maths type people.

I have it in my head that with the RAW beam system the more dice you roll the more likely it is to come out towards the average - is this true or just a QI style misunderstanding of maths?

what I mean is say you have a squadron of dastedly Minbari

A Sharlin and three Tinashi - lots and lots of beams.

now if you roll them as 8, 4, 4 and 4 dice - there is a horrible (to me) degree of randomness meaning that its quite likely each ship will get a good roll or indeed miss entirely. So you could end up with 5 hits, no hits, 3 hits and 3 hits - (seen this) - giving a total of 11 hits. (Ok conversely you might get 20 hits, 10 hits, 4 hits and 6 hits - seen that too)

However if all fire together (20 dice) and roll together it (in my mind) seems that you are more likely to get an average roll (and def not miss given the sheer amount of dice) of around 20 hits.

why, you ask, am I asking - I am just wondering if it is more beneffical to roll all together to avoid those annoying misses? If so this is something else that annoys me about the present beam system...............

 

[lastbesthope]

The dice don't know whether you are rolling them in a batch of 20, or 20 single throwws, it shouldn't statistically have an effect on the outcome.

Mechanically though, it might as 20 dice will knock off each other more often, the additional agitation might have an effect on the outcome.

The bigger the group, the more likely the result of that group is to be average. So yes, rolling 20 dice will give a more average result than you would get for each of the 4 individual groups of 8, 4, 4 and 4 respectively. but if you collated the results of all 4 groups they should be as average as the group of 20.

Make any sense?

LBH

 

[Triggy]

LBH is right with almost all that he said and not really relevant with the mechanical point.

Firstly, agitation/knocking into another die will have no statistical effect on the outcome. Period. Dice are random and like Schroedinger's cat, until the result is confirmed (by looking at the die), all results are equally likely.

Now, the short answer to whether you should be rolling your dice a few at a time is no, it makes no difference in what order or how many at a time you roll. Any individual result has no effect on the result of any other die. There is no such thing as "the law of averages". That means that the dice have no memory either and if you have bad luck early in a game, for the rest of the game your chances of good and bad results remain unaltered. Don't plan on good luck staying with you or bad luck "must end by now" either. Plan as if the rest of the game hasn't happened and you are starting afresh from wherever the game has got to.

The longer answer about rolling more dice being closer to the mean (average) result is more interesting. Basically, if you roll more dice, the chance that you will be a certain number above or below the mean will increase but the chance your result will be a certain percentage above or below the mean will decrease. In plain English - your chances of getting an exactly average score with more dice will be less but the chances of all (or even most) of your dice being above or below average will be less.

To see this in action, consider a single d6. With a single roll you have a 0.17 chance of being at least 2.5 above the mean (the mean for a single die roll is 3.5). With 2d6 the chance of being at least 2.5 above the mean is 0.17. With 3d6 the chance of being at least 2.5 above the mean is 0.26. However, the chance of 1d6 being at least a 5+ is 0.33; the chance of all of 2d6 being at least a 5+ is 0.11; and the chance of all of 3d6 is 0.037.

I hope this helped a little but I suspect it only helped those whom already understood these principles

 

[Joe_Dracos]

Well, math on paper is all well and good... but it rarely goes according to the odds :? . I found with the old beam system you were more likely to roll higher then average then average or less then average simply because there is so much room higher then average and 0 is essentially the lowest you can go.

What you might be noticing is the increase in probability because the high number of dice gives you a wider spread for potential results. The complete randomness of the core beam system is why me and the fellows I game with abandoned it for the more moderate optional beam rules. Beams are still big, just not so big as to make hull value and secondary weapons pointless.

 

[lastbesthope]

Remember the laws of probability and statistics were created by humans. As were dice, but the dice never studied probability, at least mine don't seem to have :lol:

Though I did spend a second working out whether or not it was better to use my machine gun or run over the MEA in my Challeneger at a BF Evo launch day game. Turned out I was right in my choice, can't remember what it was though.

LBH

 

[Joe_Dracos]

run em over! RUN EM OVER! :twisted:

 

[Burger]

Of course, you also have entropy to take into account.......

 

[Triggy]

Of course, you also have entropy to take into account.......

Well if we're going to do that then we may as well take paired quantum particles into account

 

[AdrianH]

It is certainly true that the more dice you roll, the closer you will get to an average score. This is true whatever mechanism you use, although some mechanisms will score closer to average than others for a given number of dice - see the alternative beam rules in S&P edition 64 or P&P, for example.

On the other hand, as has been said, dice don't always respect probability theory even when they're not loaded. Our games club sometimes plays the board game "Settlers of Cataan", in which a 2D6 roll determines which tiles of the map generate resources this turn. In theory tiles with numbers 2, 3, 11 or 12 should come up less often than tiles with numbers 6, 7 or 8. One day I want to get a statistics professor involved in such a game with the specific intention of driving him insane. :twisted:

Back to the original question, where in theory it doesn't matter if you roll the Sharlin's 8D and the Tinashis' three groups of 4D separately. True, doing it separately, you're more likely to get a runaway expansion or a flat miss, especially for the Tinashis. The same theory says they should cancel out, so one of the Tinashis might miss the target entirely while the next one slices it in half. Rolling them together, you should get the same number of hits in total, you just don't know which ship scored the kill.

In practice, if it's my Shadow ship vs. someone else's Sharlin, the total roll will probably be average - he'll get the runaway expansion, I'll get the flat miss...

 

[nekomata fuyu]

Regarding getting closer to an average score by rolling more dice, that very much depends on how you're measuring closeness.
In absolute terms, as you roll more dice, the total will tend to drift further away from the average roll. In relative terms however, the total will tend to drift towards the average roll.

I tend to say that dice do follow the rules of statistics, but that most people don't understand those rules. Whenever I see someone claiming the rules of statistics do not apply, they always seem to bring up something like "You should roll a 7 on 2d6 much more often than you roll a 12, yet I've had games where I've rolled several 12s and not a single 7!!". This is a blatant sign that they're misunderstanding the statistical rules to be hard rules as to what should happen. Statistical rules merely state what is more likely to happen, and quite happily allow the less likely options to happen. Furthermore, it is less likely for a the unlikely events to outnumber the likely events, but this in itself is still open to happening due to being an unlikely event (which may still happen).

 

[pasuuli]

why, you ask, am I asking - I am just wondering if it is more beneffical to roll all together to avoid those annoying misses? If so this is something else that annoys me about the present beam system...............

We should talk about various systems sometime.

 

[lastbesthope]

Of course, you also have entropy to take into account.......

Well if we're going to do that then we may as well take paired quantum particles into account

You mean you DON'T!!! :shock: :wink:

LBH

 

[Da Boss]

why, you ask, am I asking - I am just wondering if it is more beneffical to roll all together to avoid those annoying misses? If so this is something else that annoys me about the present beam system...............

We should talk about various systems sometime.

well we are on a forum - lets talk :wink:

 

[Dihenydd]

Now to throw everything into a spin. No really, I've done this on more than a few boards already.

The biggest factor on the results you roll is not the number and the statistical odds of getting close the normal average or mean. In fact the biggest obstacle you have is you trusty little dice.

No really!

The bulk of dice out there are a crying shame. Does it seem like you roll a lot of 1's? That's because you do. The odds of rolling a 1 on a standard d6 is to be 17% (ok 16.6666666) However most d6 (and a lot of other die out there) use a divot system of marking numbers (the little pips on the die). This actually creates imbalaces within the die itself. The '1' is actually the heaviest side of the die and due to interesting physics the heaviest side of a die is the one most likely to be face up. Also, the rounded corners on most dice manufacturers and circle facings are not entirely.... precise. These also lead to inaccuracies in the odds of a particular number coming up. There is loads of research out there if you look for it, but the most studies agree that a standard chessex d6 will roll a '1' roughly 25-30% of the time or 1 in 4.

If this sounds like wishful thinking or whining, consider this. Ever see a die at Vegas with divot pips? No, the die they use are 'precision' meaning they are weighted equally and have printed numbers or pips only. Retail value of a pair of precision die is around $30USD. Vegas of course gets them cheaper in bulk, but in an industry that lives and dies by odds, I find it interesting that Gaming Laws require use of these dice. Now, how do you feel about your 10$ for 20 chessex die? Competition backgammon also requires the use of precision dice and will not allow the standard dice in most games. If they insist, maybe there's something to this?

Ok, now for the good news. Vegas and most casino's can only use the dice for a set length of time then they must be changed, again by regulation. What happens to these $30 dice? They stamp them to mark them as used and then sell them at the gift store "These are actual used Crap Dice in Vegas" for $2 a pair. The stamping is shallow and has no effect on odds, but marks them in case someone tries to switch etc. I currently have 30 and will only use them.

The difference was instantly noticable. The numbers seem to roll fairly consistently now and my '1' has just as much chance as a '6'. On a side note, this has made many of my weapons in GW games more effective, and armour saves as well as I'm no longer rolling '1's 25% of the time.

Ok, down from soapbox. But really, invest in some good dice will make all the difference. (Plus they look cool)

 

[Joe_Dracos]

Whenever I see someone claiming the rules of statistics do not apply, they always seem to bring up something like "You should roll a 7 on 2d6 much more often than you roll a 12, yet I've had games where I've rolled several 12s and not a single 7!!". This is a blatant sign that they're misunderstanding the statistical rules to be hard rules as to what should happen. Statistical rules merely state what is more likely to happen, and quite happily allow the less likely options to happen. Furthermore, it is less likely for a the unlikely events to outnumber the likely events, but this in itself is still open to happening due to being an unlikely event (which may still happen).

The problem with statitical evaluation of certain numbers is that it is a simple sample of a given set of numbers and the potential for that given sample occuring in a particular pattern. It really doesn't take into acount alot of variables that will bend the curve. If you roll the dice in a certain dirrection (say the 1,3,6,4 dirrection) then the odds of a 2 or 5 are decreased, yet the fasion the dice is rolled (by the human hand) will also stretch the results. An old friend of mine used to flip his had right over with the 1 pip showing upwards (initially) and then a 6 would come up an inordinate amount of times when he rolled. There is also the spin on the die(back spin for example), shape of the corners, and the surface you are rolling on. Probability is a very sterile annalysis which can really only measure one variable (in this instance).

I guess what I'm saying is that the rules of statistics can apply, they just can't give you any accurate odds (in this instance) due to the inability to take the human eliment out of the equation.

 

[Burger]

I know someone who can sneeze at just the right moment, to push his dice off 1's and onto 6's. It has gotten so annoying that when I play him, I keep a good supply of tissues by my side. Whenever I see him preparing to sneeze I simply shove a tissue under his nose, and he rolls a 1! It really works!

 

[McKickaha]

Huh!,

Laws of probability, statistics, mechanics and quantum theory - Pshaw.

Everybody knows that the way to good rolling is;

(a) The lucky dice
(b) Having respect for the dice gods.

 

[Democratus]

Painted miniatures also makes dice roll better.

It's science.

 

[Triggy]

Now to throw everything into a spin. No really, I've done this on more than a few boards already.

The biggest factor on the results you roll is not the number and the statistical odds of getting close the normal average or mean. In fact the biggest obstacle you have is you trusty little dice.

No really!

The bulk of dice out there are a crying shame. Does it seem like you roll a lot of 1's? That's because you do. The odds of rolling a 1 on a standard d6 is to be 17% (ok 16.6666666) However most d6 (and a lot of other die out there) use a divot system of marking numbers (the little pips on the die). This actually creates imbalaces within the die itself. The '1' is actually the heaviest side of the die and due to interesting physics the heaviest side of a die is the one most likely to be face up. Also, the rounded corners on most dice manufacturers and circle facings are not entirely.... precise. These also lead to inaccuracies in the odds of a particular number coming up. There is loads of research out there if you look for it, but the most studies agree that a standard chessex d6 will roll a '1' roughly 25-30% of the time or 1 in 4.

If this sounds like wishful thinking or whining, consider this. Ever see a die at Vegas with divot pips? No, the die they use are 'precision' meaning they are weighted equally and have printed numbers or pips only. Retail value of a pair of precision die is around $30USD. Vegas of course gets them cheaper in bulk, but in an industry that lives and dies by odds, I find it interesting that Gaming Laws require use of these dice. Now, how do you feel about your 10$ for 20 chessex die? Competition backgammon also requires the use of precision dice and will not allow the standard dice in most games. If they insist, maybe there's something to this?

Ok, now for the good news. Vegas and most casino's can only use the dice for a set length of time then they must be changed, again by regulation. What happens to these $30 dice? They stamp them to mark them as used and then sell them at the gift store "These are actual used Crap Dice in Vegas" for $2 a pair. The stamping is shallow and has no effect on odds, but marks them in case someone tries to switch etc. I currently have 30 and will only use them.

The difference was instantly noticable. The numbers seem to roll fairly consistently now and my '1' has just as much chance as a '6'. On a side note, this has made many of my weapons in GW games more effective, and armour saves as well as I'm no longer rolling '1's 25% of the time.

Ok, down from soapbox. But really, invest in some good dice will make all the difference. (Plus they look cool)

I use Chessex dice and I can deny that the odds are anywhere near that. I've looked at odds over many battles and they are effectively normal (there may be a very slight discrepancy but it's not more than 1% out at most!)

The principle of the pips being indented though is a valid one.

 

[Burger]

Ah Chessex compensate for the indentations of the pips by using heavy paint to fill them in. Ever wondered why they are so popular? :lol: