ROLL THE DICE AND KEEP YOUR SANITY

RESULTS

TABLE 1

TABLE OF CONTENTS

TH/TK/IFT/CC     These rows deal with the dice rolls that cause damage (including residual fire)

MC/TC/RALLY    These rolls are obviously, DR’s that involve using unit morale.

OTHERS              All other DR’s not encompassed in the first two categories, including weather, entrenchment, sniper counter movement, gun manhandling etc.

TOTAL                  This is the total of all the rolls for each result.

THEORETICAL  The theoretical bell curve for the number of dice rolls per nationality. (Fractions have been rounded off.)

BURN OFF (Both)          Legion and I both “burnt off” 10 DR’s before logging any fire/rally DR’s as there is a theory in the ASL community that it takes a while for the dice-bot to start working randomly and I thought it would be a good idea to compare game DRs with the burn off DRs. (This also allowed us to have a larger number of DR’s thus giving a more accurate sample of the dicebot's random number generation.)

TOTAL (ALL)                   The totals row across the bottom is the total of German, British and burn off rolls per DR total.

THEORETICAL (ALL)   The theoretical bell curve for the total number of dice rolls for both nationalities and the burn off. (Fractions have been rounded off.)

AVG                                   This column gives the average DR per category for the entire row.

GAME: PEGASUS BRIDGE DAY 1

GERMAN PLAYER: LEGION

BRITISH PLAYER: JP

WHY DID I RECORD THE ROLLS?

    Legion and I have been playing ASL for a decade now and, although our tactics are, I feel, at an equal level – he simply manages his units a lot better than I do and I will happily admit that he is a better player than I am. One of his biggest complaints is that my “lucky” dice win games for me and so, I decided to record the rolls to show that my dice are not “lucky” it is simply a case of rolling the low dice at the crucial times in the game, in effect, that I am lucky, not the dice. (To be fair to Legion he also complains when he has a run of low dice that shatters my troops and turns a tight, interesting game into a slaughter.)

STANDARD DEVIATION

    It has been a long time since I attended a seminar on statistics and, I did try to find my notes but they are too well hidden somewhere in my house so I am unable to show you a statistical model. However, I will just explain standard deviation before we start talking about the dice rolls.

    As we can see in the table below, when we roll two dice there can only be one result out of the thirty-six possible combinations, with the totals of “2” and “12” being the rarest possible rolls and a total of “7” being the most common. If we were to roll a pair of dice 36 times we would get one of each result, correct? Unfortunately the answer is NO!! Because each roll of the dice is an independent roll and is not related to the previous roll we SHOULD have more totals of “7” than either “2” or “12” because the chance of rolling a 7 is 6 out of 36 as compared to 1 out of 36 for either 2 or 12 but it is still not guaranteed, this is called standard deviation.

    Basically 91% of the time the results would be similar to the table below, while 6% of the time the results would be noticeably different and 3% of the time the results would be wildly different. (Although I cant find the statistical model to show you, I do remember the percentages – so you will just have to trust me.)

TABLE 2

    Obviously, the more times we roll the dice, the more chances there are that the results will normalise and start to follow the table above. Including our “burn off” rolls we rolled the dice a total of 725 times which is still not enough to be called a statistical analysis, there are, however, enough to be considered a representative sample. In order to be able to start quoting the “law of averages” we would have needed a few thousand rolls, but we are able to glean some interesting information from the data at hand.

THE AVERAGES

    As we can see from the Average column on the right of the table all the various roll categories were within .5 of the true average of rolling two dice. (For those that are unaware the average should be 7) The only exception to this is the British IFT/TH row, which was .9 lower, however, the British MC/RALLY row was higher than the average of 7 and the total average for the Brits was 6.68, slightly lower than the Germans average of 6.84 but certainly not enough to claim that the Brits dice were blessed by your local deity.

    It is important to note that the Brits only rolled on the IFT/TH table 66 times thus allowing standard deviation to rear its ugly little head as compared to the Germans total of 164 so, obviously, we could expect the German average to be nearer the true average of 7 as they had rolled over two and a half times more than the Brits.

    The burn off dice averaged 7.22, which was not too far away from the true average; most importantly the total average of all the dice rolls was 7.008 indicating that the dice-bot is a fair and accurate random number generator.

    So, what about the total of our actual game rolls? As you can see in the table below the average DR for the entire game was extremely close to the true average of 7.

TABLE 3

THE BELL CURVE

    Lets face facts; a boat could sink in a river that is 3 feet deep on average. Although our dice average is close to “7” it must be remembered that 2 dice rolls with a total of 7 would average out to 7 BUT, two rolls with a total of 2 for the first roll and 12 for the second roll would still average out to 7, so we now need to look at the bell curve.

    Lets look at table 2 again, as we can see the chances of a result of “2” occurring are 1 in 36 while the chances of a “3” occurring are 2 in 36, making it twice as likely to be rolled. As we look across the table we see that the chances of a 7 occurring are 6 in 36 thus making it the easiest number to roll with two dice and, if we look even further across we can see that the chances of a “12” occurring are back down to 1 in 36 (the same chance as a “2”) If we were to plot this onto a graph it would make a curve with each end of the curve (the “2” and “12”) being the low points and the 7 being the highest point. (Called a “bell curve”)

    Armed with this knowledge, lets now go back to table 1 and look at the two rows, the TOTAL (ALL) and the THEORETICAL (ALL). The red row is the actual results for the game while the blue row is the theoretical number (the bell curve) of each result for the 725 rolls we recorded. As we can see, MOST of the results are fairly close to each other with the noteworthy exception being the “11” result, which was a massive 42% more than the theoretical. (Fortunately for our game, the majority of the “11”’s were rolled on the burn off dice.)

    Other points to note were the “3” and the “5” being 15% above and 20% below theoretical respectively, however these could be written off as standard deviation (although I will admit that 42% is a massive swing) and, eventually, I feel that the results would normalise if we were to continue recording the dice rolls. (Once again I would like to point out that we need thousands of dice rolls to gain an accurate picture of the spread of results.)

THE 2’s AND 12’s

    Lets now look at the most important dice in the game, the dreaded (or beloved) snake eyes and boxcars!! If we look at table 1 we can see that both the Germans, British, burn off, and TOTAL (ALL) rows were extremely close to the THEORETICAL row for each, in this game both of our 1,1 rolls did not cause any major damage through being either 

a)    Improbable critical hits

b)    Being fired at buildings with a +3 modifier.

    More to the point, although I could have claimed how much luckier Legion was by having rolled 7 snake eyes as compared to my 3 in reality he rolled a total of 225 times as compared to the 129 times I rolled. Therefore it is entirely feasible that he would have rolled twice as many snake eyes as I did due to the greater number of total rolls for the Germans. As for the boxcars, both of us rolled around half as many as we should have so I am sure neither of us will complain about that, although once we include the burn off dice then the number of 12’s becomes a lot closer to the theoretical result so it has evened out again.

IN CONCLUSION

    Although much more could be written about the results above the important point I was trying to make was simply that the dice-bot is fair and that both sides get an equal amount of each result. The where and when of these results do affect the game without a doubt but, we all can’t keep blaming the dice when we lose, and, at the end of the day a bad player with lucky dice will still lose to a good player with bad dice.

SO HOW DO I KEEP MY SANITY?

    Without doubt, the most frustrating part of ASL are the dice rolls, we have all gone an entire game where our biggest and baddest fire group or AFV have not been able to influence the game, but, if we adopt a more philosophical approach to our dice rolls we can we can all (hopefully) avoid ending up in a padded cell.

    For many years I would get angry with the dice and throw them across the room just to teach them a lesson, but, recently I have adopted a more philosophical approach and have certainly started to enjoy my games more because of it, written below is my belief structure when faced with bad dice rolls and I strongly suggest that you all take time to read it.

RULE 1: 

    It is only a game always remember that. 94% of the world’s population are faced with starvation, death, and diseases, if your biggest problem in life is the fact that you rolled a pair of sixes then you are doing pretty good, so get a decent perspective on it.

    Every time you roll an 11 or 12 don’t get angry, call it an I.O.U., in other words the dice owe you a 2 or 3 for every 11 or 12 you roll, it may not happen next roll or next turn and, you might have to wait until next game, BUT it will happen, because the law of averages says it will!!! (Likewise remember that every time your opponent rolls a 2 or 3 then the dice owe him an 11 or 12- unfortunately this also applies to you...) After all, the dice don’t start “fresh” just because you are playing a new scenario and every time you roll the dice it is another result added to your personal tally WHICH WILL eventually end up prescribing a perfect bell curve, all you have to do is keep playing.

    Take responsibility for your life!! It is innate in all human beings to remember the bad things in life (and blame others for it) while forgetting the good things, we remember rolling a double six and watching our tiger tank become a 60 ton pizza delivery van but we forget the fact that it took out two Shermans and rolled a critical hit which killed our opponents best leader and 2 of his squads. Make an effort to remember when the dice worked well for you and realize that when they turn against you it is just balancing out the results.

    We also tend to blame other events for our losses (mainly the dice) BUT when we win, we take credit for it and the dice don’t get so much as a mention, learn to take responsibility not just for your wins, but also for your losses. Reading some after action reports on the web it would seem that every ASL player is a military genius that can only defeated by the dice, however, the dice are only PART of the game, remember all those little cardboard counters? Their position and the way they are handled plays a major role in deciding who wins/loses a game so learn to accept when you have been outplayed. (Also remember that a good player will get the majority of his firepower into action quickly, and, the player that rolls the most dice has more chance of rolling the low (and high) numbers.) Obviously a player rolling a lot less times than his opponent can and will regularly see standard deviation turn up within his dice rolls thus giving the impression that their dice are “blessed/cursed” which of course they are not, it is just a fact that they have not rolled enough times in the game for their personal “bell curve” to start normalising their results. (See the British IFT/TH row for a good example.)

RULE 4:

    Develop a positive aspect!! On a recent game I was rolling very low dice and causing lots of damage to my opponent, when I rolled a 1,1 on an entrenchment DR he lamented the fact that I have snake eyes to spare. I was thinking “what a waste of a 1,1” and he should have been thinking, “thank god he just wasted a 1,1 on an entrenchment attempt”. When your opponent gets a critical hit and kills 2 out of your 3 squads don’t complain about it, he will get CH’s, its part of the game, instead, be happy with the fact that one of the squads survived.

    If the first four rules still haven’t bought you inner peace then buy a pair of fluffy dice (the kind you hang off rear view mirrors) and throw them when you are angry, they are bigger and easier to find and they will do less damage to your paintwork.

    I hope this article has helped you to enjoy ASL more any feedback, comments or questions are welcome, please send to thejpspinelli@hotmail.com (E-mails only, no attachments please)

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