Uncovering Warp-Tainted Dice

I've mentioned before that I've had some pretty horrible luck with my dice. In the past few months I've failed four out of about seven 3+ cover saves, failed five out of six 3+ armor saves immediately after failing five out of six 3+ cover saves, rolled absurd numbers of ones and twos during two out of three games, and, in last week's game, rolled multiple snake eyes, failed to wound three out of five Orks after hitting them with a strength 10 Demolisher Cannon, and failed three out of five artificer armor saves. As a Space Marine player, I spend a lot of points for awesome armor saves and a high ballistic skill, all of which can be completely neutralized by an excessive number of ones and twos. Space Marine armies simply aren't large enough to tolerate that kind of rolling.

Being paranoid doesn't mean
that they aren't out to get you

At first I was willing to believe that I simply perceived the rolls as being skewed due to the human tendency to selectively remember extraordinary events. After a while, I started testing my dice, repeatedly rolling each die in my box of 36 dusty blue and copper Chessex dice (yes, I chose the dice to match my army). I averaged the results for each die respectively and found that they usually produced a result close to the expected 3.5. This seemed to confirm that I was selectively remembering the bad rolls.

After last week's game, I came home convinced that something was awry with many of my dice. After a Google search, I came across several blogs and websites claiming that mass-produced dice such as those made by GW or Chessex can be irregular enough to produce skewed results. This is particularly true of the d20s that various RPGs use. Many of these unbalanced dice will tend to produce huge numbers of opposites; a die that produces too many ones or twos can often produce too many fives and sixes as well. I soon realized that my initial tests were worthless; an unbalanced die that favors mostly ones and sixes will tend to have an average roll of 3.5. As a Space Marine player who usually needs only 3+ and 4+ to do what I want, I don't want dice that will produce an unusual number of fives and sixes (which are overkill) but also give me a ton of ones and twos (which represent failed armor saves and missed shots). Instead of making the expected 66.7% of my armor saves or to hit rolls, extremely skewed dice could give me an armor save and to hit rate of nearly 50%.

I eventually came across this D&D blog, which described using a Pearson's chi-square test to validate whether or not a d6 or a d20 is fair. This test has the advantage of detecting when individual numbers come up too often or not often enough rather than depending on averaging results. The equation for a d6 is:

Σ[(O-E)^2/E] > 11.070

Where "O" is observed frequency and "E" is expected frequency. The value of 11.070 is the chi-square value for a system with five degrees of freedom; i.e., the number of possible results (six for a d6) minus 1. The equation essentially says that if the result of the equation is greater than the chi-square value, then the claim that the die is fair is probably false.

To use this equation you roll a die a certain number of times and record how many times each side shows up. For each of the six possible die results, you subtract the expected frequency that the side should appear from the observed number of times that the side actually showed up. You divide that value by the expected frequency and then add up the resulting numbers from each of the six possible results. If the sum is greater than 11.070, it is statistically probable that the die is not fair. Although 30 rolls (with an expected frequency of 5 hits for each side) is considered to be a minimum, the same D&D blog noted that a 30 roll test is likely to miss slightly unbalanced dice. A better test would use more than 100 rolls per die.

I decided to apply this test to my own dice and started by placing them in a grid and assigning each die a letter and number designation from A1 to F6. I'm crazy, but not crazy enough to roll all 36 of my dice over 100 times, so I started with just 30 rolls per die. I put the data into a spreadsheet that executed the equation and also calculated how often the die gave a result of 2+ (e.g., a Terminator armor save, the usual value needed to kill infantry with anti-tank weapons), of 3+ (e.g., a power armor save, the value needed for a Marine to hit), and of 4+ (e.g., a Scout armor save, the value to wound with most sniper weapons). I used the conditional formatting feature to automatically color code results that I thought were suspicious. After crunching the numbers, I found that none of my dice failed after only 30 rolls, but that several were close. The blog's warning about a 30 roll test being insufficient became apparent when one die failed to roll a single 1 but was still able to pass the test (although just barely).

Those dice that were close to failing or that I found suspicious (18 out of the 36) were given an additional 60 rolls (90 total rolls with an expected frequency of 15 hits per side). The additional results showed that a few of the 18 dice merely had a bad series of rolls earlier and that they were relatively well balanced. However, four dice outright failed the chi-square test. The worst offender would roll a one more than a quarter of the time (27.78%) and would make a 3+ armor save only 53.33% of the time versus the expected 66.67%. Another die would only roll a 4+ 33.33% of the time rather than the expected 50%. Of the four failures, only one rolled unusually high.

I would call this one "The Widowmaker" if Astartes had widows

Some would call this one "lucky". I retired it, too.

After more than 2,000 individual dice rolls, I decided to "retire" the four failed dice as well as five others that gave results greater than 6 (a little more than half of the chi-square value). And yes, I also removed the high rolling die, which had the second highest degree of bias. In short, I removed 1/4 of all my dice from my set based on this test. Fortunately I play Space Marines, so I don't really need all 36 dice anyway. Oddly enough, I can't bring myself to throw out the biased dice. They're segregated in their own little Ziploc bag labeled with dire warnings.

I would recommend the above test for any player who thinks his dice are giving him a raw deal. I was somewhat relieved to find that, although a lot of my bad luck may be a matter of perception, a significant amount of it may be due to biased dice. And if your dice don't turn out to be biased, then at least you have mathematical proof that it's all in your head.

I guess the question is, what can a tabletop gamer do about the problem? There are a variety of dice companies that promise balanced dice, but they charge as much for five dice as Chessex does for 36. Plus, Chessex sells a greater variety of colors and styles that are great for those players who want to match their dice to their army. I've simply decided to order a second box of Chessex dice (blue and white to match Ultramarine veterans) with the intention of performing another set of chi-square tests to weed out the biased ones. The test takes me about as long to finish as two long games of 40K. If that saves me from any more dice-sabotaged games, then it was worth it.

Space Marine Stormtalon

So Games Workshop finally released some of the flyers they've been promising for quite a while. I love the design of the Ork flyer; it looks like an Orky Korean War-era fighter. The new Necron vehicle, on the other hand, could be called the "Doom Croissant" (not my joke, I'm not that clever). Obviously, the flyer I'm most interested in is the Space Marine Stormtalon Gunship. I've already seen a lot of hatred directed towards its design, but I actually like it quite a bit. I admit that the chin turret with the twin-linked assault cannon looks a bit oversized, but the Imperium in general, and the Space Marines in particular, aren't known for their subtlety.

Stormtalon with twin-linked lascannon

I was originally concerned that the Stormtalon would take up a Heavy Support slot. The leaked sketches of the gunship showed that it has some significant weaponry, but if I had to choose between bringing the Stormtalon and taking a Predator, Land Raider, or Vindicator, the new flyer would be out of luck. However, once a few clear photos of the model were leaked, it became obvious to the eagle-eyed that the crossed double-headed arrows on its hull and wings meant that it was destined for a Fast Attack slot. Photos of the June White Dwarf pages that list the rules for the gunship have confirmed this.

The base points value is 130, for which you get a twin-linked assault cannon and a twin-linked heavy bolter. You also get the Aerial Assault rule (you can fire all weapons even if you moved at cruising speed) and the Supersonic rule (you can move 36" when moving flat out). This non-upgraded arrangement makes the Stormtalon a glorified Tornado-pattern Land Speeder, which can have a heavy bolter and an assault cannon in a slightly slower and less armored chassis for 90 points. I really can't see myself fielding a standard Stormtalon, but the upgrades make the gunship more attractive. For 20 points the twin-linked heavy bolter can be exchanged for a twin-linked lascannon (I wish it was that cheap to upgrade a Razorback). For 25 points the heavy bolter can be upgraded to a Typhoon Missile launcher or the new Skyhammer Missile launcher (strength 7, AP 4, heavy 3). Although the new missile's strength and AP are inferior to those of Krak missiles, the new launcher gives you more shots with missiles that have a range of 60". At that distance only the Imperial Guard and the Tau could possibly reach you.

Stormtalon with Skyhammer Missile launcher

My only worry about this vehicle is that it's heavily armed but only has armor 11. The best description for this arrangement would be "fire magnet". While the Skyhammer Missile launcher might be able to keep your vehicle out of range of most enemies, it could take a long time for three strength 7 shots per turn to pay for your shiny 155 point flyer. However, I'm banking on the Escort Craft rule to make the Stormtalon worth it. This rule allows the gunship to be assigned to a unit that is arriving from reserve. When the reserved unit arrives, the Stormtalon automatically arrives within a short distance. Unfortunately, early assumptions that it could escort deep striking units were premature; the White Dwarf rules specifically prohibit it. Now, if the gunship were to escort an outflanking unit, then your opponent could find quite a mean little force suddenly appearing much too close to his own lines. The Stormtalon may last only one turn, but it could end up being one very effective turn.

I've started to incorporate the Stormtalon into a few theoretical army lists, particularly those that make use of outflanking units. The most effective arrangement I can think of involves Captain Sicarius, a Stormtalon gunship, a Razorback, and the close-combat oriented half of a Tactical Squad that's been divided into combat squads. With Captain Sicarius' Battle-forged Heroes rule, the Tactical Squad can be given the Scout or Infiltrate special rules. With one or the other rule, the Squad is allowed to outflank. Since the Razorback is a dedicated transport, it can also be part of the outflanking maneuver as long as the Squad is embarked in it at the time. Thanks to the Escort Craft rule, when this outflanking Razorback arrives with twin-linked heavy bolter or lascannon blazing (and containing a Space Marine captain with artificer armor, feel no pain, and a plasma pistol, as well as five power armored Marines with various weapons intended to breach armor and wreak havoc), the Stormtalon will also appear with its own twin-linked assault cannon and twin-linked heavy bolter, twin-linked lascannon, Typhoon Missile launcher, or Skyhammer Missile launcher blasting away.

Of course, you'd have to hope that the tactic is immediately successful; the following turn is likely to see a downed Stormtalon and/or a burned-out Razorback.

40K Cabal Tournament

During our previous game night, Bryce, Carl, Jon, and I played a four way free for all that lasted for four or five hours. Although we all had fun, by the end we were completely exhausted. Of course Bryce, who has played 40K since he was young, is the fastest player in the group. Hoping to improve our speed, Bryce set up a mini-tournament for the Cabal this past week. It consisted of three games organized as follows:

Game 1: A 500 point army with at least one unit of Troops and one of Elites.
Game 2: A 750 point army with at least one HQ, one unit of Troops, and one of Elites.
Game 3: A 1000 point army that meets standard force organization requirements.

We were allotted only 15 minutes to set up (this is a lot less time than us newbies usually take). The 500 point and the 750 point games were limited to one hour each while the 1000 point game was allowed to go for an hour and a half. To provide a variety of settings, Bryce pre-arranged scenery on the group's 4'x4' table and on the two sides of our 4'x8' table, which had been partitioned into two playing areas.

In the past we've tailored our armies for a known opponent, usually producing our final list only after arriving at Bryce's house. This time he required Kevin, Carl, Jon, and I to design our lists in a vacuum and submit them before the competition. As usual, Kevin was to play his Dark Eldar, Jon was going to play his Orks, and I brought my Ultramarines. Carl, who usually plays Grey Knights, decided to play the Cabal's Daemon army this time around. Bryce served as moderator and judge.

Game One (500 points):
Bryce assigned the Orks and the Ultramarines to one table and the Dark Eldar and the Daemons to another. I didn't follow the Dark Eldar/Daemon game at all, but I know that the Daemons won handily. The Soul Grinder that Carl was generous enough to add to the army proved to be unstoppable. It's hard to match that monster's front and side armor of 13, an immunity to stunned and shaken results, and its immensely powerful array of ranged and close combat weapons.

As for the Ultramarines/Orks game, as can be expected for a 500 point match-up, Jon's army vastly outnumbered mine and had a lot more variety. In my opening move, I tried to hit Jon's Lootas with my Vindicator and came up one inch short. The 10 man Tactical Squad was too far away to hit anything and my five Sniper Scouts rolled very poorly. My only hope was to send my multi-melta Dreadnought into his mob and attempt to tie it up for a few turns.

Unfortunately, one of Jon's Killa Kans hit the Vindicator's side armor and destroyed over 1/5th of my entire army with a single shot. The Lootas wiped out the Scouts in a single salvo (not a single one made its cover save) while an Ork mob charged towards the remainder of my rapidly dwindling army. Although my Dreadnought was able to engage the mob, it was destroyed within a couple turns by a power klaw.

In yet another run of fantastically bad luck, I consistently rolled ones and twos for both shooting as well as armor saves. An army with only one tank, a walker, 10 Marines, and 5 Scouts can't tolerate too many rolls like the ones I was making; my army was wiped out halfway into our allotted time.

Game Two (750 points):
The second game matched up the Ultramarines with the Dark Eldar and the Orks with the Daemons. Although I saw little of the Ork/Daemon game, I know that the Soul Grinder again did its job. Additionally, Carl's luck with rolling was the polar opposite of my own. Fives and sixes turned up a little too often for the Daemons, with at least one roll of four dice resulting in nothing but fives or better. And thus the denizens of the Warp consumed the Green Horde.

...and the Greenskins were messily devoured

My 750 point list was somewhat experimental in that I forewent the Tactical Squad and used a Telion-led six man Scout Squad as my sole unit of Troops. I then spent much of my points on a seven man Sternguard Squad with two missile launchers. Since my Tyrannic War Veteran-themed Sternguard isn't quite ready yet, I proxied seven standard Marines for a Sternguard Squad. (Yes, I know that the only visible difference between Sternguard Marines with bolters and Tactical Marines with bolters are the white helmets, but I try to keep my army strictly WYSIWYG.) Also in the army was a Venerable Dreadnought with an assault cannon, a Vindicator, and a Captain.

As usual, Kevin embarked all his forces into several Venoms and a Raider. Hoping to take advantage of his night shields, which take 6" off an opponent's range, he placed all his vehicles into a far corner of the table. While this temporarily hampered the Venerable and the Vindicator, it couldn't save him from the Sternguard's two missile launchers or the Scouts' missile launcher that benefited from Telion's ballistic skill. Fortunately for me, the Emperor chose to smile on the Ultramarines during this game (or, at least he thwarted Tzeentch and allowed them to roll averages), and the Dark Eldar skimmers started coming down. Although Kevin's Venoms made an amazing number of 5+ flickerfield saves, they couldn't keep up with the number of Krak missiles that hammered them throughout the game.

The embarked Dark Eldar and their vehicles could put out an considerable number of shots, but most of the Marines were actually able to make their saves. My Scouts, on the other hand, again had the misfortune of failing a huge number of 3+ cover saves (I really don't know why this happens so often). Although the Vindicator was eventually destroyed, it didn't go down before landing its strength 10 AP 2 pie plate on an unfortunate group of Dark Eldar who had been spilled from their vehicle. Despite the effect of the Wyches' shardnets, the Captain was also able to whittle down the number of forcibly disembarked Dark Eldar.

Being a Space Marine captain means going into battle in style

Eventually, the Venerable Dreadnought got within range of the Venoms and threatened to do some serious damage with its assault cannon. A lucky blaster shot penetrated its armor and Kevin triumphantly announced a "vehicle destroyed" result. However, Kevin got to know the pain of fighting a Venerable Dreadnought when I said (with as kind a smile as I could muster) "Venerable rule: re-roll the damage result". The "vehicle stunned" result he rolled definitely wasn't what he wanted, especially when a missile stunned his Venom and its blaster-wielding crew in my following turn. The last of the Venoms went down to the Venerable's assault cannon while the remaining Dark Eldar were unequipped to fight a walker. The Ultramarines scored a narrow victory with a Venerable Dreadnought and two Sternguard Marines left standing.

It was during the 750 point game that Bryce held the painting competition, which was judged by his wife. Since we're still fairly new, we were judged on a best figure rather than best army. Kevin entered one of his Wyches, Jon entered a Nob, and I entered Sergeant Telion. The Daemon army wasn't eligible since it was originally painted by an eBay seller and was finished up by Bryce. It turned out that Jon had unknowingly stacked the deck; he paints a bloody wolf paw print on the back of each of his Orks and Bryce's wife is a dog lover.

Sadly, Telion also lost the swimsuit competition

Game Three (1000 points):
We finished out the night with an Ork/Dark Eldar match and an Ultramarines/Daemons competition, both of which were played on the partitioned 4'x8' table. Once again, I was so involved in my own game that I didn't see the results of the game happening immediately to my left. Although neither army was able to annihilate the other within the allotted hour and a half, the Orks finished with the most points left.

Unfortunately, Carl's amazing luck continued while the luck I had during the 500 point game came back to haunt me. Let's just say that five Sternguard firing wound-anything-on-a-2+ Hellfire rounds can't do much good when three of the five miss the shot while their opponents are consistently able to make their 5+ saves.

The Vindicator was actually able to damage the Soul Grinder, disabling the walker's primary weapon, but that didn't eliminate the walker's ability to assault the tank. An attempt to prevent the Soul Grinder from destroying the Vindicator by deep striking my Terminator Squad behind it backfired when the only damage result I could roll was "stunned" (a.k.a., "ignored") and the squad was quickly engaged by Pink Horrors. After the daemonic machine had dispatched the Vindicator, it joined in the fight with the Terminators, whose rolls to hit were plagued by ones and twos.

I soiled my armor I was so scared!

On the other side of the table, a unit of Daemonettes and a Daemon Prince deep struck a short distance from my Tactical Squad and Sternguard. With time for only one turn of shooting between their appearance and their assault, I really couldn't afford all the ones and twos that I was rolling. The Marines were quickly overwhelmed.

They're tougher than they look

A couple feet away from the Tactical Squad, my Sniper Scout Squad found itself under attack by three Flamers of Tzeentch. Three of the Scouts survived the initial attack and returned fire, to little effect. This was one of the worst tactical decisions I made that night. Flamers of Tzeentch have an amazing shooting ability, but aren't particularly adept at close combat. I choose to have my Scouts fire their sniper rifles at them rather than to fire their pistols and assault them. The return fire did very little and allowed the daemons to kill two more Scouts. By the time I got into close combat, I had too few attacks to do anything.

After having previously snacked on Dark Eldar and Orks, the Daemons finished the night with 1000 points worth of canned Space Marine.

Conclusion
At the end Bryce handed out the awards: Best General, Most Valuable Model, Best Painted Figure, and Best Sport. Best General obviously went to Carl and the Daemon army for handily defeating all comers. Most Valuable Model went to Kevin's Venoms, which made an unlikely number of 5+ flickerfield saves in all three of his games. Best Painted Figure went to Jon's Nob with the bloody paw print. And Best Sport went to myself for not throwing things despite having the most appalling luck.

Ultramarines Blue vs. Altdorf Guard Blue

I was recently requested to compare Ultramarines Blue to the new Altdorf Guard Blue. To do this I simply pulled out an extra Rhino top hatch bit leftover from my Vindicator and painted the two colors side by side. Since this was a quick comparison, I didn't undercoat the hatch and I laid the paint down pretty thickly. This left quite a few brush strokes, especially in the Altdorf Guard Blue. Here are the results:

Left: Ultramarines Blue. Right: Altdorf Guard Blue

Ultramarines Blue is on the left and Altdorf Guard Blue is on the right. At the top of the hatch I painted a small streak of Altdorf into the Ultramarines and at the bottom I painted a small streak of Ultramarines into the Altdorf.

The Altdorf appears to be slightly darker, but It's similar enough that I doubt I could easily tell the difference between a model painted with Ultramarines Blue and a model painted with Altdorf Guard Blue, especially if a generous wash were used. The most noticeable difference is that Altdorf is most definitely a "layer" paint. The Ultramarines Blue covered the gray plastic with only two or three coats. The Altdorf Guard Blue, on the other hand, required four or five coats before it completely covered the gray. Altdorf should probably be painted over a blue base coat for best results.

For my Ultramarines I've primarily used Mordian Blue for the power armor and reserved Ultramarines Blue for highlighting. However, I use Ultramarines Blue on my vehicles so they contrast slightly with the Marines. Given how much Altdorf Guard Blue was needed to cover a color other than blue, I'll definitely be priming my vehicles with Army Painter's Ultramarine Blue spray rather than a black or gray undercoat.