Sunday, July 15, 2012

Munitorum Dice Redeemed (Mostly)

I said recently that I removed six of the twelve limited edition red Munitorum dice from my collection. This afternoon, as I was about to mark the dice to designate them as marker dice only, I decided to chi-square test them one more time before defacing them.

The more you roll the dice, the more likely you are to find a truly imbalanced die. As I said before, not a single Munitorum die had failed after 120 rolls (unlike several of my Chessex dice, which failed within 90 rolls), but several almost failed and a few seemed suspicious. I knew I would feel better if the dice had genuinely failed, so I decided to increase the number of rolls to see if they would fail.

The first die I tested was rolled 210 times; 75% more times than the first test. Lo and behold, not only did the die not fail, but it tested with a chi-square value of a mere 0.74 (0 is perfectly balanced and 11.07 means that it's statistically probable that the die is imbalanced). I calculated the P-value as being 98.1% or, in other words, that 98.1% of all balanced dice would give results that deviated from the theoretical value more than that particular die. Finding that a die I had removed from my collection was actually one of the most balanced ones started a spree of re-testing.

I gave the second die 300 rolls in an attempt to make it fail. Although its chi-square value was relatively high compared to that of other dice I've kept, I had more confidence that the apparent imbalance really could be a coincidence.

The third and fourth dice received 510 and 600 rolls respectively (I was really trying to see if those two would fail). According to the blog that first gave me the idea to test my dice, a test of 500 rolls has a nearly 100% chance of detecting an imbalanced die. Although the two dice tended to roll ones and twos a bit more than I'd like, the fact that neither actually failed the test indicated that they are at least mostly balanced.

The fifth die was rolled 300 times. Its chi-square value was low enough that I decided to stop.

It was the sixth die that was the odd one. After showing that five out of the six dice I had rejected as imbalanced were actually fine and just needed a significant number of rolls to prove it, I figured that the sixth one would be just like its companions. It took 510 rolls to do it, but the sixth die actually failed the test. For whatever reason, four showed up 114 times versus the expected 85. Contrary to every obsessive compulsive instinct in my brain, I decided to keep the die. The four seemed to show up to the detriment of the three and the five which, for a Marine player, usually makes little difference.

The best part of this is that I have more confidence that the soon to be released black and white Munitorum dice will be properly balanced.

[Update 7/29/12: Tonight's game using the full set of 12 Munitorum dice went very well. The dice seemed to roll fairly and even made a few memorable snap shots. I very nearly damaged/brought down a Voidraven Bomber with a plasma pistol shot, but the penetration roll was just short of glancing the armor.]

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