CHESSEX block dice fairness test

 The dice of Zeus always fall luckily. Sophocles

In this, the second test of Blood Bowl dice, I used CHESSEX block dice and again rolled them 1000 times.

I again decided to set the measure of statistical significance
again at 5% (p-value >= 0.05). That would mean that the actual dice outcomes would have to deviate by 5% or more from the expected outcomes for the test to indicate a potential problem. I figured 5% over 1000 rolls should be safe enough. 



Test results:

Outcomes	Total	Expected	% diff
Pow	179	166.67	7.40
Pow!	155	166.67	-7.00
Skull	174	166.67	4.40
Pow/Skull	165	166.67	-1.00
Push	327	333.33	-1.90
Check	1000	1000	0.00

Conclusions

The dice finished outside the 5% threshold for both Pow and Pow! and so from this test, I have to highlight a potential issues as to the fairness of the CHESSEX block dice. More specifically, teams heavy in the DODGE skill could have problems due to the higher than normal occurrence of Pow and lower than normal occurrence of Pow!

As for the test itself, rolling more dice would, as always, provide a greater degree of certainty, so the results would be safer after 10,000 or even 100,000 rolls. Also, any study could provide a set of fluke results and so these outcomes would need repeating in a second test for significance to be assured.

NAF block dice fairness test

The dice of Zeus always fall luckily. Sophocles

Dice are funny things. If you play games a lot, especially wargames, you get use to how fickle they can be. In Blood Bowl, "Nuffle" the god of luck, has cost me more game than I care to remember by punishing me for daring to roll dice. Some people have mad rituals around dice and how they roll them, change them after they roll low, blow on them for luck etc. For me a dice is a random implement and so superstition has no place at my table. I do though, often wonder, if any dice are truly random, especially custom dice.


So I decided to test a set of NAF Blood Bowl dice by rolling them a thousand times and seeing how far they deviated from what would be expected by randomness.


A simple test but one that should highlight any potential problems with the fairness of the dice.


I decided to set the measure of statistical significance
at 5% (p-value >= 0.05). That would mean that the actual dice outcomes would have to deviate by 5% or more from the expected outcomes for the test to indicate a potential problem. I figured 5% over 1000 rolls should be safe enough. 


Test results

Outcomes	Total	Expected	% diff
Pow	171	166.67	2.60
Pow!	160	166.67	-4.00
Skull	162	166.67	-2.80
Pow/Skull	163	166.67	-2.20
Push	344	333.33	3.20
Check	1000	1000	0.00

Conclusions

The dice all stayed within the 5% threshhold and so from this test, I am pretty sure, the NAF Blood Bowl block dice are safe to use.

Rolling more dice would provide a greater degree of certanty, so the results would be safer after 10,000 or even 100,000 rolls but even at 1,000 the results seem pretty sound to me.

Blood Bowl Zombie vs Skeleton resilience comparison

....it ain't about how hard you hit, it is about how hard you can get hit and keep moving forward, how much can you take and keep moving forward. That's how winning is done! Rocky Balboa (2006)
 

I was talking to Lycos at the Chelmsford Bunker Bowl in October 2011 and we got to discussing the undead team, in particular my loathing of the over-costed Skeletons. They used to cost 30K but recently (in Blood Bowl terms) moved to 40K for the addition of "Thick-Skull".


So Lycos, NAF president and all round good guy (he got my vote again this year), said that he always takes at-least one Skeleton in his Undead team. He explained that he took them mainly for the increased movement but also because they are just as resilient as a Zombie due to the "Thick-Skull" skill.


I, on the other hand am a Zombie guy, sure he is only movement 4, but he is a top drawer meat shield and foul bot. I personally never go near Skeletons unless I am playing Khemri.


So I thought I would have a quick scan over the numbers and see what comes out.


The challengers

1. Skeleton AV7 with Thick-Skull
2. Zombie AV8 

Percentage chance of breaking armour for each

1. Skeleton 41.67%
2. Zombie 27.78%

 Percentage chance of getting a KO of better for each

1. Skeleton 11.58%
2. Zombie 11.58%

 Percentage chance of getting a injury for each

1. Skeleton 6.95%
2. Zombie 4.63%

So the conclusion is, that if you are looking at the narrow band of getting a KO or better then the Zombie and Skeleton come out identical. However, in regards to both Stunned and Casualty results, the Skeleton is 50% more likely to be on the receiving end than the Zombie. Is that increased Stunned and Casuality rate worth the trade for the increased movement value? Not in my books, but then I have won exactly zero NAF tournaments and Lycos has a houses full of trophies.