The problem is that your sample size is too small. You are only looking at your own dice rolls, thinking that they are a closed set. They are not. They are tied into a larger dice sampling pool, that may very well, when examined in the aggregate, comply nicely with statistical probability.
Also, are you paying attention to how often you win the dice rolls? Often we only pay attention to the pain points.
Even if you play 50 game rounds a day, with maybe 10 dice rolls per round, that's only 500 dice rolls of what has to be millions of dice rolls per day. Since your rolls are not isolated, it's hard to determine a global set statistic based upon such a small and very localized sample size.
Ironically, this is very close to how political polls are done, and how they can often be wildly off target.
Also, if you really want to examine the results, you have to ignore "battle results", and only focus on "dice rolls" The dice roll engine will not be aware of situational issues, such as "3x1". The backend system simply will respond to a need for 4 dice rolls, and will generate and deliver 4 dice rolls. They would then be read and placed in order to determine result. The dice roll system is also unaware of the environmental factors that determine a "win" or "loss".
I found an interesting article at
This Link that basically re-creates your complaint, but with the PSX version of Risk from Hasbro.
Calculated Probability
[spoiler=Probability]Attacker: one die; Defender: one die:
Attacker wins 15 out of 36 (41.67 %)
Defender wins 21 out of 36 (58.33 %)
Attacker: two dice; Defender: one die:
Attacker wins 125 out of 216 (57.87 %)
Defender wins 91 out of 216 (42.13 %)
Attacker: three dice; Defender: one die:
Attacker wins 855 out of 1296 (65.97 %)
Defender wins 441 out of 1296 (34.03 %)
Attacker: one die; Defender: two dice:
Attacker wins 55 out of 216 (25.46 %)
Defender wins 161 out of 216 (74.54 %)
Attacker: two dice; Defender: two dice:
Attacker wins both: 295 out of 1296 (22.76 %)
Defender wins both: 581 out of 1296 (44.83 %)
Both win one: 420 out of 1296 (32.41 %)
Attacker: three dice; Defender: two dice:
Attacker wins both: 2890 out of 7776 (37.17 %)
Defender wins both: 2275 out of 7776 (29.26 %)
Both win one: 2611 out of 7776 (33.58 %)[/spoiler]
Conclusion: heads up with three dice versus 2 dice, the attacker has an advantage in the long run. Similar interpretations can be made for the remainder of the data, which can be summarized as follows:
* Attacker 1 versus defender 1: defender has the advantage, winning about 4 out of 7 battles
* Attacker 2 versus defender 1: attacker has the advantage, winning about 4 out of 7 battles
* Attacker 3 versus defender 1: attacker has the advantage, winning about 2 out of 3 battles
* Attacker 1 versus defender 2: defender has the advantage, winning about 3 out of 4 battles
* Attacker 2 versus defender 2: defender has the advantage, winning about 3 out of 5 battles
* Attacker 3 versus defender 2: attacker has the advantage, but the advantage is much more narrow than any of the battles described above. The attacker's advantage is such that he will win about 7 out of 13 battles on average.Now his main result of the argument was there may be a bug in the RNG code for the Hasbro PSX version. My only two comments with regards to CC is this: 1) random.org's RNG code is likely superior and 2) playing local on a PSX has a order of magnitude smaller number of entities in the set than what is being generated here.
So, even though 3x1 should net 2 out of 3 wins, it won't necessarily relate to the statistically small number of times you execute it. Someone else might be getting 3x1 wins like crazy.
A single player can not likely generate a statistically relevant set size to sample from. you would have to be playing 1000's of game rounds a day. You would also have to be collecting all of the dice roll statistics perfectly.
Sometimes it's just Poker.
The true task, IMHO, is taking into account how the system works, and playing on a macro level with much more precision, not relying on luck rolls. You will get beat, but if you average over time too gameplay, it will result in a higher than average win rate.