So far, after 4500 rolls, some stats are in...

[WestWind]

Well I figured I shouldn't start criticizing dice unless I at least gather some data first, so here's the first round of comparisons.

Attacking average roll- 3.4727
Defending average roll- 3.5326

3v2 Battle Outcomes
Expected W/T/L %: 37.17/33.58/29.26
Actual W/T/L %: 34.88/33.33/31.78

3v1 Battle Outcomes
Expected W/L %: 65.97/ 34.03
Actual W/L %: 65.86 / 34.14

The other roll types don't have enough data because I'm not crazy enough to try them very often.

Now, the attacking/defending average rolls aren't that far apart, so I'm not going to say the rolling is skewed. However, the 4.8% gap in the 3v2 outcomes is kind of alarming. I'm not quite sure if it's a significant difference at this point, but I would venture to say that it's had at least a noticeable effect so far. It's nice to see the 3v1 outcomes are hovering about where they should be, especially after all the "OMG I LOST 7 TROOPS TO 1 GUY" threads.

This is by no means a comprehensive evaluation of the random battle system. 4500 rolls, while a decent size, is nowhere close to a large sample size...this is more just a brief look at the raw data.

Anyways, just wanted to publicize the rolls of one humble CC player. At the moment, it seems like I'm having less than good luck, but once I get more data we'll see what happens

[phantomzero]

Very interesting. How did you collect the data?

[WestWind]

I've just been using the Dice Analyzer...if there's better programs out there for this I'm not sure what they are..

[BrutalBob]

You know what would be interesting would be a script that logged rolls for all players in a game and then reveals them at the end.

[MeDeFe]

Where's a 4.8% gap?

[natty dread]

You know what would be interesting would be a script that logged rolls for all players in a game and then reveals them at the end.

Then all players in the game would need to use the script.

[WestWind]

Where's a 4.8% gap?

Basically, I should win 7.91% more 3v2 battles than I lose. At the moment, I'm only winning 3.1% more. 7.91 - 3.1 is about a 4.8% gap between what I should be winning and what I actually am winning. If this is bad statistics I apologize, since I'm not exactly a statistician.

[ljex]

Actual Stats Ideal Stats
3v2 859 / 808 / 644 (37.17% / 34.96% / 27.87%) (37.17% / 33.58% / 29.26%)
3v11 880 / 996 (65.37% / 34.63%) (65.97% / 34.03%)
2v2 15 / 15 / 28 (25.86% / 25.86% / 48.28%) (22.76% / 32.41% / 44.83%)
2v1 146 / 115 (55.94% / 44.06%) (57.87% / 42.13%)
1v2 7 / 16 (30.43% / 69.57%) (25.46% / 74.54%)
1v1 75 / 97 (43.6% / 56.4%) (41.67% / 58.33%)

These are my dice after 16394 rolls.

[MeDeFe]

Where's a 4.8% gap?

Basically, I should win 7.91% more 3v2 battles than I lose. At the moment, I'm only winning 3.1% more. 7.91 - 3.1 is about a 4.8% gap between what I should be winning and what I actually am winning. If this is bad statistics I apologize, since I'm not exactly a statistician.

Ah, I see, you're talking about percentage points. You've actually won (2-0) closer to 6.2% fewer 3vs2 than could be expected and lost (0-2) 8.6% more.

How many 3vs2 rolls have you recorded?

[WestWind]

Where's a 4.8% gap?

Basically, I should win 7.91% more 3v2 battles than I lose. At the moment, I'm only winning 3.1% more. 7.91 - 3.1 is about a 4.8% gap between what I should be winning and what I actually am winning. If this is bad statistics I apologize, since I'm not exactly a statistician.

Ah, I see, you're talking about percentage points. You've actually won (2-0) closer to 6.2% fewer 3vs2 than could be expected and lost (0-2) 8.6% more.

How many 3vs2 rolls have you recorded?

Yikes, that makes it sound even worse. I've only recorded 516 total battles...if there's 5 rolls for each battle, that puts it at 2580 rolls. Like I said, it's not a massive sample, so I think a little bit of shift is expected...maybe not to this degree though.

[alster]

Attacking average roll- 3.4727
Defending average roll- 3.5326

Well - dice average roll is the only thing that matters here if measuring whether the dice are random or not. The game engine draws the dice externally, I assume that each dice is drawn independently (i.e. 5 draws per roll). The battle outcomes are just given depending on the "random" dice draw. Now, you tell us that average attacking/defending dice pretty much hoovers around 3.5 having made 4,500 rolls (guess no of individual dice having been rolled then would be around 19-20,000), so that looks pretty much along what one would expect of an average, individual dice over time.

[WestWind]

Attacking average roll- 3.4727
Defending average roll- 3.5326

Well - dice average roll is the only thing that matters here if measuring whether the dice are random or not. The game engine draws the dice externally, I assume that each dice is drawn independently (i.e. 5 draws per roll). The battle outcomes are just given depending on the "random" dice draw. Now, you tell us that average attacking/defending dice pretty much hoovers around 3.5 having made 4,500 rolls (guess no of individual dice having been rolled then would be around 19-20,000), so that looks pretty much along what one would expect of an average, individual dice over time.

True, but I think what a lot of players have contention with is the fact that, even though the dice average out to be random, they are not distributed in a random manner. Theoretically, if all the dice were distributed randomly, they should follow the basic W/T/L percentages. I think some players think that the dice are often "linked" into streaks.

[MeDeFe]

Where's a 4.8% gap?

Basically, I should win 7.91% more 3v2 battles than I lose. At the moment, I'm only winning 3.1% more. 7.91 - 3.1 is about a 4.8% gap between what I should be winning and what I actually am winning. If this is bad statistics I apologize, since I'm not exactly a statistician.

Ah, I see, you're talking about percentage points. You've actually won (2-0) closer to 6.2% fewer 3vs2 than could be expected and lost (0-2) 8.6% more.

How many 3vs2 rolls have you recorded?

Yikes, that makes it sound even worse. I've only recorded 516 total battles...if there's 5 rolls for each battle, that puts it at 2580 rolls. Like I said, it's not a massive sample, so I think a little bit of shift is expected...maybe not to this degree though.

By "battles", do you mean "number of times you attacked a territory"?

Because 516 really isn't that much then, not at all, especially not if those 516 include the 3vs1s.

[WestWind]

Oops, thought you meant only 3v2 battles. Overall there's been 970 battles. Anyways, looks like once I hit ~16k rolls everything should turn out fine

[MeDeFe]

Oops, thought you meant only 3v2 battles. Overall there's been 970 battles. Anyways, looks like once I hit ~16k rolls everything should turn out fine

ok, but 516 rolls of 3vs2 still isn't very much. Being off by 8.6% means you have lost 13 times more often than the statistic average predicts.

13 times.

That's nothing.

[Georgerx7di]

Where's a 4.8% gap?

Basically, I should win 7.91% more 3v2 battles than I lose. At the moment, I'm only winning 3.1% more. 7.91 - 3.1 is about a 4.8% gap between what I should be winning and what I actually am winning. If this is bad statistics I apologize, since I'm not exactly a statistician.

meh, when you word it that way it exaggerates the difference. You're supposed to win 37%, you actually win 35%. Come on, let's not bend the truth. The real difference is 2% (2.3% but I didn't feel like typing all the sig figs).

Anyway, I would expect the numbers to slowly get closer to the expected as the number of rolls goes up. I suppose anyone would for that matter.

[isaiah40]

Here's mine after 3661 dice rolled. Defender threw 1893
Actual Ideal
3v2 (37.68% / 31.8% / 30.52%) (37.17% / 33.58% / 29.26%)
3v1 (65.47% / 34.53%) (65.97% / 34.03%)
2v2 (22.22% / 66.67% / 11.11%) (22.76% / 32.41% / 44.83%)
2v1 (63.64% / 36.36%) (57.87% / 42.13%)
1v2 (33.33% / 66.67%) (25.46% / 74.54%)
1v1 (56.25% / 43.75%) (41.67% / 58.33%)

I also included the tie's as well.

[Fruitcake]

I have been keeping mine for some time now...and they do ultimately start to settle....kind of

Attack dice distribution - Defender dice distribution
1s 55607 329854 (16.86%) - 29366 176488 (16.64)
2s 55559 329854 (16.84%) - 29351 176488 (16.63)
3s 54816 329854 (16.62%) - 29209 176488 (16.55)
4s 54408 329854 (16.49%) - 29353 176488 (16.63)
5s 54720 329854 (16.59%) - 29800 176488 (16.89)
6s 54744 329854 (16.60%) - 29409 176488 (16.66)

In the early days (when the situation caused me to tear my hair out) the stats were far worse.

Attack dice distribution - Defender dice distribution
1s 5178 / 28220 (18.35%) - 2151 / 13378 (16.08%)
2s 4704 / 28220 (16.67%) - 2178 / 13378 (16.28%)
3s 4806 / 28220 (17.03%) - 2218 / 13378 (16.58%)
4s 4558 / 28220 (16.15%) - 2198 / 13378 (16.43%)
5s 4538 / 28220 (16.08%) - 2245 / 13378 (16.78%)
6s 4436 / 28220 (15.72%) - 2388 / 13378 (17.85%)

e_i_pi (who did an analysis of all this for cc) sent me this info some time back.

Your defence dice are high, the highest there are so far, but they're pulling back in from a few weeks ago. Also, I only have 11 results, and we already knew you were about a 1 in 800 occurrence. That's pulled back to 1 in 100 or so, so the defence results are getting better for you.

I'd be more worried about your attacking dice. Seriously, they are atrocious. I'm aghast that they could be so bad. Mind you, I too have had terrible runs of dice. One run left me 0/19 over a three week period. There was one game where I remember only killing 2-3 enemy armies. I'll be very interested to see what comes of your attacking dice over the next 2-3 months. At the moment, they're ... well ... terrible. I feel for you man, I don't know how you retain Colonel with dice like that. It's results like this though that will be able to tell us in the future if there are problems with the dice.

Uh yeah, I just calculated the chances of your attacking dice being that bad. It's like 1 in 400 billion. Yep, billion, not million. Honestly dude, I feel for you.

As the months went by I got some great dice (which in its own way was really weird) but looking at the numbers above, one can see the % have settled and the legacy of the early, appalling, dice has reduced slowly but surely.

[WestWind]

Where's a 4.8% gap?

Basically, I should win 7.91% more 3v2 battles than I lose. At the moment, I'm only winning 3.1% more. 7.91 - 3.1 is about a 4.8% gap between what I should be winning and what I actually am winning. If this is bad statistics I apologize, since I'm not exactly a statistician.

meh, when you word it that way it exaggerates the difference. You're supposed to win 37%, you actually win 35%. Come on, let's not bend the truth. The real difference is 2% (2.3% but I didn't feel like typing all the sig figs).

Anyway, I would expect the numbers to slowly get closer to the expected as the number of rolls goes up. I suppose anyone would for that matter.

Eh, I'm just wording the way most percentage comparisons are worded. When a president wins a popular vote 55% to 45%, they say he won by 10%, not 6. Anyways, that's just mincing words.

I already said that the amount of data I have is small. Honestly I'm not really complaining about anything....but I wouldn't mind if my "luck" turned and I started winning some more battles

[MeDeFe]

Where's a 4.8% gap?

Basically, I should win 7.91% more 3v2 battles than I lose. At the moment, I'm only winning 3.1% more. 7.91 - 3.1 is about a 4.8% gap between what I should be winning and what I actually am winning. If this is bad statistics I apologize, since I'm not exactly a statistician.

meh, when you word it that way it exaggerates the difference. You're supposed to win 37%, you actually win 35%. Come on, let's not bend the truth. The real difference is 2% (2.3% but I didn't feel like typing all the sig figs).

Anyway, I would expect the numbers to slowly get closer to the expected as the number of rolls goes up. I suppose anyone would for that matter.

Eh, I'm just wording the way most percentage comparisons are worded. When a president wins a popular vote 55% to 45%, they say he won by 10%, not 6. Anyways, that's just mincing words.

I already said that the amount of data I have is small. Honestly I'm not really complaining about anything....but I wouldn't mind if my "luck" turned and I started winning some more battles

I think they say he won by 10 percentage points, or possibly by 10 points. In your example those 10 percentage points translate into a 22% lead, btw, since one candidate got 22% more votes than the other.

In any case, revisit this topic when you have logged 2000 attacks or so and we'll see. 13 out of ~170 is not statistically significant.

[frogger4]

It is interesting how it can be quite skewed with a very small sample. I started using the dice analyzer only last week, so although it is statistically insignificant, my luck the past week in 3v2 has been quite poor: actual (25.53% / 37.59% / 36.88%) Ideal (37.17% / 33.58% / 29.26%). Also, attacker dice average of 3.44 versus defender dice average of 3.66
I will be interested to see how this changes over time

[Mr Changsha]

I have been keeping mine for some time now...and they do ultimately start to settle....kind of

Attack dice distribution - Defender dice distribution
1s 55607 329854 (16.86%) - 29366 176488 (16.64)
2s 55559 329854 (16.84%) - 29351 176488 (16.63)
3s 54816 329854 (16.62%) - 29209 176488 (16.55)
4s 54408 329854 (16.49%) - 29353 176488 (16.63)
5s 54720 329854 (16.59%) - 29800 176488 (16.89)
6s 54744 329854 (16.60%) - 29409 176488 (16.66)

In the early days (when the situation caused me to tear my hair out) the stats were far worse.

Attack dice distribution - Defender dice distribution
1s 5178 / 28220 (18.35%) - 2151 / 13378 (16.08%)
2s 4704 / 28220 (16.67%) - 2178 / 13378 (16.28%)
3s 4806 / 28220 (17.03%) - 2218 / 13378 (16.58%)
4s 4558 / 28220 (16.15%) - 2198 / 13378 (16.43%)
5s 4538 / 28220 (16.08%) - 2245 / 13378 (16.78%)
6s 4436 / 28220 (15.72%) - 2388 / 13378 (17.85%)

e_i_pi (who did an analysis of all this for cc) sent me this info some time back.

Your defence dice are high, the highest there are so far, but they're pulling back in from a few weeks ago. Also, I only have 11 results, and we already knew you were about a 1 in 800 occurrence. That's pulled back to 1 in 100 or so, so the defence results are getting better for you.

I'd be more worried about your attacking dice. Seriously, they are atrocious. I'm aghast that they could be so bad. Mind you, I too have had terrible runs of dice. One run left me 0/19 over a three week period. There was one game where I remember only killing 2-3 enemy armies. I'll be very interested to see what comes of your attacking dice over the next 2-3 months. At the moment, they're ... well ... terrible. I feel for you man, I don't know how you retain Colonel with dice like that. It's results like this though that will be able to tell us in the future if there are problems with the dice.

Uh yeah, I just calculated the chances of your attacking dice being that bad. It's like 1 in 400 billion. Yep, billion, not million. Honestly dude, I feel for you.

As the months went by I got some great dice (which in its own way was really weird) but looking at the numbers above, one can see the % have settled and the legacy of the early, appalling, dice has reduced slowly but surely.

Your attack dice really were atrocious back in the day however I always felt comedically so...and in the end you still held your rank so it enabled you to post them and subtly say "Look how high I WOULD be if..." As I remember one of my first ever posts was needling you about that very thing. Of course now the dice have equalised you are sitting in the top 25.

Yet you are all still considering the dice from the level of the ape. To hit true dice zen one must factor in when we get good dice or not. It is all very well whacking in great dice once a game is already over and you need to roll worse than a chap with no hands attempting to throw with his tongue to lose, the trick is to get great dice on the first 6 on 3, or when you need 35+ on a 190 vs. 200 (+ moving) to gain a tight win. That is when dice matter. One could have ridiculously poor overall stats and still do fine as long as the dice come good at the key moments...both in attack and defence. Hence I don't collect overall stats (for in my mind they are irrelevent as what percentage are basically nothing rolls?) but rather consider my dice at key moments and remember those. Thus I remember the games where the dice lost it for me, I remember the games where they won it for me and I remember the games where they held true (the most usual outcome) give or take a minimal amount.

Therefore I maintain - and have always maintained - that overall dice statistics have bugger all validity. Even while Fc was on his terrible run, to have maintained a high colonel rank playing trips his dice MUST have still come good at key moments...in fact he MUST have been LUCKIER than almost all as his good dice must have come when he just needed it to get the wins required to maintain score. Therefore he was rolling terribly once games were already over (for good or ill) and whacking out the spunky stuff at key moments.

So one can see that in fact Fc is the luckiest player on CC.

No need to thank me for turning you world upside down Fc, for giving you hope, for giving you Obama in the written form...