Dices credibility

[Linho]

Hello all!

I'm really doubting of the dices behaviour.

Every game I play, rare results happens several times, like 11v3 ice, 8v2 ice, 6v1 ice, even an absurd 14v5 ice I got. I'm not saying that it would be not possible for this to happen, but the problem is that it happens all the time, almost every turn, every game.
And I'm not complaining only because it happens to me a lot, I also notice when my opponents get screwed by this things, and I use to mention that in the game's chat.

If these virtual dices are supposed to emulate real dices (those made of plastic, wood or any other material for those who don't know :laugh they're failing badly in that task cause bad luck rolls happens, but not all the time.

 

[Ted-Nugent]

Gives the underdog a chance...
Who does not like a good underdog???

 

[KungFuDuet]

Unfortunately mate - you have just seen something like this:

You’ve amassed an unstoppable juggernaut. Your 15 troops go up against 2 defending armies and…

Ice, ice, ice, ice. You’ve just lost 8 troops, and now you’re 7 vs. 2. Do you continue your assault or retreat like a coward? “Well,” you think, “I just lost a bunch, so mathematically I’m more likely to win if I keep attacking”.

But alas, those 2 troops seem invincible, and your once formidable army is decimated. “What’s wrong with Major Command?! This isn’t possible! This isn’t random!” Does this sound familiar? You, comrade, have just been bitten by the so-called “Law of Averages”.

Each roll of the dice is a random event, but even more important is that each roll is an independent random event. In a random process like the die roll, any string of results is not any more likely to be evened out by a string of opposite results in the future. Each dice roll is statistically independent, which means that the occurrence of one result makes it neither more nor less probable that another result will occur next time. For example, rolling a 6 (the best number you can roll) never ever influences the next roll. The first roll is independent from the second roll, which is independent from the third, into infinity and beyond.

Speaking of infinity, the only time that the Law of Averages would work is if you had troop numbers that approached infinity – for example, a gajillion - then you could expect the random results to average out over time. But when dealing with troop numbers you see at Major Command, the results are always random and unpredictable. Although we've seen some drawn out escalate games here on MC, we still haven't had any troop numbers approach a gajillion yet. You can use the dice probabilities below to guesstimate how many troops you need to win a battle or eliminate an opponent, but you can never be entirely sure when it comes to the dice.

Because each dice roll is a random event, sometimes you will have a hot streak and roll amazing dice over and over again, decimating your opponent. On the other hand, you will probably also have cold streaks, ruining your immediate plans for world domination. Because of the way the human brain works, you are much more likely to remember the cold streaks than the hot ones. This is analogous to being stuck in traffic - you notice when cars in the other lane are passing you, but you barely notice when your lane passing other cars. Likewise, in Majorcommand you remember when you get stomped, but tend to forget successfully stomping others. The randomness of the dice will cause streaks to happen. Because we see the streak in the context of a battle or assault, we tend to connect all those independent results in our mind. To the dice, however, every roll is a completely separate event. There will be streaks, but you will never be able to predict when a streak will happen, how long the streak will last, or when the streak will end.

Sometimes a bad run of luck can seem totally absurd or unfair. You have 10 to defeat 1, and you lose 9 straight. In that situation you have a 99.987% chance of victory. It feels so certain, but yet you pull that .00013% chance and come up with the loss. How is that possible? It's simple probability. Let's say you have been playing for 2 months, and have played 20 games. In each game you roll the dice about 100 times in total. We are talking 2,000 results at this point. For something that has a .00013% chance of occurring to be likely, you need make about 7,692 attempts. If you have made 2,000 attempts then there is a 38% chance the event has occurred. The event being 10 losing to a 1. So in the end its just a matter of time and rolls before those crazy rolls show up. The one in a million outcome is likely to have happened after a million rolls. As stated earlier, you will remember that one in a million outcome much more than the million or so rolls that come before it.

Above article from The nature of Dice Luck and Streak off our Wiki

KFD

 

[rob6483]

– for example, a gajillion - KFD

That is a fantastic numerical example there! All true though. I would also like to point out that praying to the dice gods is in no way beneficial. They do not have hearts. They are cold, cold gods that laugh at statistical improbabilities and allow crushing defeats despite impeccable strategy.

 

[Cardinalsrule]

you can, however, prostrate yourself to the great god Bado and pray that he turns off the "dicerape" function on your account.

 

[codanostra]

There's only so many ways you can generate random numbers. Computers don't really do 'random', they can only emulate random. You will never see statistical equivalency to real life randommnes with a computer because its just not possible. That said, i can guarantee you we try our best here to have the most random dice we can. We don't load the dice; there is no purpose in that.

 

[rob6483]

you can, however, prostrate yourself to the great god Bado and pray that he turns off the "dicerape" function on your account.

Son of a... I KNEW IT!

 

[Dreadnought]

:rofl: but just in case this is to Bado :adore:

 

[doogin]

In case you have not seen this study, this is a great analysis of win probabilities

http://www.datagenetics.com/blog/november22011/index.html

Following up on KungFuDuet aboce, you need 13 on one for 100% victory.

 

[Chilly]

In case you have not seen this study, this is a great analysis of win probabilities

http://www.datagenetics.com/blog/november22011/index.html

Following up on KungFuDuet aboce, you need 13 on one for 100% victory.

Great link and cool discussion about programming this stuff.

However, you don't get a 100% victory condition at 13v1. You're just getting closer to it. The chart on that link just rounded to the nearest thousandth of a percent. That's only 10,000 samples. Given that over 57,000 games have taken place on this site already, I expect that we will see the 13v1 worst dice record fall.

Starting        Defender         1 in X 
Condition       Win Chance       chances
---------       ------------     ---------
13v1            5.11E-06	 195,506 
14v1            1.74E-06	 574,548 
15v1            5.92E-07	 1,688,467

On a separate note: We need a scroll bar feature on the dice roll pop-up so we can really see these cool streaks.

 

[Badorties]

there is a scroll on the dice popup.

 

[chefsmitty]

You guys can post your stats and formulas all you want. As long as we're all playing with the same "dice", does it matter? Your opponent is going to have the same statistical advantage/disadvantage you are.

 

[chefsmitty]

though I found all the info you guys gave to be very educational as far as the statistics of the dice are concerned

 

[Chilly]

...and I'd like to point out, dice is already a plural noun. :wink:

What I would LOVE to see however, is the advanced statistics added that has been discussed in another thread. Show us what our average rolls are, what our opponents rolls are, what is our track record of success when attacking 2v1, 3v1, 3v2, etc. Show them in aggregate across the whole site. Keep a rolling log of the last 10,000 attacker and defender rolls.

...and tie some of it to upgrading to a gold account.

 

[B1G4NF]

I am currently playing in a game where I rolled 623 against 36 n got double ice cubes... surely it should have been fire and ice each... shouldn't it?

 

[Dreadnought]

looks right to me: defender had 6 and 3 versus your two best: 6 and 3, defender wins both when you have same numbers.

 

[rob6483]

I am currently playing in a game where I rolled 623 against 36 n got double ice cubes... surely it should have been fire and ice each... shouldn't it?

Ha! I just rolled an 11 on 3 and wound up with FOUR sets of ice cubes! I'm not sure where the record is at, but I think it's 8 sets of ice cubes (in a row) last I checked.

 

[mark]

I am currently playing in a game where I rolled 623 against 36 n got double ice cubes... surely it should have been fire and ice each... shouldn't it?

Maybe I am misunderstanding. Your total number of armies only indicates how many potential chances you have to roll the dice. Otherwise it is just like rolling a single die...you get three dice against the defender's two if you have three or more armies but the total number of armies does not otherwise impact each individual roll.

 

[Trapper1221]

Every game I play, rare results happens several times, like 11v3 ice, 8v2 ice, 6v1 ice, even an absurd 14v5 ice

I've even gotten the 14v1 ice. I second this.

 

[mark]

I've even gotten the 14v1 ice. I second this.

Does that beat this one?
Double Ice

You need to have a screenshot utility at the ready for cases like this.