Forum adverts like this one are shown to any user who is not logged in. Join us by filling out a tiny 3 field form and you will get your own, free, dakka user account which gives a good range of benefits to you: No adverts like this in the forums anymore. Times and dates in your local timezone. Full tracking of what you have read so you can skip to your first unread post, easily see what has changed since you last logged in, and easily see what is new at a glance. Email notifications for threads you want to watch closely. Being a part of the oldest wargaming community on the net. If you are already a member then feel free to login now.

Wondering how people deal with situations where one player seems to be very lucky, or when statistical impossibilities seem to happen with him more frequently than they should.

Have been thinking about a game I watched a couple weeks ago. This kid was matched up against a SM player and took out 6 Centurions through shooting in the second round of combat. The kid was having a really good day with the dice, rolling 5s and 6s when he needed to, and the SM player was not. Both players were using the same dice and there's nothing to suggest there was any cheating involved.

The thing is, it's usually this way with this kid. He plays straight CSMs, there's nothing very special about his list, and it would be hard to call him a gifted player. He just gets his army into situations where you would think it's about to be smashed and then some statistical miracle happens. Another time, it was with autogun cultists shooting up a Seer Council on jetbikes - highly improbable, no cheating involved, but it happened at exactly the right time and made all the difference.

I know statistics is the law of averages and over the course of a thousand trials things would work out differently most of the time. But how often do things like this happen, where disasters turn into victories and really improbable events change games? Have I just been playing 40k the wrong way all these years and need to forget about the math?

Obviously he is a Tzeench cultist in miniature disguise

I mean, didn't the CSM army give it away?

You can describe events in terms of means and standard deviations.

If you plot a histogram of test scores you might get something that looks like a normal distribution. Most students will cluster somewhere in the middle, and the prevalence of a given score will decrease as it increases in distance from the mean.


These statistical improbabilities should be rare, but it depends how you're defining them. Use mathhammer to decide the "test score" then use probability to place it along that continuum. That should give you a more accurate understanding of just how often you can expect a given outcome.



40k is an incredibly complex game. We can apply mathhammer in discrete situations but over the course of an entire game, lots of dice are rolled. You might roll 10 6's in a row, but if it's for things like leadership checks (uh oh), run moves, difficult terrain rolls, etc., you're hardly likely to notice it. Likewise, you roll all 1's for these things you may not notice either.

On the other hand, if you have a model with a 5+ save and you roll 10 5+s in a row against your entire opponent's army worth of shooting...well...everybody will notice that.

I had one lone SM scout in melee with two plague drones.
With my one attack
I....
Hit on a 4+
Wounded on a 5+
He fails his 5++
1/20 odds already

Now....the fun part.

He rolls his four attacks,
hits with 2 on 4+
Wounds with 1 on 4+
I save on a 4+

1/8 odds

He rolls leaderships
Rolls a 12 on 2d6
Squad wipes from instability
I need 6 inches on 1d6 to consolidate onto objective to win
get "6"
Game ends on 1 o 2
Game ends on 2

odds for that was .1%

Odds....overall of this happening in a turn??
.000009 or .0009%

The whole store was watching in disbelief...myself included.

I'm usually on the losing side of statistical probability. I roll badly, and the Grey Knights don't get enough dice for those rolls to statistically even out.

There are shows like "Scam School" which explain how con-artists can roll a non-weighted dice a certain way to almost always get the result they want. I know statistics, but that comes to mind whenever an opponent is consistently rolling too well, especially when they insist on rolling one dice at a time.

The only times I've seen a person roll dice one at a time, is

a) mixed saves or character in a unit.
b) major game-changing event.

For example.

a) squad of Guardians with Warlock in front, saves will be rolled 1 at a time, until the Warlock dies. Then batch rolling until you get to the Weapon Platform.

b) Warlord is down to his last Wound, game is almost over, killing the Warlord will give the player the win. In this case it's more of a hype thing then anything else, trying to build up the tension.

 Happyjew wrote:
The only times I've seen a person roll dice one at a time, is

a) mixed saves or character in a unit.
b) major game-changing event.

For example.

a) squad of Guardians with Warlock in front, saves will be rolled 1 at a time, until the Warlock dies. Then batch rolling until you get to the Weapon Platform.

b) Warlord is down to his last Wound, game is almost over, killing the Warlord will give the player the win. In this case it's more of a hype thing then anything else, trying to build up the tension.

A couple people at my local gaming store roll all of their Invulnerable Saves one at a time, and remarkably pass over 3/4 of their saves which have a statistical 1/3 chance of success.

I've had some of my HQ choices pass 40+ 2+ armour saves when they've been on their last wound. I've seen a bunch of Meganobz (in 5th) charge an immobilized Land Raider and get 7 1s and a 2 for Damage Result. I've seen a friend of mine roll for his Shokk Attack Gun turn 1 three tournament games in a row.

The dice gods are real.

Isn't it obvious? The guy clearly has a horseshoe up his ass and 4 leaf clover in his pocket...

What happened wasn't statistically impossible(that would be him rolling 7s on a D6)

I think you meant statistically improbable. Anyway, just sounds like he's an incredibly lucky guy.

I used to field an Anvil of Doom with my WFB Dwarf army, before the current codex.

I had to stop using it because it exploded. Regularly. Every game I tried to use one of the powers on it, it would fail to cast and then suffer a catastrophic explosion. Six or seven games in a row, every game it blew up the first time I tried using one of the powers on it.

I dunno what the statistical chances of that happening where but it was enough that my gaming group re-named it the 'Anvil of Boom'....

I think the chance of the old Anvil exploding was 1 in 216 on any single dice roll.

Over the course of a game that probability increases dramatically.

 Grey Templar wrote:
What happened wasn't statistically impossible(that would be him rolling 7s on a D6)

I think you meant statistically improbable. Anyway, just sounds like he's an incredibly lucky guy.

This. I can say with a high amount of statistical probability that you've never experienced a statistical impossibility when playing 40k. You probably experience countless improbabilities though.

Technically any roll which deviates from the average is statistically improbable.

I am just as likely to fail all my 3+ saves as I am to pass all of the same number of 5+ saves. Both would be a statistical improbability.

Its statistically improbable that, when rolling five 2+ armor saves, that I will roll five 6s. But it wasn't statistically improbable that I would pass all 5 saves. there was an 83% chance of that.

If there is a large variance, the average itself is also somewhat statistically improbable compared to the chance of getting NotAverage. On 2d6, your average total is 7 but you will only get that 1/6 of the time.

 Grey Templar wrote:
But it wasn't statistically improbable that I would pass all 5 saves. there was an 83% chance of that.

Actually you only have a 40% chance to pass five 2+ saves out of five. Each individual save has an 83% chance to pass but with five events your chance of failure gets to 60% of at least one failure.

Right, I keep forgetting to multiply them by each other.

How to deal with those situations? Just accept that they'll happen.

Really, do anything except what the people at my lgs do: whine and moan and make sure your opponent has 0 fun.

Some people are just inherently lucky. I used to play DnD with a guy who would always roll 18s, 19s, or 20s. I even made him roll some of my dice, and he still did the same (I was the DM). Over the course of games, it somewhat evened out, he'd roll poorly sometimes, but the guy was just good at rolling dice. As long as he isn't cheating, don't worry about it. Maybe the dice gods are blessing their chosen one

 Grey Templar wrote:
I think the chance of the old Anvil exploding was 1 in 216 on any single dice roll.

Over the course of a game that probability increases dramatically.

I never really got as far as the course of the game. Just the first damn time I tried to use it in every game.....

Remember, the dice giveth and they taketh away.

I always roll badly. My vendettas have never shot down another enemy aircraft, they always miss, fail to pin, or then they make a jink save.
Then they get shot down next turn because i can't make any jink saves. For instance a chaos biker with a plasma snap fired into the rear of my vendetta hit it, pinned it, and caused an explosion result. I then failed my jink.

My snap shooting is awesome when i use plasma though. twice in one game i got double 6s.

techsoldaten wrote:Wondering how people deal with situations where one player seems to be very lucky, or when statistical impossibilities seem to happen with him more frequently than they should.

The thing is, it's usually this way with this kid.

I know statistics is the law of averages and over the course of a thousand trials things would work out differently most of the time.

So, the deal with the law of large numbers is that it's the law of LARGE numbers. Actually large. In any game of 40k there are probably only a dozen die rolls that make up the bulk of how the game goes (who gets first turn, etc.). Over the course of several games, you're talking about a relative handful. Come back when you're talking about hundreds of thousands or millions, and then the law of large numbers will start taking effect.

As a result, it is very, very possible for a person to be consistently lucky or consistently unlucky over the course of many games. I've seen it happen myself a lot, and my battle reports bear written testimony to some of the stranger streaks.

It is easily possible for a person to win a few games in a row due to luck. It's just the nature of 40k. Any game where the outcome of decisions is mediated by dice, and some decisions are more important than others will necessarily have this problem. It's why 40k isn't a terribly serious strategy game, and why the idea of 40k tournaments is rather silly.

As for how to deal with it, you pretty much have two options, flip the table in rage or shrug it off and play a rematch.

I once psychic shreaked an invisible wraithknight to death with only throwing 2 dice at the power (opponent declined to attempt to deny). Something like a 0.4% chance of happening. We just kind of went 'well that's funny' and moved on

 Mulletdude wrote:
I once psychic shreaked an invisible wraithknight to death with only throwing 2 dice at the power (opponent declined to attempt to deny). Something like a 0.4% chance of happening. We just kind of went 'well that's funny' and moved on

It's not that improbable. Psychic Shriek doesn't roll to hit, so invisible or not doesn't really matter. 2 dice doesn't really matter as each dice you roll gives you a 50/50 on getting the power off given a WC1 power. Then it's just a matter of rolling well on the 3D6 roll. They're LD10 so 3 6's would net you 8 wounds...5 5 and 6 and you've got a dead Wraithknight.

Psychic Shriek is one of the best powers out there for killing invisible units!

Once my boyz nob got challenged by a Daemon Prince.

DP attacks, misses all hit but 1. I take 1 wound, then retaliate.

On 4 Dice. 5s and 6s to hit. And 3s 4s and 5s to would. It dies. I am happy.

Basically my Boyz nob killed a Daemon Prince without dying

Anything with low numbers of rolls you're more likely to get large deviations (if you have an average of 5 successes on 10 dice you're more likely to roll only 3 vs having an average of 50 on 100 dice rolling only 30).

Whenever your average is quite low, and the number of trials is low (which is the case with most 40k rolls) you actually have a pretty high chance of being miles off the average..

Bear in mind that if you roll six sixes on a die you chance of rolling a six on the next roll in one in six.

 Kilkrazy wrote:
Bear in mind that if you roll six sixes on a die you chance of rolling a six on the next roll in one in six.

Yeah... each dice roll in and of itself is independent, it's the cumulative chance that is dropping. If you roll 1000 6's in a row the chance of that happening is extremely slim, but when you go to roll dice number 1001, it's still a 1/6 chance.

You see, a friend of mine is a fun fellow. He claims that his superpower is being "lucky sonofa*****" (more or less his wording).

I've seen him pull some amazing combo's like naming a correct suit of the card on the top of the deck for like eight or nine times straight or throwing a d20 and yelling "4" when it's in the air and getting it.
He even once won 10 euro's from his mother by simply promising that his next roll was to be a six.

People always ask his secret and he says that it is being arrogant (which we all believe is the main reason).
But I've known him for a while and unlike other people I know his secret. It is that he is actually not that lucky, it's just what people see.
For every time he has guessed the right suit there are at least couple of times when he guessed wrong thrice in a row.
People see him do it once, it fails and no-one remembers it the next day.
Some other people see him do it once, it succeeds and they praise his luck.
It's just that I often see both of those and know the truth.

Do I have a point? Of course. And that is that it rarely has truly anything to do with "being lucky". If you have played for 3+ years, threw millions of dice, then of course there will eventually become that one combo of throwing 5 sixes.

Nobody remembers how many times Thomas Edison failed when inventing the light bulb. They just remember that he invented it.

Automatically Appended Next Post:

 iGuy91 wrote:
I had one lone SM scout in melee with two plague drones.
With my one attack
I....
Hit on a 4+
Wounded on a 5+
He fails his 5++
1/20 odds already

Now....the fun part.

He rolls his four attacks,
hits with 2 on 4+
Wounds with 1 on 4+
I save on a 4+

1/8 odds

He rolls leaderships
Rolls a 12 on 2d6
Squad wipes from instability
I need 6 inches on 1d6 to consolidate onto objective to win
get "6"
Game ends on 1 o 2
Game ends on 2

odds for that was .1%

Odds....overall of this happening in a turn??
.000009 or .0009%

The whole store was watching in disbelief...myself included.

I think the possibility for all that to happen is something like 0,043%. Note that I calculated all the results of Daemonic Instability that would've wiped them out. And might be something wrong.
Still, that is awesome! I hope that the Scout got promoted!

I would say this thread has some very valid points. I would like to point out the differences between impossibility and improbability. Improbability is an action that has a very low percentage chance of being successful. Impossibility is an action that has no chance of success.

An example of improbability is an Imperial Guardmen trying to shoot down a Flying Hive Tyrant. He needs a 6 to hit on a D6. He needs a 6 to wound on a D6. And the Hive Tyrant can pass his save on a 3+ roll of a D6. The percentage chance of that Imperial Guardmen causing a wound on the Flying Hive Tyrant is 2/216 or .92%.

An example of impossibility is the same Guardsmen trying to assault any vehicle with just his close combat weapon/lasgun. No matter what he rolls upon the D6 roll, he will not be able to penetrate or glance the Armor Value of the vehicle in question to cause any damage to the vehicle. His success percentage is 0%.

I would say that the smaller the force/unit is, the more variance of luck will play a part in its attacks. Larger units/forces tend to roll more dice, which in turn, brings those units closer to the mean of probability on a regular basis. Hence, larger units are more predictable in the outcomes of their actions.