Help support TMP

"What are the odds of..." Topic

39 Posts

All members in good standing are free to post here. Opinions expressed here are solely those of the posters, and have not been cleared with nor are they endorsed by The Miniatures Page.

For more information, see the TMP FAQ.

Back to the Game Design Message Board

956 hits since 11 Sep 2017
©1994-2018 Bill Armintrout
Comments or corrections?

Madan Mitra11 Sep 2017 9:50 a.m. PST

Hi guys can anyone tell me what the odds are for some one to drill…

1 in 6 four times in a row…?

Played a game the other day and some one ruled 4 consecutive 1's…?

Ta muchly

Madan Mitra11 Sep 2017 9:50 a.m. PST

Hi guys can anyone tell me what the odds are for some one to drill…

1 in 6 four times in a row…?

Played a game the other day and some one ruled 4 consecutive 1's…?

Ta muchly

Madan Mitra11 Sep 2017 9:51 a.m. PST

Hi guys can anyone tell me what the odds are for some one to drill…

1 in 6 four times in a row…?

Played a game the other day and some one ruled 4 consecutive 1's…?

Ta muchly

Madan Mitra11 Sep 2017 9:51 a.m. PST

Hi guys can anyone tell me what the odds are for some one to drill…

1 in 6 four times in a row…?

Played a game the other day and some one ruled 4 consecutive 1's…?

Ta muchly

Personal logo Extra Crispy Sponsoring Member of TMP11 Sep 2017 9:58 a.m. PST

1/6 * 1/6 * 1/6 * 1/6 = .00065%

Way, way, way less than 1%

advocate11 Sep 2017 9:59 a.m. PST

1/6*6*6*6 = 1/1296

Under 0.1%

Ottoathome Inactive Member11 Sep 2017 10:23 a.m. PST

I've seen it happen.

ONCE in my life of 64 years.

Perris070711 Sep 2017 10:55 a.m. PST

What are the odds of posting the same thing 4 times in a row? 100% on TMP.

USAFpilot Supporting Member of TMP11 Sep 2017 11:18 a.m. PST

I'd make sure you are both using the same die or dice just to keep it fair in the case that the die used is unbalanced.

Blutarski11 Sep 2017 11:19 a.m. PST

I once failed four consecutive 1D6 crew initiative tests by throwing 6's the only possible failing score for a Veteran crew in my AoS rules. Several years later, a friend bested me by failing five consecutive tests in exactly the same circumstances.

It happens.

The psychological reaction is interesting, especially when the situation involves an expectation that your veteran crew will always behave itself. The first failure is chalked up to bad luck; the second failure is annoying; the third failure generates an angry response which could not be repeated on this forum. Anything beyond that just produces hilarious rounds of laughter all around the table.


Personal logo etotheipi Sponsoring Member of TMP11 Sep 2017 11:33 a.m. PST

No, but DOM can tell you the odds of rolling all ones on three six-sided dice twice in a row during a MechWarrior game, "Bleeped text you, that's what the odds are!"

Oh, yeah 1/6^4, significantly less than one in a thousand.

Madan Mitra11 Sep 2017 1:04 p.m. PST

Hahaha. So the astute spotted the post 4 times…silly joke, made me giggle for 4 seconds.

Thanks for the replies really appreciate it. I'll go with the 1/1296 number.

And yes, hotels of laughter as the army went home.

mumbasa11 Sep 2017 1:28 p.m. PST

I threw 3 sixes in a row at a DBA game. I switched out the die and promptly threw another six. My opponent was not amused ;) At this past Historicon, I threw 3 sixes in a row at the Kadesh Triump game.When my ally next to me needed to throw a die, he picked up my die and threw a three. Yes, I snickered out loud. A few turns later he started to throw my other die. The game master saw this and asked if he had taken my die. "Yes…twice!" I replied. The guy gave them back to me. So, the odds of getting a jerk like that playing on your side is 1/2500 ???

John Leahy11 Sep 2017 4:38 p.m. PST

My oldest son was probably about 12. He was playing the Rebels in a Star Wars Battle of Hoth game that has been running at local shows for many years now. This was the first year it was run. My son kept killing all the Imperial troops and vehicles on the board. You used d20's. He would consistently roll 19 or 20. This was tilting the game in a way the GM had not anticipated. Finally, the only thing alive were 2 At-At's. My son proceeded to kill the first one. Everyone was astounded. You needed 16-20 to make a hit the 19-20 to damage it. There was then only a single At-At left. The GM then adjusted the damage rolls for a 20 to inflict damage. You needed 3 or 4 20's to kill it. He then proceeded to roll 3 or 4 20's in a row. Everyone was silent. They couldn't believe it. It was the greatest streak of incredibly lucky die rolls I have ever seen.

Never, ever underestimate the power of 'kid dice'!

Cyrus the Great11 Sep 2017 6:05 p.m. PST

I rolled 48 dice needing a 6 for a hit and didn't roll one 6.

robert piepenbrink Supporting Member of TMP11 Sep 2017 6:28 p.m. PST

In an old CLS game, I once held on Combat efficiency--1 or 2 on a D6--four times in a row. It was when the militia held--1 on a D6--that my opponent about gave up. It may have been more than four times for the regulars. No failures that day.

Wolfhag11 Sep 2017 10:31 p.m. PST

These dice anomalies are why I like to use binomial tables rather than rolling lots of dice.


Blutarski12 Sep 2017 8:19 a.m. PST

Robert Piepenbrink –
I recall that those CE rolls often came at pivotal moments in CLS and rolling "immortal" was cause for great celebration.

Wolfie -
A 2D6 throw produces a natural (if slightly crude) binomial distribution.


basileus66 Inactive Member12 Sep 2017 10:36 a.m. PST

W40K game: needed to take six save rolls with my Terminators. One of them, my Warlord in Termie armour. It was an artillery round (S8). I rolled the dice, and six 1s! All my termies dead.

It was in that same game that a Imperial Guard sergeant armed with nothing but a pistol and a chainsword killed a Deamon Prince of Khorne in hand to hand combat.

It is the game with the oddest results ever.

Personal logo etotheipi Sponsoring Member of TMP12 Sep 2017 3:20 p.m. PST

I recall that those CE rolls often came at pivotal moments

I think any time you cause a less than 1:1000 event to happen in a game becomes a pivotal moment.

Personal logo McLaddie Supporting Member of TMP12 Sep 2017 4:29 p.m. PST

These dice anomalies are why I like to use binomial tables rather than rolling lots of dice.


The problem with randomness is that 48 rolls and no '6' isn't an 'abnormality'. Getting 8 sixes in 48 rolls is just as abnormal. What

The way statisticians can tell when numbers 1-6 have been created by humans and not a die roll is that there is too much 'normalcy', lie 8 sixes in 48 rolls.

Binomial tables have the same 'abnormalities', only far more restricted. [OR controlled and less random than equal chances of 1-6 or 1-10 or 1-20]

Wolfhag12 Sep 2017 5:12 p.m. PST

I understand that there is not that much of a difference. However, I like the idea of having a % chance to hit rather than a specific hit # with multiple dice. Using a binomial table I roll 2D10 for a 1-100 result. I can have outcomes from 1% to 99% if I wanted it that granular. I don't have to roll the "buckets of dice" either but I understand people do like that too.

I guess I don't use "real" binomial tables but slightly modified ones. With 10 targets having a 10% chance to be hit theoretically there is a chance for all 10 to be hit but that will not happen. I have it tweaked to a 1% chance for 4 hits, 6% for 3 hits, 19% for 2 hits, 39% for 1 hit and 35% chance for 0 hits.

One reason why is that in a few games we have had the unusual result of needing a 6 to hit and rolling eight 6's on ten dice. Everyone felt that anomaly was unrealistic and killed the overall experience as it happened early in the game.

It comes in handy to determine the outcome of large artillery barrages, small arms fire, and naval gunfire broadsides with guns less than 6in that have a high ROF.


Blutarski12 Sep 2017 5:45 p.m. PST

If a granularity as fine as one percent is required, a 2D10(100) spectrum is perfectly understandable.


Madan Mitra12 Sep 2017 11:44 p.m. PST

All this reminds me of one of my favourite quotes from Discworld

"If the odds are exactly 1 Million to 1, then they happen 9 out of 10 times"…The Magicians.

Personal logo McLaddie Supporting Member of TMP13 Sep 2017 10:59 a.m. PST

Regardless of the die rolls, the results are tied to some combat resolution system or table.

That means that regardless of the type of die used, the results are always in the control of the designer. If you get results that strike gamers as 'unrealistic', then one has to determine what the parameters for 'realism' are, whether statistically determined or rendered by impressions like the eight '6's out of 10 rolls, and design the results system accordingly.

Personal logo etotheipi Sponsoring Member of TMP14 Sep 2017 7:58 a.m. PST

Everyone felt that anomaly was unrealistic and killed the overall experience as it happened early in the game.

History is full of low-probability occurrences that stopped events from becoming long, drawn-out (interesting) battles. It may be "realistic", just not interesting or particularly insightful (fun to play).

Wolfhag14 Sep 2017 9:36 a.m. PST


The example was a Union Regiment advancing on a Rebel stronghold (Battle of the Crater). The Rebel player rolled his bucket of dice and ended up putting 45% causalities on the Union Regiment on the first turn of the game when 5% was expected. We were using a D6 hit# with a cover save. At this point, there was no way the Union would have been able to mount an assault, the game was effectively over.

This was a play test for a convention and we didn't want something like that happening. Purists will disagree with me and that's OK. That's when I redesigned the system attrition using binomial tables with the restrictions built in not the D6 hit and save. I admit they are not "true" binomial probabilities because there is not that one in a million potential result. Dana Lombardy and Frank Chadwick were players at the convention and liked how the system worked. The game battle played out pretty historically.

There are other ways to have low probability occurrences occur like SNAFU's, tactical advantage force multipliers, C3 breakdowns, poor Situational Awareness, leadership intervention, etc.


Blutarski14 Sep 2017 10:23 a.m. PST

I'm frankly a little troubled by this notion of legislating "luck" out of the gaming experience in order to guarantee a "fun game" where no players have to endure any unexpectedly unpleasantness.

I foresee the result of such a path being a game in which only results "expected" by the players will be represented. Players will never lose a game on turn 2 because their commanding general takes a ballista bolt in the forehead (Hi Skeeter!!!). Or when a cascade of bad morale checks routs half your army off the table on turn 1 (I was on the winning side for that one). Or when some perfidious Greek (Hi Paul!!!) blows up your Invincible Class BC on the very first turn of gunnery.

It's one thing to fiddle with the extremities if you honesdtly believe that the system in UNREALISTIC – I'm perfectly OK with that. But, Great Googamugga, don't do it just to avoid a potentially unpleasant but perfectly possible wargame outcome.


Personal logo etotheipi Sponsoring Member of TMP14 Sep 2017 10:48 a.m. PST

this notion of legislating "luck" out of the gaming experience

I agree, but don't think that is what Wolfhag is describing. He is describing being very deliberate about bounding the effects of random chance.

As McLaddie often points out, what is in the game is what we put in the game. I am an advocate of understanding (not necessarily explicitly enumerating) the entire state space of possibilities that we put into a game. As most probabilistic systems expand that state space geometrically (at least) with respect to elements in the system, those state spaces can be big.

I don't think employing a few extra grey cells on the extreme cases is the same as eliminating randomness.

Wolfhag14 Sep 2017 12:39 p.m. PST

Sorry if I was not clear. I'm not trying to legislate "luck" out of a game. I purposely put in risk-reward decisions for players to try their luck to gain an advantage. I'm all for extremely unpleasant effect IF it is because of poor tactics or a backfired risk-reward decision. Luck must also play a part too, that why dice are used. No outcome is guaranteed.

Using my Battle of the Crater example: If the Rebels in a 1:1 ratio had a 1% chance of each figure causing a causality and I used a digital random number generator to determine the results (cannot roll hundreds of dice) there is a chance that ALL of the figures would score a hit. Very lucky, mathematically probable but historically unrealistic. That's what I want to eliminate.

The last game I ran a Russian T-34/85 company of 12 tanks attacked four Panthers and a Tiger II starting from 2000 meters. The Germans set up with a clear line of fire but the Russians used terrain masking to get closer and jinking to make the Tiger II miss. I told the Germans what was going on and how to counter it but they decided to stay put. Eventually, the Russian player broke into LOS about 300 meters away from the Germans. He knew he'd take a few causalities but decided to continue to move at high speed and jink to get flank shots while splitting his force to envelope on both flanks to guarantee that hits would penetrate.

The Russian player was new to the game but just finished 5 years in the Marines with four deployments and survived many close range fire fights and commanded a squad in an urban environment. He did say he played WoT and was familiar with the strengths and weaknesses of the vehicles involved. He understood maneuverability, gauged the expected results, used his strengths against the opponents weakness and refused to stop and engage in a long range duel. He didn't get any lucky die rolls but his timing for a 1st shot was better than the Germans because of his envelopment maneuver. He lost six tanks to the four Panthers and Tiger II.

He achieved an improbable victory because of good tactics and poor German decisions. The dice had very little to do with it. The Russian did have some "lucky" turns but it was because of decisions in a previous turn, not the dice or some random activation failure. The Tiger II was knocked out a split second before it was to fire back. That was the roll of the dice.

Players need to be able to gauge the risks of using different strategy and tactics. If the game engine delivers unbelievable or very unhistorical results it can be a real downer, even for the winner.

I like to hear players post game discussions centering around the use of sound historical tactics and risk-reward outcomes, not poor die rolls deciding the outcome. But that's just me.

One more thing. Whenever I tried to give the Russian player advice he told me to keep my mouth shut as he had it all under control.

During the game, there was a 5% chance of a SNAFU each time a vehicle fired. Hits on rounded armor surfaces like rounded mantlets had a chance to ricochet so there was no guarantee of a penetration. There was also a 5% chance of hitting a weak spot like the turret ring so no tank was immune at any range. Within 500 meters players could alter the hit location die roll to purposely target a weaker area. While moving they could fire or jink to avoid a hit. No guarantees anywhere.

Using binomial tables to help generate believable and historical outcomes is a good idea. If you really want to win, rely on good tactics, not the lucky dice. I try to set up scenarios where no outcome or decision is guaranteed.


Great War Ace Inactive Member16 Sep 2017 8:26 a.m. PST

As GM, I rolled three consecutive snake eyes for the bad guys' side. Pleased the heroic players on the outnumbered good guys' side enormously. And lost the battle for the bad guys, of course. They were morale rolls, all failures in the epic sense……….

Madan Mitra21 Sep 2017 8:24 a.m. PST

All this reminds me of one of my favourite quotes from Discworld

"If the odds are exactly 1 Million to 1, then they happen 9 out of 10 times"…The Magician.

Der Krieg Geist Inactive Member27 Sep 2017 7:41 p.m. PST

My dice have done many a strange thing to me over the years, none of them good. :) Two examples off the top of my head. WHFB, unit or thirty magically jacked up High Elf archers needing 4,5,or 6 on a die 6 to hit: rolled twenty-eight hits, then needed 3,4,5 or 6 to wound enemy unit….rolled twenty-eight ones and twos.
A couple of years later while playing in a 3.0 D&D game ( which I rarely did as I DMed for years) I was playing a Ranger in a party who found themselves surrounded by zombies. They were poring out of the woods from every direction and our party was totally cut off from escape and to weak to defeat them.( DM had a habit of deliberate total party wipes that was not so obvious, until we played multiple games with him and he repeatedly sandbagged us. Oddly his wife always played in his games and got wiped also)
Sooooo….to drive the point home, that we were in fact doomed, I rolled nineteen ones on a die twenty, critical fumbles, in a row without interruption. After the sixth one, I started borrowing everyone else's dice, including the DMs. But to no avail. We were all laughing at first but after the tenth "1" we were mostly dumbstruck and by the nineteenth "1", I simply had the character lay down and wait to die.
Thirty plus years of roll playing and I never rolled two critical hits (20) on a D20 in a row. Not as a player ,not as a DM. Nineteen 1s has got to be some kind of a freakish world record.

Blutarski28 Sep 2017 6:03 a.m. PST

Der Krieg Geist – Clearly, your D&D game was somehow transmogrified the into a paranormal experience.


Personal logo etotheipi Sponsoring Member of TMP28 Sep 2017 9:20 a.m. PST

That's when I redesigned the system attrition using binomial tables with the restrictions built in not the D6 hit and save.

So it really wasn't the binomial PDF, but the conditions you placed upon it.

As long as the magnitude stochastic state space is large enough (without a significant relatively prime factor problem), any resolution system can be handled by any die system. F'r'ex, you can't get numbers 1-6 from a coin flip, but you can get a coin flip from a d6 (or d4, d8, 10, d12, d20). You can get numbers 1-12 from a d6 and a coin. You can get close to numbers 1-6 from a d10 and closer (but not exact) from a d20 or d%.

The real question is how "torturous" you want the mechanism to be.

With an opposed die roll (hit and save) bonuses and penalties do not apply linearly in the state space (which is geometric, not linear).

I'm glad you found something that worked and made sense to the players at the same time. Good job!

grahambeyrout25 Nov 2017 6:04 a.m. PST

If we are talking about luck or otherwise in throwing dice. Once at school many years ago, I threw five D6 simultaneously and got 5 sixes. The first time ever for me. Later the same day I was cross examined by my friends about the circumstances. They assumed there was some flaw in the methodology. Accordingly I demonstrated how I simply thrown them by throwing them again onto the floor of the school corridor. I got five sixes again. The odds of doing this is 1 in 7776 or roughly 0.013%. That was over 50 years ago. Needless to say, I have never thrown five sixes in all the intervening years. This is in itself odd, since I must have thrown five dice several thousand times since then.

Russ Lockwood25 Nov 2017 4:29 p.m. PST

In the WWII naval rule set Panzerschiffe, torpedoes hit on 3s (using d6s -- I don't know why the author chose 3s and not 1s or 6s, but that's the die roll you need), with the number of dice rolled dependent on the number of torpedoes fired, the angle of the attack, the speed of the target, and the distance from the firing ship. Yes, you need a calculator.

When firing, you write down the torpedo angle from the firing ship and how many you are firing and put a marker on the table. Then, all the ships move and after firing, you resolve the torpedo attacks.

As the Japanese player, I managed to put four torps dead perpendicular broadside and at minimum range into a US battleship, and, if that wasn't enough, the angle intersected a cruiser behind the BB -- any torps that missed the BB would get a shot at the CA.

The umpire punched in the numbers and I wound up with 21 dice against the BB.

I shook the handful of dice and let them fly… Are you kidding me? No 3s? Well, there's nine other guys around the table all looking at the dice…and no 3s.

So, out came the calculator and it was 15 dice against the CA. The mighty cubes were shaken and soon tumbled across the tabletop…

No way! No 3s?

And we 10 plus the umpire stared at the dice and the US players laughed and laughed and the Japanese players shook their heads in disbelief.

But wait! I had placed a different torpedo "spread" shot just off the bow of a US CL. Only 6 dice…

No 3s!

These dice do have three pips on a face, don't they? (Yup)

I leave it to others more mathematically inclined to figure the odds of NOT rolling a 3. Maybe it's 5/6 x 5/6 etc until you have 42 5/6s? Dunno. Above my mathematical grade.

That said, for my birthday, one of the players gave me a ship and a d6 -- stickered with 3 pips on every face.

RudyNelson27 Nov 2017 8:45 a.m. PST

To determine odds, draw out the resulting rolls charts.
For my play testing I have a one, two and three chart on my wall.
Should be easy since you are talking about single dies and not multiple rolls.

El Jocko02 Dec 2017 9:15 a.m. PST

The odds of rolling 21 dice and not getting a single 3 are just over 2%. Unlikely, but not crazy unlikely. 42 dice without a 3 is a different matter. That's about 0.05%. Now we're in the crazy unlikely realm.

Sorry - only verified members can post on the forums.