Can anyone explain how to calculate probability?

[daddymaykadarobots]

Hi all,
I was wondering if anybody can help us with working out how unlikely a result on a recent game was?
Allow me to set the scene:
We are on my last turn (4) of a game (8dp 2r) of dig in and climb out. By far our favourite for a quick game. As per usual my mates rolling is impeccable throughout with all his in range units making kills, including panzerfaust on infantry.
Then the killer, he bust out his action stored up action card, 2 staffing runs and masks masks (yes his first born will go to the great card God, dice God got everything else : ) )
That puts pay to practically all my potential scoring units, that all game have been shooting with their eyes closed.
This leaves me with a handful of riflemen in range, and a fighter plane. At least the table looked cool, as he went first he has nearly all of the 24 deployment points of units spread all over with multiple Faust's in objectives, cue smugness and sudden optimism for my chances of 'clawing it back.'.
So that's it game won, he went first so I thought stuff it, right, bring on the pounder rain.
I bring all four out to clear the field and grin a little.
Plane scores two fives for a kill and a secret objective point, yah.
Then it happens, I have 26, yes 26, dice rolls to use, mostly in twos four the pounders. Aaaaand I get exactly zero 5+ rolls.
Stunned silence in the room, and unanimous decision to call it a night all round, apparently that allied wave shopped exclusively at the wonky barrel factory.

So can anyone tell us the odds of this disastrous round of shooting?

Hope you all enjoyed the snap shot, if anyone else has similar tales I'm sure others would love to hear them too. : )

 

[nels0nmac]

Hiya. Daddy. Well it's fair to say that you did have a particularly bad set of dice rolls. Here's the math - what you need to do is calculate the odds of not rolling a 5 or a 6 with any of the dice. So with a single D6 it's 4/6 which is roughly 66%. Where you have multiple dice where the same condition has to be met on each dice you multiply the odds together. So with 2 D6 the odds are 4/6 x 4/6 = 16/36 roughly 44%. 3D6 its 4/6 x 4/6 x 4/6 and so on. So for 26 dice you get 4/6 times itself 25 times ( also known as 4/6 to the power 25).

So in your case the chance of not getting a 5 or 6 with any of the dice works out to be roughly 4 thousandths of one percent - or to put it another way over 25,000 :1 against.

There's rum luck and then there's rum luck...... And on that day boy did you hvae rum luck.

 

[armrek]

Poor bastard! ;-)

 

[Decar]

That's not quite right.

There are 26 events, assuming each event is mutually exclusive, which they will be in this example: There will be 26 events to multiple (not 25).

Or put another way:
Then N * (P(1D6 <5)) = (2/3)^N
Where N is the number of dice.

So if N=26 (ie: 26 dice) then it's:
(2/3)^26 = 0.00002640141

or as a reciprocal: 1:37876.75

 

[nels0nmac]

Quite right Decar - for some reason in my mind I had it that it should be 2/3 ^(n-1).

 

[Decar]

Glad you agree, I was starting to confuse myself!
When I read it I think you were thinking it was 2/3 × itself 25 more times.

Either way 1:25k or 1:38k; it feels pretty unlikely!
That's some bad dice rolls!

 

[daddymaykadarobots]

Thanks guys, didn't expect qite those odds though, just as well I don't gamble!
And once again thanks to decar and others for all help offered, now if only I could get rid of the damned repeating images every time I post, sigh.
Shortly, either tonight or tomorrow I'll be updating it again with some big stuff I've been doing.
Also thinking of trying an expanded version of dig in climb out on a 4 x 4 tile map, so basically when you popout on either 3 or 4 you can't get straight into an objective, but maybe that's one for you decar? Speaking of which, you got any new ones in the works? Yours so far have been ace : )

 

[Decar]

Thanks again Daddy; I can't take all the credit, my wife's input has been invaluable too.
I've had some interesting ideas but found it difficult to commit the time to experiment and play test them as thoughly as ths Telberg campaign.
I often find myself making notes in margins for new scenarios; but I'm finding it hard to collate anything and the proto-scenarios are too weak to share just yet.
Hopefully I'll get something out soon!

 

[daddymaykadarobots]

See now I'm really envious an education that clearly sunk in, and a Mrs that doesn't refer to a game of strategy and planning as 'Playing with your toys again.' : )
Pass on my praise to all concerned, can't wait for more of your ideas/campaigns/scenarios.
Had a thought how about a more hero focused campaign. Maybe if a hero is alive at the end of a game then he can be deployed at the start of the next for free, maybe the same for other units like tanks too, but retaining any previously sustained damage?