So I am playing the new Battles for Normandy game. part of the landing process is to drop your naval support units into place to provide NGF support.
I just put down ten naval units. Each unit rolls 1 1d10 to see if it hits a mine and is removed from the game.
Rolled 5 10s out of the ten dice.
What are the odds of rolling x 10s on ten d10 dice?
I know is is not as simple as one would think, but is there a formula to figure out just how unlikely this result would be?
An "average" roll is obviously 1, but how do you figure how much more unlikely 2 is than 1, 3 than 1, 4, than 1, etc?
:goodboy:
Err, we learned this in college it can't be that hard... altough I dont remember much of it : (
If X is the number of 10s:
((9/10)^(10-X)) * ((1/10)^X) * (10!/(X!*(10-X)!))
0: .349
1: .387
2: .194
3: .057
4: .011
5: .001
:lol: 0.1%
Generalizing, if X is the number of desired results, P is the decimal probability of getting the result and N is the number of attempts:
(1-P)^(N-X) * P^X * N! / (X! * (N-X)!)
It is unlikely that very unlikely events occur.
What's "!" ?
Factorial. 3! is 3*2*1. 10! is 10*9*8*7*6*5*4*3*2*1
Alright, thanks.
Quote from: frunk on January 12, 2010, 02:04:35 PM
If X is the number of 10s:
((9/10)^(10-X)) * ((1/10)^X) * (10!/(X!*(10-X)!))
0: .349
1: .387
2: .194
3: .057
4: .011
5: .001
You don't need all of that effort since the probabilities aren't unconnected. To get 5 out of 5, he had to roll every die a 10, meaning it's just (10%) * (10%) * (10%) * (10%) * (10%). Still .001% though.
But we are not talking about 5/5, but 5/10.
Quote from: ulmont on January 12, 2010, 03:05:58 PM
You don't need all of that effort since the probabilities aren't unconnected. To get 5 out of 5, he had to roll every die a 10, meaning it's just (10%) * (10%) * (10%) * (10%) * (10%). Still .001% though.
He's not talking about 5 dice rolling 10s, he's talking about 10 dice, with 5 of them coming up 10s. If it was 5 dice needing all 10s you'd be right. Note that my numbers are decimal, not percentage, so 0.1% for rolling 10 dice and 5 of them coming up 10s.
Quote from: Berkut on January 12, 2010, 03:08:18 PM
But we are not talking about 5/5, but 5/10.
Ah, I'm sorry. I thought you were whining about getting diced, not just having a weird streak.
Quote from: frunk on January 12, 2010, 03:09:47 PM
He's not talking about 5 dice rolling 10s, he's talking about 10 dice, with 5 of them coming up 10s.
You're right. I thought he got more seriously diced than that.
That's a hundred times as unlikely as what did happen.
Quote from: ulmont on January 12, 2010, 03:14:13 PM
You're right. I thought he got more seriously diced than that.
It's one in a thousand (actually 1 in 672 (0.001488035) or so if you pull more digits), which is certainly ugly but not nearly as bad as one in a hundred thousand.
I think the worst run I saw was my opponent in a game of Memoir 44', with a ~ one in 2000 chance of missing. Still wasn't quite enough for me to get the next round of the tourney though (I won but not by a high enough score), but it did ruin his chances.
Quote from: frunk on January 12, 2010, 02:04:35 PM
If X is the number of 10s:
((9/10)^(10-X)) * ((1/10)^X) * (10!/(X!*(10-X)!))
0: .349
1: .387
2: .194
3: .057
4: .011
5: .001
This is correct. It's quite unlikely, but unlikely events do have to happen some of the times.
I once played a game of risk against my sister, and attacked Russia with 12 armies against her lone one.
12 consecutive rolls of defensive 6 later, I had to call off the attack on account of all my men lying dead on the field.
Needless to say, I've avoided playing games of chance against her ever since.
Quote from: Slargos on January 12, 2010, 06:42:59 PM
I once played a game of risk against my sister, and attacked Russia with 12 armies against her lone one.
12 consecutive rolls of defensive 6 later, I had to call off the attack on account of all my men lying dead on the field.
Needless to say, I've avoided playing games of chance against her ever since.
Now that is a highly improbable event, about a 1 in 2 billion. Are you sure you're not exaggerating, or that the dice actually had something other than a 6 on it?
Slargos is a pretty and unique snowflake.
Quote from: DGuller on January 12, 2010, 06:53:36 PM
Quote from: Slargos on January 12, 2010, 06:42:59 PM
I once played a game of risk against my sister, and attacked Russia with 12 armies against her lone one.
12 consecutive rolls of defensive 6 later, I had to call off the attack on account of all my men lying dead on the field.
Needless to say, I've avoided playing games of chance against her ever since.
Now that is a highly improbable event, about a 1 in 2 billion. Are you sure you're not exaggerating, or that the dice actually had something other than a 6 on it?
I dunno - the thing about Risk is you roll so many freaking dice in a game that weird streaks are bound to happen.
But yeah, I can find that Slargy's sister beating him on 12 dice rolls is a lot more likely then rolling 12 consecutive sixes.
You don't have to believe me.
I didn't believe it myself, and I was there, watching in horror as it happened.
Highly improbable doesn't mean impossible.
Call me a liar if you will, though, I'm not going to invest any prestige in it. It's just a funny story. :D
Quote from: Tamas on January 12, 2010, 01:36:37 PM
Err, we learned this in college it can't be that hard... altough I dont remember much of it : (
I remember learning these things in middle school. I thought you commie countries were always ahead of us in math.
If you have 12 armies, she can only win 11 times before you have to call off the attack.
Quote from: Slargos on January 12, 2010, 07:16:48 PM
You don't have to believe me.
I didn't believe it myself, and I was there, watching in horror as it happened.
Highly improbable doesn't mean impossible.
Call me a liar if you will, though, I'm not going to invest any prestige in it. It's just a funny story. :D
Maybe she used loaded dice?
Quote from: Peter Wiggin on January 12, 2010, 09:44:05 PM
If you have 12 armies, she can only win 11 times before you have to call off the attack.
Which means 9 attacks with three dice, 1 attack with two dice and 1 attack with one die. Assuming she won and not with just 6s that's still only a 1 in ~66526 chance of happening. If Slargos was a moron and only attacked with one die at a time it drops precipitously to 1 in ~376.
Quote from: Razgovory on January 12, 2010, 09:19:08 PM
Quote from: Tamas on January 12, 2010, 01:36:37 PM
Err, we learned this in college it can't be that hard... altough I dont remember much of it : (
I remember learning these things in middle school. I thought you commie countries were always ahead of us in math.
Yeah now that you mention it, we did cover it in high school, but did not spend much time on it, unlike in college.
Quote from: Peter Wiggin on January 12, 2010, 09:44:05 PM
If you have 12 armies, she can only win 11 times before you have to call off the attack.
:huh:
I obviously had 13 armies in the territory from which I was attacking, if I was attacking with 12.
I don't think I've ever played with a rule that says you can't attack with one army.
Edit: Nevermind. Difference of terminology. I've always regarded "attacking" armies as total -1.
I don't care what the math is, but the chance of rolling x 10s (while mathematically described above) depends on who is rolling and what the desired result it.
Quote from: Viking on January 13, 2010, 10:56:55 AM
I don't care what the math is, but the chance of rolling x 10s (while mathematically described above) depends on who is rolling and what the desired result it.
:D
It sometimes appears that probability is just a well educated guess, and that reality does indeed load the dice. :ph34r:
So this happened in the first play through of the new "monster-light" Normandy wargame from GMT.
It is a team game with me and Justin Rice (one of the playtesters, I think) against Habs and another friend of ours. I am playing the CW forces.
Here is the situation at the end of the June 6th, Sword beach and 6th Airborne sector.
6th Airborne mostly dropped well, and is formed up to defend Pegasus bridge. The Germans left one of the airborne battalions unscreened however, and it managed to sneak into the suburbs of Caen, hiopefully blocking the bridges across the Orne north of Caen to German traffic. Probably going to be a suicide mission, but I hope to gum things up a bit for the Germans.
(https://languish.org/forums/proxy.php?request=http%3A%2F%2Fimg16.imageshack.us%2Fimg16%2F3040%2Fjune6thpmswordandairbore.jpg&hash=59b0c2ff4d1fe777f6afb04492165ad833160c89)
Just wait till the 21st Pz and their odd tanks steamroll you!
Quote from: PDH on January 13, 2010, 12:34:00 PM
Just wait till the 21st Pz and their odd tanks steamroll you!
I am hoping that they will have great fun trying to steamroll that poor Airborne battalion in the middle of the city.
Situation behind Gold and Juno beaches is interesting. Gold is pretty bottled up, but Juno is clear, and the Germans did not cover the road between bayeux and Juno beach, allowing the Canadians to send a regiment in behind the defenders at Gold beach, and siezing the important crossroads at Creully.
(https://languish.org/forums/proxy.php?request=http%3A%2F%2Fimg11.imageshack.us%2Fimg11%2F8153%2Fjune6thpmgoldandjuno.jpg&hash=46c0d27aea994c7794a83eaaad49886f8b35f549)