DR probability in Tuomo's Basic Infantry Example of Play

[seh]

On page 19 of Tuomo's Basic Infantry Example of Play (http://www.mindspring.com/~tqr/xop/InfXOP.pdf), we find the following discussion on SAN reduction in the Russian Prep Fire Phase:

This shot reduces the German SAN to 5 for the duration of the scenario.

This may seem small, but the SAN reduction from 6 to 5 cuts the probability of activating the German sniper by 33%. In ASL you need to have an appreciation for the bell curve of rolling two six-sided dice.

How do we come up with 33%? There are 4 ways to roll a 5 ([1,4], [2,3], [3,2], [4,1]), 5 ways to roll a 6 ([1,5], [2,4], [3,3], [4,2], [5,1]). Dropping from 5 to 4 is a 20% reduction. The IFT analysis at http://www.geocities.com/CapitolHill/Congress/1418/waslift4.htm confirms these percentages.

Is this an error in the Example of Play or in my interpretation?

 

[Anonymous]

The odds of rolling a 6 are 16.6 percent (6/36 you forgot that there are two ways to do the 3-3)

The odds of rolling a 5 are 11%.

5% drop on 16% is about a 33% reduction.

 

[seh]

You forgot that there are two ways to do the 3-3.

I was thinking about this before I posted when considering how one can come up with 33%. But how are [3,3] and [3,3] separate outcomes? All even DRs would have an "extra," identical combination by this argument.

Do we also say that there are two ways to roll a DR of 2: [1,1] and [1,1]? Are you disputing the layout shown at http://www.geocities.com/CapitolHill/Congress/1418/waslift4.htm?

 

[Anonymous]

> But how are [3,3] and [3,3] separate outcomes?

In the same way that 1,5 and 5,1 are seperate outcomes.

 

[Anonymous]

you forgot that there are two ways to do the 3-3

That's incorrect. There is only one way to get a 3, 3 result.

Here's the complete set of results possible when rolling two six sided dice.

1,1
1,2
1,3
1,4
1,5
1,6
2,1
2,2
2,3
2,4
2,5
2,6
3,1
3,2
3,3
3,4
3,5
3,6
4,1
4,2
4,3
4,4
4,5
4,6
5,1
5,2
5,3
5,4
5,5
5,6
6,1
6,2
6,3
6,4
6,5
6,6

As you can see, there is only one possible 3-3 result.

1,2 and 2,1 are two complete different results (Dice A was 1 and Dice B was 2 in one case, and Dice A was 2 and Dice B was 1 in another). That's why they're counted twice. They're two separate events. Re-ordering the dice doesn't count as a seperate event (Dice A is still 3 and Dice B is still 3).



Nat

 

[Anonymous]

There are 36 possible die-rolls. Try enumerating all of them and you'll find that 3,3 comes up twice. If you do it your way you will end up with far less than 36 possibilities.

 

[Fred Ingram]

There are 36 possible die-rolls. Try enumerating all of them and you'll find that 3,3 comes up twice. If you do it your way you will end up with far less than 36 possibilities.

Hmmm - if you look at the list of possible die rolls listed above your comment, and then actually count them - you end up at 36

I would suggest that due to your lack of knowledge about probabilities (and an inability to count), you do not provide your name to us and remain as GUEST

 

[seh]

If you do it your way you will end up with far less than 36 possibilities.

Whose way? Nat came up with exactly 36.

 

[huskerfan]

Ummm... no, I do believe Nat is correct... only one way to roll 3,3

"I roll a 3 with the red die and a 3 with the white die... or I roll a 3 with the.. red... and a... 3.... with.... the...... errrrr... that's the same thing... okay.... There is only one combination of 3,3 here..."

2 = 1,1
3 = 2,1 1,2
4 = 1,3 3,1 2,2
5 = 1,4 4,1 2,3 3,2
6 = 1,5 5,1 2,4 4,2 3,3
7 = 1,6 6,1 2,5 5,2 3,4 4,3
8 = 2,6 6,2 3,5 5,3 4,4
9 = 3,6 6,3 4,5 5,4
10= 4,6 6,4 5,5
11= 5,6 6,5
12= 6,6

Neat looking curve, too!

 

[Anonymous]

Sorry guys. My apolgies. Not enough sleep these days.

 

[seh]

So, we have concurrence on the 5/36 v. 4/36 SAN probability reduction. Is the 33% mentioned in Tuomo's Basic Infantry Example of Play incorrect, or is there some other factor involved besides pure DM probability?

 

[huskerfan]

The odds of rolling a 6 are 16.6 percent (6/36 you forgot that there are two ways to do the 3-3)

The odds of rolling a 5 are 11%.

5% drop on 16% is about a 33% reduction.

seh,

I think Toumo was referring to this aspect of SAN number changes.

 

[seh]

I think Toumo was referring to this aspect of SAN number changes.

By "this aspect," do you mean flawed probability analysis? Per our enumeration above, rolling a 6 has a 5/36, or 13.88%, probability; 5 has 4/36, or 11.11%. Now divide them and find a 20% reduction.

 

[huskerfan]

I think Toumo was referring to this aspect of SAN number changes.

By "this aspect," do you mean flawed probability analysis? Per our enumeration above, rolling a 6 has a 5/36, or 13.88%, probability; 5 has 4/36, or 11.11%. Now divide them and find a 20% reduction.

Could I have been ANY less clear in my last post.... blech.

Please ignore previous post by huskerfan... he was suffering from delusions of intelligence...


Let me try again...

Toumo was stating how big a deal it is to go from a SAN of 6 to a SAN of 5... your probability drops by 33% (16% to 11% is a 33% reduction in probability)... Gads, I hope that makes SOME sense... if not, please hit me with a herring...

 

[Nat Mallet]

Toumo was stating how big a deal it is to go from a SAN of 6 to a SAN of 5... your probability drops by 33% (16% to 11% is a 33% reduction in probability)... Gads, I hope that makes SOME sense... if not, please hit me with a herring...

That's correct, assuming Tuomo's odds were good. But we've determined that they are not. As seh has mentioned, the actual odds are 13.88% (5/36) and 11.11% (4/36). That's roughly a 20% reduction.

A 20% reduction is still significant, so Tuomo's point is still valid, even if his number are not.

Nat

 

[peterk1]

Hi Seh,

That earlier "2 ways of rolling 3,3" was not one of my better moments. Serves me right for trying to do stuff like this from work. I'm an engineer and am usually pretty intelligent but those earlier messages are embarassing.

Mind you - I did get the flawed numbers to fit nicely!

In short, yeah you're right.

And just for the record, I think there's a minor mistake in the CC section of the same article with some of the attack odds if I remember correctly. I went through it last week. Keep an eye out for it.