Friday, October 30, 2009

A statistical modification

It seems possible we have been making an erroneous assumption.

For example, when discussing the possibility of getting Irresistible Force, we several times have said there is a 1-in-11 chance. Seems logical...you roll a pair of dice and you can get a 2,3,4,5,6,7,8,9,10,11, or 12. 11 possible outcomes. Or are there?

The only way to get a "2" is to roll a one on each die. One possible way.

The only way to get a "3" is to roll a one on one die and a 2 on the other. Since there are 2 possible ways to do that, there are actually 2 chances to score a 3.

Add in a "4" and it gets more complicated. You can roll a "4" and a "1" or each die can be a 2, so three possible ways.

By the time you get to rolling a "7" the numbers add up exponentially. You can roll a "6" and a "1", a "5" and a "2", or a "3" and a "4", more possible combinations than any other which is why statistically speaking, a "7" is the most frequent outcome for rolling a pair of dice.

So there are actually 36 possible combinations, not 11.

This changes things drastically.

Just something to think about.

3 comments:

Fullur said...

Interesting. Yes, when speaking of chances we have only considered possible result totals, not possible combinations of dice. Taking actual rolls into account does alter things considerably.

kennyB said...

It's funny, because we have said it both ways, one for Irresistable and one for Leadership. We have always (so far as I know) used correct odds calculating (chance x chance) on Leadership tests, including re-rollable stubborn tests and rolling on 3 dice. Pretty humorous.

Darth Weasel said...

I at least have been doing them both wrong...thinking I had a 1 in 11 shot at Irresistible and thinking a Stubborn 8 with re-roll was 89% against breaking when in truth it is....lets see...10 could fail out of 36, then of those 36 10 could fail so roughly....93% pass rate instead of 89. SO not a huge difference...but still, a 4% edge has made a lot of poker players rich. Just sayin; :-)