Re: [HOE] probabilities

[J Tolle <jwtolle@altavista.com>]

On Thu, 12 April 2001, Theo McGuckin wrote:

> 
> > > Probability wise, what type of dice is best?
> > 
> > That depends on the target numbers you have to make most often.
> > 
> > 
> > By the way, has anyone failed to notice that you'll go bust
> > more often with three dice than with two?
> 
> I think this is a common misconception:
> 
> (Check me) To make things simple let's look at 2d10 vs. 3d10. Now there is
> ONE way to go bust on 2d10 (both 1's), and FOUR ways to go bust on 3d10
> (1st and 2nd die, 1st and 3rd, 2nd and 3rd, all three). So that's 4x the
> odds!
> 
> No it's not because there 100 possible die rolls on 2d10 (2 x 10) and 1000
> possible die rolls on 3d10 (10 x 10 x 10).
> 
> So for 2d10, the odds of going bust is 1/100
> And for 3d10, the odds of going bust is 4/1000 -> 0.4/100
> 
> Am I missing something?
> 

BZZT.

And you were doing so well, too.  You compared apples and oranges here - a common mistake in probability.

There are 4 possible "bust dice combinations" here, but you then compare that two total possible dice outcome.  You really should count the number of "bust outcomes" and compare that to the total possible outcomes (ie apples to apples)

Think of it this way.  If you roll the three dice one at a time, and your first two rolls came up as one's, you would know that you went bust, right.  You counted this as one possible outcome - But look closer.  Probability wise, there are ten possible outcomes of that last dice roll.  Game wise it don't matter if you roll that dice, BUT PROBABILITY WISE it sure does.

So rethinking the above logic (rolling a 3d10 still) you still get 4 dice combinations ending in bust, but those 4 combinations affect 28 possible outcomes*, giving you a ratio of 28/1000.  Greater than the 10/1000 you get for rolling 2 dice.

*(ADD: 1 on all three dice - 1 possible outcome.  1 on the first die and second die, and number but a 1 on the third die (since we counted already a 1 on all three dice) - 9 possible outcomes.  Repeat second step for when you roll a 1 on the first and third - 9 outcomes, and second and third - 9 more.  You get a total of 27.)

Jeff "If you dont believe me make a grid of all the possible rolls.  Honest, it works" Tolle


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