February 25, 2002

Lessons from the Slopes

I just got back from a ski trip to Big Bear (with a brief stopover in Santa Barbara to visit Rachel). Joining me on the trip were Nancy, Mike, Eric, Susan, Byron, and Karen. My philosophy is that all trips are in some way educational. On this particular excursion to exotic Southern California, I learned the following:

• Rachel is doing fine, but she has become very annoyed with another graduate student who is working with her on the same giant project. "I've decided to use my knowledge from my sociology classes to crush her," Rachel said. No, Rachel, no! You must learn to use your powers only for Good, never Evil!

• Rachel's husband Ben seems to be doing just ducky. He always seems to be doing just ducky. I think I'm not very good at reading him.

• It is good to know friends who have friends who have large cabins with vaulted ceilings in which you may stay for free.

• Lucky Charms are, cup for cup, healthier than Kellogg's Raisin Bran. Lucky Charms are equal or better in every vitamin/nutrient category, and they actually have fewer calories. The one category where Raisin Bran wins is fiber: 28% RDA to 7% RDA. But who needs regular BMs when you can have purple horseshoes and red balloons?

• Skiing in 50 degree weather is really nice, aside from the occasional slushy patch.

• Skiing in rental boots is not so nice, particularly when they give you blisters on your calves.

• Proficiency in Boggle does not translate into proficiency in Scattergories (vindication for the domain-specific knowledge theory of intelligence?)

• The official legal way to refer to "insider trading" is to call it a "Section 10(b)-5 violation".

• Contrary to popular myth, in blackjack a "bad" third base player does not affect the odds of another player winning or losing. Consider the following example:

  Dealer is showing 12, and so will bust if he draws a 10.
  The deck has N cards:  
    G   "good" cards (tens), 
    N-G "bad" cards (non-tens).
  
  If the third base player stays, the dealer's odds of busting are
  simply G/N.
  
  If the third base player hits, there are two cases:
  
    Case 1: a G/N chance he receives a "good" card.  There are then G-1 
    good cards left, so the dealer's odds of busting are now (G-1)/(N-1).
  
    Case 2: a (N-G)/N chance he receives a "bad" card.  The dealer's odds
    of busting are now G/(N-1).
  
  The total odds of the dealer busting are therefore:
  
    (odds of Case 1) x (odds that dealer busts given Case 1)
      + (odds of Case 2) x (odds that dealer busts given Case 2)
  
  Or:
  
    (G/N) x (G-1)/(N-1) + (N-G)/N x G/(N-1)
  
  which is, putting everything under a common denominator:
  
     G x (G-1)   (N-G) x G
     --------- + ---------
     N x (N-1)   N x (N-1) 
  
  which is, expanding and cancelling terms:
  
     G^2 - G + GN - G^2      GN - G       G x (N-1)     G
     ------------------  =  ---------  =  ---------  =  -
          N x (N-1)         N x (N-1)     N x (N-1)     N
  
  Which is the same result as if the third base player had stayed.