Shamrock & Coke

This infused vodka took me three days to make, although the vanilla beans may not really need that long to contribute their flavor. My first test batch (in smaller quantity) was way too minty, so I reduced both the amount and time for the mint.

Shamrock Shake vodka

Supplies:

• two 1-liter glass bottles (I used these)
• Fine mesh strainer
• Funnel
  

Ingredients:

• 1 liter of decent vodka (I used Smirnoff)
• 6 vanilla beans
• 1 teaspoon of dried spearmint

Procedure:

1. Place vanilla beans in glass bottle.
   
2. Fill bottle with vodka, close bottle, shake vigorously, then set aside.
   
3. Shake a few times per day for three days. (Not sure how much the shaking really matters.)
   
4. After three days, add mint to bottle, close bottle, shake, then set aside for three hours, shaking occasionally.
   
5. After three hours, set up the strainer (to catch the mint) above the funnel above the second (empty) bottle.
6. Slowly pour the vodka from the first bottle through the strainer (into the funnel and second bottle). The goal is to transfer the liquid to the second bottle with as few solid bits as possible, and the strainer's job is made easier if you keep as much of the mint in the first bottle as possible. (Pouring slowly works well enough that I have no interest in using a coffee filter, paper towel, cheesecloth, etc.)
7. Store at room temperature.

Interesting when sipped. My preferred concoction, however, is...

Shamrock & Coke

Do you really need instructions? Take glass, add ice, add desired amount of vodka, add Coca-Cola. Drink. Tell your friends how awesome it is. When they respond unenthusiastically, pour yourself another one.

UCL quarterfinal draw - English odds

The sun rises in the east, and all four English clubs make the Champions League quarterfinals. Now that we're here, what are the odds of none of the four facing each other in the quarters? What are the odds of all four being placed in the same half of the bracket? I'm sure I could find this on the web somewhere; I do my best thinking in the shower, however, so the numbers below are brought to you by Johnson & Johnson shampoo and Dial soap. Let's dive in...

I'm mainly going to consider how to group 8 teams into 4 pairings, without regard for home and away legs or position of the pairings in the bracket. There are 8! ways to arrange 8 objects in order, except we don't care about the 4! ways in which the 4 pairs can be arranged, and we also don't care about the 2! ways in which each of the 4 pairs can be ordered. This can be expressed as

8!
--------------------
4! * (2!2!2!2!)

which equals 105. So there are 105 possible pairings for the quarterfinals. (Note that I've ignored the position of the pairings in the bracket, and I'll continue to do so for the most part.)

Starting over, if we only consider each club as English or not, there are three cases for possible pairings:

1. EE EE xx xx
2. EE Ex Ex xx
3. Ex Ex Ex Ex

Case 1 has each English club facing another English club. Within this case, each English club may face any of 3 opponents, although once that selection is made, the other all-English matchup is determined. Likewise, there are 3 possible matchups for the 4 non-English clubs. There are 3 * 3 = 9 pairings with two all-English matchups. Please note that if Case 1 occurs, there is only a 1-in-3 chance that both all-English pairings will be placed on the same side of the bracket.

Case 2 has exactly one all-English matchup. Selecting this matchup requires choosing 2 objects from 4, and there are 6 possibilities. There is also exactly one non-English matchup, for which there are also 6 possibilities. We then know the clubs for the remaining two games, although there are 2 possibilities for selecting which English club will play which non-English club. There are 6 * 6 * 2 = 72 pairings with exactly one all-English matchup. Please note that if Case 2 occurs, there is a 2-in-3 chance that the all-English matchup and the non-English matchup will be on opposite sides of the bracket.

Case 3 has no all-English matchups, so that each pairing includes one English club and one non-English club. For each English club, we need to select the non-English club it will play, which is simply arranging 4 objects in order. There are 4! = 24 pairings with no all-English matchups.

Note that 9 + 72 + 24 = 105; two different methods, same result.

A couple of calculations to sum up:

• Chance of at least one all-English matchup in quarterfinals:
  81/105 = 77.1%
• Chance of all English clubs being placed in the same half of the bracket:
  9/105 * 1/3 = 2.9%
• Chance of Liverpool knocking out Chelsea:
  (no math required)