Friday, November 25, 2005

P(Angry, Confused) = 1

My brother has been getting confused with time zones and calling me at all hours of the night to ask me questions about card probability. He has been having poker nights with mates in Aspen and want to know the following:

If four cards are placed face down on a table, what is the probability of two of them being hearts?

Originally we though it could have been dependent on the order in which they were turned, i.e. 1 at a time would amount to: P(2H) = 1/4 + 13/51 + 13/50 etc.; while all at once would be P(2H) = 1/4 + 1/4 = 1/2. The answer of a half was what we went with. After thinking about it this didn't make sense. For example, if the question was asked:

If four cards are placed face down on a table, what is the probability of FOUR of them being hearts?

By following the logic above, the probability would be P(4H) = 1/4 + 1/4 + 1/4 + 1/4 = 1. Therefore, the head will explode in a puff of logic.

Therefore, TO GOOGLE ANSWERS! and the return of the old combinations and permutations from high school. Below for your perusal (Shaun) are what I believe to be the results of a few combinations. They are likely to be wrong, so feel free to correct me (Snook). I've given the method by which I worked the first two out as well. Okay...

If 5 Cards are dealt face down on the table, what is the probability of ONE of these being a heart

In a 52 card deck there are 52C5 possible combinations for a five card deck.
52C5 = (52!)/(5!.47!) = 2,598,960 possible hands

Of the 5 cards dealt, from the 13 hearts in the pack, there are 13C1 possible combinations of a hand with 1 heart
13C1 = (13!)/(1!.12!) = 13

If only one card can be a heart, the other cards in the hand have to be something else. Therefore from 39 possible non-hearts to draw the 4 cards from, there are 39C4 possible combinations.
39C4 = (39!)/(4!.35!) = 82,251

Therefore, the number of possible 1 heart, 4 other card combinations (1H, 4O) is 13 x 82251 = 1,069,263

Therefore P(1H,4O) = 1069263/2598960

P(1H,4O) = 41%

Make Sense? Lets try 2 hearts.

If 5 Cards are dealt face down on the table, what is the probability of TWO of these being a heart

Number of possible five card combinations = 2,598,960

Number of 5 Card combinations containing 2 hearts is 13C2
13C2 = (13!)/(2!.11!) = 78

Number of 5 Card combinations containing 3 other cards is 39C3
39C3 = (39!)/(3!.36!) = 9139

Therefore, the number of possible 2H, 3O combinations = 78 x 9139 = 712842

Therfore P(2H, 3O) = 712842,2598960
P(2H, 3O) = 27%

Other Combinations:
  • P(0H, 5O) = 575757/2598960 = 22%
  • P (1H, 4O) = 1069263/2598960 = 41%
  • P (2H, 3O) = 712842 / 2598960 = 27%
  • P (3H, 2O) = 211926 / 2598960 = 8%
  • P (4H, 1O) = 27885 / 2598960 = 1%
  • P(5H) = 1287 / 2598960 = 0.05%

    Please note. I am often full of shit and may be wrong. Doesn't happen often, but it has been known to

  • Monday, November 21, 2005

    Galileos at the Observatory

    The Wife and I recently celebrated her 27th Birthday at Galileos at the Observatory Hotel. We've often wandered past on our way down to the Lord Nelson for drinks and wondered what it we be like to be sitting in those comfy, antique chairs. Courtesy of the Entertainment Book, off we went.

    We started with a Martini at the Globe Bar as we were a little early and didn't want to rush. There were only around four people in the restaurant the entire night, so as they wern't busy we went for the degustation menu. Not that we normally wouldn't, but when it's quiet, the kitchen will normally have more time to put into the food.

    Appetiser was a Egg Cocotte - a smooth egg custard with foie gras and creamed truffles. The truffles were very strong, but it got the juices flowing.

    Next up was a platter of Tasmanian Oyster with Roe, a Veal Carpaccio which tasted exactly like a packet of Kettle Smoked Ham Chips, and a piece of Big Eyed Tuna wrapped in Prosciutto with a Pureed tomato sauce. The Tuna was the worst of the night, the Oyster one of the best. The tomato sauce had fennel infused through it and completley overpowered everything else.

    Following this was a serving of beetroot noodles with a fish broth and a citrus paste. Think soba noodles - cold, but not unpleasant. The citrus paste was a milder type of wasabi. It didn't have the nasal kick that the wasabi does. I liked this one, but the wife wasn't a huge fan. She's had bad run ins with Soba Noodles in the past.

    We took a bit of a breather for a while before we started our meat and fish courses. The fish came first, an encrusted ocean trout served with a japanese root vegetable that I'll be buggered if I can remember. This one was The Wifes favourite. The meat was a Grade 5 marble Wagyu Beef, in a veal jus reduction. Top notch - the beef reminded me of an nice al dente gnocchi - firm, but as tender as anything. We had the beef with a glass of a nice cab sav that I can't remember the name of.

    After another breather, we took on the desserts. The first was a mango sorbet with a chocolate truffle in a coco-pop cream sauce (I'm kidding about the coco-pops - texture apparently). The second was a selection of gelatos - pistachio, hazelnut and coffee. We though they came in the wrong order. The sorbet should have come first followed by the gelato and the chocolate truffle, but it worked anyway.

    At this stage we undid the belts, and prepared to fall asleep in our chairs, but the waiter woke us up and served us a complimentary plate of petit fours with our coffee. The late was decorated with "Happy Birthday Steph". Smooth Mr Japanese Chef.

    At the end of it all we could barely walk out. Four hours of eating and drinking and a hefty hunk out of the credit card, but it was worth every cent. The best spot I've been to in a long while.

    Monday, November 14, 2005

    Get behind him!

    Your vote, is a vote for the death of Idol

    Happy Birthday to My Darling Wife

    27 Today! And not looking a day over 30!


    p.s. shes the one in the green

    Tuesday, November 01, 2005

    Melboure Cup Tips

    Tips for the Cup:

    1. Railings (7)
    2. Maykbe Diva (1)
    3. Mr Celebrity (23)

    Both Railings and Maykbe Diva are paying well ($6.50 and $4.20), and Mr Celebrity is a nice outsider ($16.00) who would be good for a placing.

    Giddy Up!