michiexile: (Default)
2006-04-07 10:03 am
Entry tags:

Fibbing it!

As a
New meter
Are proposed in a
Blog. Examples proliferate.
The enquiring mind would want to know if you can build
Lukoids - being fibs built instead on the Lukas sequences: Fibonaccis starting
Not with zero and one, but with any two numbers
Proceeding with the sum of pairs
To a sequence like

Would then be as
This sample shows my readers
Starting with one, then three, then onwards with sums
In the manner of fibs - it leads perchance to a more explosive line growth.

Could be thought out too.
This is a Cataloid - each line has just as many
Syllables as the corresponding Catalan number - though combinatorial explosion here quickly leads to bizarre lines which might degrade the quality way too much.
michiexile: (Default)
2006-02-07 11:00 pm

Borsuk-Ulam and West Wing

I have updated my blog with a short semi-popular article on the Borsuk-Ulam theorem. Please, go and read it! It's all mathy goodness!
michiexile: (Oh! My! God!)
2005-08-30 09:25 am
Entry tags:

On lotteries and gambling

I just answered the phone and spoke for a short while with a telemarketer. This time, I was apparently listed in the "previous customer"-section of "Kombilotteriet" - a swedish lottery. The (rather nice) lady on the phone spent several minutes explaining the current lottery setup, how buying one ticket (at SEK 200) would not obligate me automatically to buying more later et.c. et.c. up until the point where she was done with the spiel and wanted my input.

My input being "I have studied game theory enough to know that I will be playing a losing game against any company that has sane business practices." And I am not interested in lotteries for the excitement either - which pretty much clears out any and all reasons for participating.

Now, how can I be this certain that I won't be interested in gambling? I'm using a gauge from game theory called "Expected return". The expected return is the value measurement of an event (in this case the amount of money - or the amount of happiness due to the excitement - but since I don't care for exciting lotteries, I look at the money) times the probability that that money will return to me. At this point I have a 100% probability of losing the ticket price, and there will be some lottery-specific set of probabilities for various returns.

If the sum of winning*probability exceeds the ticket price, it would be worthwhile to actually participate in the game. I could in the long run expect to gain money on participating. However: positive expected return for me means negative expected return for the lottery company. Thus any lottery which would attract my interest would also automatically stop running since it's rather impossible to sanely run a business on the premise "Let's give other people our money!"

If I were to play, I would be playing roulette - which with the mean loss of 1/37 of everything I gamble is one of the very most fair games available. (With US roulette, this figure is 2/38) Swedish state lotteries with about 60% losses are things I avoid like the plague. (which DOESN'T mean I won't play if I get the ticket for free - that would mean I can expect 40% of the ticket price back! :)