Iron Man

Last night Betsy and I went out on a double date with friends to see the movie "Iron Man"--it was a fine movie for what it was, a summer popcorn flick. Not the sort of thing that teaches you anything new about the human experience, or changes one in any significant way, but it was entertaining enough!

After the movie we went to the Duke of York pub for supper. It was nice walking in the Yorkville area at night with the lights and the people milling around. Got home feeling pleasantly full. Betsy and I have a great life.

Last night I dreamt that I forgot to take the communion bread out of the freezer for the Chancel Guild when I came to church Sunday morning. I do forget to do that sometimes, but it's a minor thing, they can always throw one into the microwave. I had some other unusual dreams, too, including one where I was playing Black Jack at a casino and doing quite well using the Martingale System.

The Martingale System is a betting strategy useful in situations where you are making consecutive bets, with approximately 50% chance and win the amount bet. Basically, every time you loose you double the amount your are betting in the next round. For example, after loosing four dollars you bet bet eight, which means that you recover the loss if you win. If you loose, you bet sixteen. So even if you loose several times in a row, you will make back your money when you finally do win.

The problem is that this model assumes infinite wealth and no limits on how much you can bet. In real life, neither of these are true--all it takes is a few losses in a row to exceed the available cash for betting and also exceed the table limits. In fact, that's one of the reasons why casinos have table limits--to defeat this kind of betting strategy. But it doesn't really matter, since you can mathematically demonstrate that as long as the amount of money you have available for betting is finite, you will eventually run into a loosing streak long enough to bankrupt yourself!

Here's the math, for those of you that like math:

Let q be the probability of losing (e.g. for roulette it is 20/38). Let y be the amount of the commencing bet (e.g. $10 in the example above). Let x be the finite number of bets you can afford to lose.

The probability that you lose all x bets is qx. When you lose all your bets, the amount of money you lose is

The probability that you do not lose all x bets is 1 − qx. If you do not lose all x bets, you win y amount of money. So the expected profit per round is

Whenever q > 1/2, the expression 1 − (2q)x < 0 for all x > 0. That means for any game where it is more likely to lose than to win (e.g. all chance gambling games), you are expected to lose money on average. Furthermore, the more times you are able to afford to bet, the more you will lose. (source)

The trade in this system is steady gain at the risk of a string of losses.

I think they should teach game theory in seminary. It's important to be able to evaluate strategies in any kind of leadership.

-t