I just wanted to share this wonderful find that my friend brought to my attention. enjoy.

I found this image while surfing the net. This of course is a paraphrasing of the actual indicated passage but the meaning is accurately captured.

In the casino, the cardinal rule is to keep them playing and to keep them coming back. The longer they play, the more they lose, and in the end, we get it all. Ace Rothstein (Robert De Niro), Casino

Blackjack is the only fair game in the casino. It’s the only game where you don’t expect a net loss after repeated play. Ever other game will cost you money in the long run. Take roulette for example. For any bet the expected earnings is negative. If you make the same bet over and over and add up what you have at the end you will always find that you have lost money. Therefore, if the casino keeps you playing, they will eventually win your money. Its statistically inevitable.

I came across a “strategy” to win at roulette that I wanted to discuss. A quick google search will reveal that this strategy is everywhere and some pages offer some discussion as to why it is supposed to work. The strategy is as follows:

Now, before any of you go running to an online casino to win big money consider yourself warned: This strategy does not work. The flawed reasoning behind the strategy is simple. A progressive series of losing numbers is increasingly unlikely and by continually betting on the red you are essentially betting on the change of such a series occurring. Since that chance is increasingly small your probability of winning the next round in the series approaches one.

The problem with this logic is two fold. The most serious of these errors is that the roulette wheel has no memory of what occurred in the previous round. A bet on red has a 18/38 = 47.37% of winning regardless of what occurred in the past. There is a probability that is approaching zero but it’s the probability that a specific sequence occurs in a particular order. The sequence “black, black, black, black, black, red” is just as likely as the sequence “black, black, black, black, black, black” which is also just as likely as the sequence “black, red, black, red, black, black” or any other specific sequence of six outcomes. (Here i have neglected the difference between black/red and loss/red, which produces slight difference in the probabilities but does not change the discussion appreciably.) However, the probability of any of these three is approaching zero as the length of the sequence grows. What drives the probability to zero is the fact that the number of possible sequences is growing exponentially.

The second flaw in the logic is that the strategy ignores the fact that you have to have enough money to cover the geometrically increasing bet size. Everyone enters the casino with a finite amount of money to bet. Even if they allow themselves to mortgage their lives there is still a finite amount of money from which to draw. Since the probability of 5 loses and a win is a little less likely as 6 loses, the odds are, that next bet is going to cost you a lot. If you continue to play you will eventually hit a sequence where you cannot afford to bet the increased amount and collect your net dollar. And what is worse is that that final bet will wipe you out financially.

To make this more concrete I decided to model the strategy numerically by simulating repeated plays of a game of roulette. Starting with some initial pot size, the program will play the outlined strategy above. However, once the pot size hits zero or less, the pot size is set to zero for the remainder of the simulation – once you have lost all your money it stays lost. I then repeat this process thousands of time and average the size of the pot after n bets to obtain the expected pot size at the nth bet. The results are plotted below as a percent of the initial pot size.

The red, green, blue and black lines correspond to initial pot sizes of 100, 200, 300 and 400 dollars.  The results are striking and the strategy clearly fails.  Even for the large pot sizes the player is broke, on average, before 5000 pays have been made.  Furthermore, the player expects to begin losing money immediately.  This is steaming from the fact that a red bet has a negative expectation value and geometrically increasing your bet to cover your loses doesn’t change this fact.

The reason the larger pot sizes result in a slower rate of loss is because the initial bet of one dollar was used for each of the cases.  As a result, the player is betting a smaller percent of the pot per turn and thus the rate of loss is slowed.  If you scale the initial dollar bet accordingly all of these curves would fall on one another, as shown below.

Happy Halloween everyone.

I found this clip on Darren Brown’s blog this morning. It appears that a group of Christian fundamentalists are warning America about “the potential for curses to be passed through candy during Halloween”. You even have to avoid the stores because demon’s cannot differentiate between store bought candy and the spoils of Trick or Treating.

Clearly the woman responsible for this is nuts and I am glad to see the reporter had someone from the Christian community on the program to point that out.

Oh, and watch out for demon infused candy canes at Christmas.

I just finished listening to the Non Prophets podcast from October 10th of this year. P.Z. Myers, of the science blog Pharyngula, was on as a guest. The topics covered Bill Maher’s award at the AAI convention, Maher’s crazy ideas on vaccination, Ray Comfort’s forward for “The Origin of Species” and some of the sexual scandals in the church.

You can download a copy here . It’s well worth listening to.

As the title says, I am not a fan of Glenn Beck and so I particularly enjoyed these two videos. One is from the youTube user Thunderf00t, who I have mentioned in the past. The second is from another youTube user, The Liberal Viewer. The best I can tell, he is an ACLU lawyer working out of Sacramento CA, and he makes quality political commentary videos.

Elinor Ostrom and Oliver Williamson have been awarded the 2009 Nobel prize in economics.

Ostrom (USA) is the first woman to ever win the prize and was awarded half for “her analysis of economic governance, especially the commons.”

Williamson (USA) was cited for “his analysis of economic governance, especially the boundaries of the firm” and awarded the remaining half.

In a recent work Professor van Wolde concludes that the first line of Genesis may in fact be a mistranslation from the original Hebrew.

Excerpt:

Professor Ellen van Wolde, a respected Old Testament scholar and author, claims the first sentence of Genesis “in the beginning God created the Heaven and the Earth” is not a true translation of the Hebrew.

She claims she has carried out fresh textual analysis that suggests the writers of the great book never intended to suggest that God created the world — and in fact the Earth was already there when he created humans and animals.

Full Article

Some friends of mine from high school carved these gems over the weekend.

As you are no doubt aware, the Nobel Prize winners were announced this past week. The most talked about award was the Nobel Peace prize which was awarded to President Obama. The official citation was for “his extraordinary efforts to strengthen international diplomacy and cooperation between peoples” but the decision has a number of people wondering if it was warranted given his relatively short time in office.

But perhaps that is a discussion best left for another post. Today, I just wanted note the recipients of the remaining awards (the Economics prize will be announced on the 12th of October).

The physics prize went to three American researchers for their work on fiber optics and light sensor technology which were key to the advancement of information technology. Half of the prize was awarded to Charles Kao. The remaining half was split between Willard Boyle and George Smith.

The chemistry prize was split equally between Venkatraman Ramakrishnan (UK), Tomas Steitz (USA) and Ada Yonath (Israel) for their studies on the structure and function of the ribosome.

The Americans also did well in the field of medicine. The prize was split between three Americans, Elizabeth Blackburn, Carol Greider and J. Szostak for their contributions to the understanding of how chromosomes are protected by telomeres and the enzyme telomerase.

Herta Muller (Germany) was the sole recipient of the Nobel Prize in Literature for her poetry and frankness of prose depicting the landscape of the dispossessed.

If you’re interested, detailed write ups of the academic background for each of the awards this year can be found on the Nobel Fountain’s website.