Trial, re-trial Probabilities and Superstition

Trial, re-trial Probabilities and Superstition

When evaluating the probabilities of an outcome, I’ve seen many superstitious behaviors, from kissing dice to wearing a lucky shirt. The core nature of superstition relates to trial re-trial probabilities, and it’s worth a closer examination.

When you toss a fair coin five times and it always comes-up “heads”, what is the probability of a “heads” on the sixth roll? A scientist will tell you that the probabilities between trials are always exactly the same regardless of previous outcomes, but real-world experience documents “streaks” which cannot be explained by science.

So, is the belief in “streaks” superstitious? How do we reconcile the fact that trial, re-trial probabilities are always exactly the same with the equal fact that “luck” runs in streaks? After all, it’s silly to leave a table when you are winning every hand, and it’s not too bright to stay at a table when you are loosing every hand.

Clinically, superstitious behavior occurs when the subject feels that their outcomes are governed by random chance, and there is a natural tendency to search for causation, even when none exists. Hence, it’s no surprise that many professional gamblers indulge in superstitious behavior.

When lightening strikes thrice

In real-world observations, streaks do exist, and random number analysis shows that winning-losing “streak” combinations occur quite frequently. Is it superstitious to stay at the gaming tables when you are “on a roll”?

We are at a client site where there is little to do after work but gamble in the casinos. Janet was at the roulette table today, and she bet straight-up on black 25, plus a 5x street bet. She was thrilled to win the first time, and left the bet on the table.

The second time the wheel landed on black 25 again (with Janet retaining her original bet) , a probability of (38**2) , or a 1,444 chance of “lightening striking twice”. But that not the end of the tale.

To further confound probability theory, the third roll also returned a black 25 (with her same bet retained), and the roulette croupier stopped play to show the pit boss about this amazing event, as he handed Janet her stack of $100 chips. (we were afraid that they would throw her out, as casino’s are not public places, and large winners are frequently ejected).

The statistical probability of the same number hitting three times in roulette are 38 cubed, of (38**3 = 51,942), a 50k chance that the same number would come-up three times, and even more remarkable that Janet would retain bets on these numbers.

Now, we loose as much as we win in roulette, but nobody can deny that amazing statistical “streaks” occur. Any professional gambler will tell you to “ride the wave” when you are hot and “lay low” when the cards are against you.

Beginners luck

I believe in beginners luck and I’ve seen enough first-hand anecdotal evidence to believe in the beginners luck. The very first time that Janet played in a Texas Hold-em tournament, first hand, she got a royal straight-flush, something that occurs once out of 65,000 hands.

On Janet’s first time playing bingo, she won a cruise ship jackpot of over $4k, and call me superstitious, but I’m a firm believer in beginners luck.

Psychologists have done many studies on superstitious behaviors. This paper titled “An Exploratory Investigation of Superstition, Personal Control, Optimism and Pessimism” is great, and check out the great book “Believing in Magic: The Psychology of Superstition” for a great read about superstitious behaviors and scientific probabilities.

Cruise the Panama Canal

Janet and I recently completed a trans-continental cruise and we got the pleasure of going through the Panama Canal.

With Manual Noriega safely locked-up is an American prison, it’s a safe and fun ride. The Panamanian authorities are always on the lookout for drug smugglers, seeking suspicious ships (like the one below) that may be carrying marijuana:

We have first-hand experience with locks ourselves, as Janet and I took the kids on a cross-country barge boat trip in Ireland a few years back, a 45-foot floating mobile home, complete with kitchen, bathroom and head.

As we traversed the Emerald Isle, we had to operate the locks ourselves and Andy and Jen became competent lockmasters, elevating us up to 15 feet at a time to bypass the weirs (waterfalls) that dot the ancient canals.

Transition Cruising

A great way to traverse the Panama Canal is on a “transition cruise”, which happens in the late spring and fall, when the ships shuttle between Alaska in the summer and the Caribbean for the winter. You can also go through the canal on the around the world cruises.

When riding a cruise ship through the Panama Canal, it’s best to have your breakfast on your veranda so you can watch your ships pass through the locks. Here is a view of the east entrance of the Canal Zone:

The cost of the Panama Canal crossing for the ship is over $200,000 for the nine-hour voyage, a relative bargain when you consider that the fuel costs alone to go “around the horn” costs over $800,000 and takes three weeks. The Panama Canal serves over 15,000 ships per year, with dozens of ships queuing-up in the pre-dawn darkness:

A Man, a Plan, a Canal: Panama

The Panama Canal is the engineering triumph of the 20th century, built at a cost of over 25,000 lives lost, mostly due to accidents (landslides) and disease (yellow fever and malaria). Disposing of the dead bodies was such a problem that the canal construction firm started pickling the corpses in oak barrels and selling them to medical schools for research. Barrels of pickled construction workers were neatly stacked in the dissection labs, a morbid side-benefit of the Panama Canal project.

The strange geography of Panama is like an “S” laid on its side, such that a westward passage actually travels in a southeastern direction:

The largest ships (called Panamax ships), barely fit through the giant locks, and you can literally touch the side of the locks from your balcony. The ships queue-up by the dozen awaiting their turn to enter the Canal, and a Panamanian pilot takes-control of the ship. The first westward-bound locks are the famous Gatun locks, raising the ship 85 feet to Gatun Lake:

The panamax ships barely fit, with just inches to spare. Some of the largest cruise ships (i.e. the QE2) cannot fit in the Panama Canal. Panama recently announced plans to create new, wider lock channels at a cost of over four billion dollars, a project that will not be completed until 2022.

The “cut” is where it was necessary to chop through the continental divide to expand Gatun Lake. Here is a part of the cut, where landslides still occur:

On the pacific side we have the Pedro Miguel lock:

Statistical Probabilities in Blackjack

All casino games favor the house and the “Law of Large Numbers” guarantees that you will loose in the long-haul. However, there are some games that approximate a fair deal:

Single deck black jack – If you learn to accurately count cards (a perfectly legal practice as long as you don’t use artificial appliances), and recalculate probabilities you can win big money. It’s not hard to develop a mental mnemonic for card counting (Hint: remember than ten-value cards comprise 30% of the deck).

Blackjack probabilities

Blackjack is a non-zero sum, two person game (you play against the dealer), with well-defined decision rules. If you are not able to count into a single-deck, the rules of blackjack are very straightforward, and fully quantifiable. I’ve won several blackjack tournaments, and it amazes me how many people do not fully understand the decision rules for playing blackjack.

Many people only know the basic rule for blackjack (hit 16, stand 17), but many people forget that the dealers up-card also influences your chances of winning. The most common value of cards in the deck is a ten-value (16 cards, or 30% of the deck), so many experienced blackjack players will assume a ten for the dealers hidden card.

The probability of the dealer busting on the first draw

More sophisticated players will factor the probabilities of the dealer’s down-card, assuming at there is a 30% change that the down-card is a ten-value. Using this maximum assumption of a ten down-card, you can develop a set of hit-or-stand rules.

For example, if the dealer has a six up-card, then the dealer probability of busting is over 18%, and the black jack rules state that the dealer must hit up to 16.

Note: These probabilities have been simplified for easy understandability. Sophisticated players will mentally adjust these probabilities based on the known cards in their hand.

Dealer with a deuce up = Dealer busts with a face-card or a ten =
(16/52)*30% = 9%

Dealer with a three up = Dealer busts with face-card, ten or nine =
(20/52)*30% = 11%

Dealer with a four up = Dealer busts with card greater than seven =
(24/52)*30% = 14%

Dealer with a five up = Dealer busts with any card greater than a six =
(28/52)*30% = 16%

Dealer with six up = Dealer busts with any card greater than five =
(32/52)*30%) = 18%

When it’s safe to hit

Remember, it’s always safe to take a hit if you have eleven or less (always go down for a double with eleven), or any “soft” combination (where one card is an ace), up to seventeen.

When to stay?

As we see above, if the dealer has an up-card of a six, the dealer has an 18% chance of busting on their draw, and you must compare their probability of busting with your probability of busting.

For example, if you and the dealer have a total of 16, both you and the dealer have an 18% chance of busting, and many players (me included) will stand and let the dealer draw out.

Of course, it’s the random nature of blackjack that makes it exciting (plus the challenge of single-deck blackjack, where you get a change to practice remembering the played cards), so these probabilities only serve as guidelines. Remember, anything can happen with the dealer has a five-deck shoe (nobody but Rain Man can count into a five-deck shoe), but these basic probabilities still apply.

BC Oracle Cruise for 2007

Computer Classes at sea!

With the super-cheap cruise specials these days, Janet and I decided to do a computer class on a cruise ship. We are having our senior staff aboard and opening-up the class to the public:

Oracle Cruise 2007

At these cheap prices, we are bringing quite a crew and it has some really cools ports of call, and we get to visit some of our clients as-well:

Nassau – Nassau is one of the world’s most popular cruise ports. With the Atlantis mega-resort on Paradise4 Island dominating the skyline, Nassau is would renowned for great scuba diving and you can join your instructor for a dive in the pristine waters.

St. Thomas – One of the most pristine areas of the Caribbean, St. Thomas rises hundreds of feet out of the turquoise seas for breathtaking panoramas. St. Thomas is also known for great duty-free shopping and Meagan’s bay, one of the most beautiful beaches in the world.

St. Maarten – Located in the Netherlands Antilles, St. Maarten retains much of its original charm. For the more adventurous, travel to the French side of the island for amazing French food and culture.

We are all certified scuba divers, so it should be a great time, combining learning and fun.

We are all fat, but still able to scuba, as this picture of me, taking time-off after working with a client:

Our last company cruise was huge fun and we expect this one to be the best cruise yet.

New markets for cruise ships

Cruises expand into new markets

We have many clients in the Caribbean and I was amazed to discover that Cruises are now competing with business travel. The sheer numbers of megaships plying the turquoise seas are mind-boggling, and we recently noticed three ships docked at USVI on a single day. Janet and I cruise frequently, and it’s great that it’s now cost-effective for business travel.

The high-end cruise passengers are demanding larger and more glamorous ships such as the new Noordam and the Royal Caribbean Freedom-class monster ships, with their ice skating rink and giant shopping malls, gleaming 21st century cruise experiences, like this photo from my favorite, Geek cruises:

These mega ships have everything imaginable, but most of all they provide “cruise ship envy”, as they are clearly the coolest ships in the ocean right now. Gladly for us, this demand has lead to amazing cruise bargains, as the lines try to keep the less-attractive older ships full:

Tiered cruising

This creates a multi-tiered cruise market, and we see these “classes” of cruising, and “cruise ship evny” from those aboard on the less-fancy ships:

First Class – Lines such as Cunard and Crystal Cruises offer-up first-class cruising and more than double the price of the “economy” class cruises.

Moderate – Royal Caribbean, Holland America and Celebrity are next on my list, with huge, amazing ships, pay-extra restaurants and great service.

Economy – Carnival cruises low cost less than staying in a Holiday Inn, and the Costa ships are designed for the economy-minded traveler, with very few balconies, just portholes:

Now, the really cheap cruise rates are on the older ships, the 1970’s “Love Boat” style ships that your grandparents enjoyed. Cruising has been going-on since ancient days, and they are regularly replaced by new models. This is the “original” Noordam:

New Cruising markets

I’ve noticed three areas where cruising has become an amazing bargain, especially for technical training, assisted living and for business travel. Now, these are the “classic” cruise ships, the smaller ships that have a classic charm. They still have skeet shooting, on-deck driving ranges and roulette wheels with a bias that Forrest Gump could figure-out:

Classroom Cruises – Our good friend Neil Bauman at Geek cruises spends his days on cruise ships conducting some great technical seminars at-sea. They are great and we have been on two so-far.

Business travel – It’s amazing that cruise prices are now lower than business class airfare. Today, one of our people is visiting a client in the Caribbean and for less than the price of one plane ticket they were able to get a great 5-day cruise (with a nice veranda room). The client is happy that we saved them money, and the consultant is ecstatic for the free vacation. I like to go to Chile in the winter (It’s summertime there), and for the cost of a plane ticket we can take a 11-day cruise and visit ports along the way! It’s also cheaper than flying to cruise to the south pacific, but you are stuck on a 20-day trip, visiting ports like Bora Bora, Tahiti and Samoa. Bummer:

Assisted Living – Grandma and Grandpa can live on a cruise ships for less than $5k a month, far cheaper than the average cost of assisted living homes. It’s perfect. Grandpa thinks you are spoiling them (and mention you in their will), and you save thousands of dollars a year while you have the peace of mind of knowing that Granny has Bingo every single day as they float-away their golden years.

“Living on a cruise ship provides a better quality of life and is cost effective for elderly people who need help to live independently, according to a study published in the Journal of the American Geriatrics Society”

Staying Connected while cruising

Janet and I rent a satellite phone while cruising, the giant brick phones like we used back in the 1980’s:

They only cost about $100 per week to rent plus $1.75 per minute (call anywhere in the world), so they are not prohibitively expensive. Col. John was even able to hook-up his laptop to the sat phone to server a client from the middle of the ocean.

Being cheap, I use the same technique that we used back in the 1990’s with TAPSYS, a CompuServe tools that would quickly connect, upload and download your e-mail and then quickly disconnect, saving cash on connect time and allowing you to answer your e-mail at a leisurely pace.

Andy Rooney pwned by Ali G.!

Ali G and Andy Rooney

Borat movie mania is striking the USA, with hundreds of people queued-up for tickets to the Borat movie here in North Carolina.

Don’t miss the music album of songs from the Borat movie including the hit song “Throw the Jew down the well”!

However, most folks don’t know about Ali G. the rapper-wannabee played by the talented Sacha Cohen, a fellow with the Moxie to interview the old curmudgeon himself, Andy Rooney:

This hilarious video shows Andy Rooney taking-on Ali G. (Borat), with great results, actually intimidating Cohen, a rare event indeed:

Ali G. vs. Andy Rooney

Ali G. pretends to be a black rapper, and Rooney rips him a new one!

Borat attracts lawsuits

The Borat movie is expected to clear 60 million dollars by this weekend, so it’s no surprise that Cohen is also being sued by German gypsies and by the glorious nation of Kazakhstan, for defamation! The glorious nation of Kazakhstan is way-pissed at Borat, and for good reason:

“Borat has told the world that Kazakhs are addicted to horse urine, enjoy shooting dogs, view rape and incest as respectable hobbies, and are fond of pursuits like “running of the Jew” festivals”

Since the official movie title is “Borat!: Cultural Learnings of America for Make Benefit Glorious Nation of Kazakhstan”, it would make sense that Kazakhstan should benefit from the hundreds of millions of dollars that this move will make.

But you have to admit, Cohen is very, very funny. Check-out this wet-your-pants funny Ali G. skit with an ER doctor

Cohen also plays Brüno, a gay Austrian, very offensive and funny, as shown here: Brüno the queer Aussie – Video

Offensive Gay Aussie Brüno

But Cohen is very different in real-life, a rare Brit who is friendly and funny. I spent hours watching you-tube video’s of Cohen, laughing until I cried:

You Tube video’s with Sacha Cohen

(Don’t miss the interview with Butros Butros Gali, where he gets him to admit that Arabic people sound funny!)

In real-file, Sacha Cohen is a refined Brit with an English degree from Oxford:

The “Real” Cohen on the Daily show – Hilarious