Survived Vegas

Vegas was worth the visit. Not being much of a gambler, I didn't spend much time inside the casinos. Most of my time was spent touring the giant hotels that line the strip. Thanks to gambling, the hotels freely open up their hotels (at least the areas near the casinos) to the public. If it wasn't for gambling, the giant hotels wouldn't be built. If they were, the hotels wouldn't be nearly as open to the public. But thanks to gambling and the hotels' effort to attract gamblers, there are a bunch of magnificient hotels with amazing designs and attractions (and much of it free to see.) So by avoiding gambling, I felt like I had a good deal in Vegas.

Although I didn't gamble much, I did spend quite a bit of time watching my brother and others gamble. At first I thought it might be possible to predict a range of numbers that the roulette wheel may fall based on the velocity of the wheel when it starts. However, I quickly gave this effort up after seeing how it's implemented. The wheel moves in one direction and the ball is thrown in the opposite direction. Plus, there are a bunch of little metal obstacles on the table that often deflects the ball and thereby adds more randomness to where the ball lands. Thus, I concluded that roulette is extremely random. The same goes with blackjack and the slots. I guess that should be expected...

One thing I noticed about gambling is that it is only entertaining if you win at least occasionally. It seems somewhat obvious, but it's very important psychological phenomemon that casinos take full advantage of. If every game only had tiny odds of winning anything, most people would get dissatified quickly. But by keeping the odds close to 50%, people do win some and that keeps them trying to win more. But probability does work. The casinos' odds are always above the gamblers. And casinos end up making big money, enough money for them to invest hundreds of million of dollars in these gigantic hotels.

But for those who can resist the temptation to gamble, they are rewarded by free access into some amazing hotels.

Other Things to See While in Vegas

There are a lot of other interesting things to do and see in southern Nevada besides casinos. I especially liked our tour of the Grand Canyon. We flew on a small plane from Vegas to a small airport just south of the Grand Canyon. The flight alone was worth the $160 tour price. Then we took a bus to two Grand Canyon overlooks where we had about 90 minutes at each stop to see the Canyon. The Canyon was an amazing view, better than I had anticipated. In addition to the Grand Canyon, Hoover Dam was great place to visit. Vegas also has some nice state parks nearby (Red Rock and Vallery of the Fire) with some nice trails.

The 3-Door Game

Calculating the odds of different gambling games can be difficult. You may sense that you know the odds, but you probably don't. Here's one example of a simple game that is very simple, but determining the odds is confusing. Here's the basic premise:

A gameshow host gives you a choice of three doors. Behind one of those doors is the prize. There's an equal chance that the prize is behind one of the three doors.

After you pick a door, the host opens up one of the other two doors which does not have the prize. The host then gives you another choice. You may keep your original guess, or you may pick the other door. What should you do to maximize your chance of picking the door with the prize?

Many people who I have told this puzzle to think the odds of keeping the original door and the odds of switching to the other door are equal. But that is not the correct answer.

Here's the easiest way to think of it. First, the probability of the first guess being right is 1/3. The probability of the first guess being wrong is 2/3. Now suppose your first guess is wrong. That means the first door you pick does not have the prize behind it. So it has to be behind one of the other two doors. Then the host opens up a door that you didn't pick and that does not have the prize behind it. If your first guess is wrong, there is only one door left that he can open. So if you switch doors, you will win. In other words, if your first guess is wrong and you always switch doors, you will always win. The probability of guessing wrong is 2/3. So by switching, your probability of winning is 2/3. If you decide to keep your original guess, your probability is 1/3. Thus, switching doors improves your probability to win the prize.

As you can see, determining this probability of this simple game wasn't easy. So if you think the odds favor you at some casino, don't be so sure. Unfortunately, I didn't find the 3-door game at Vegas....

posted by Ken on 1:40 PM permalink and comments  

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