Saturday, December 29, 2007

Game Theory in Las Vegas

I tried to use a bit of game theory to increase my odds when gambling in Vegas. Of course, I already know that the casinos have a house advantage so I wasn't surprised to see negative expected utilities when calculating the odds of a game. The rational choice would of course be not to gamble. Instead I just gambled a little.

After doing a bit of research on Wikipedia, some of the games with the worst odds are Keno and slot machines. However, these are the games I ended up playing. The games with better odds such as blackjack and roulettes had much higher minimum bets (especially compared to the one cent slots). Games which involve skill allow you minimize the house advantage.

Keno was slightly more interesting than slots because each casino had different paytables and specialty bets. You can choose bets with different payoffs and different probabilities of winning. I could calculate when one type of bet had a lower expected utility than another.

My brother came into Vegas with his own gambling strategy. Given a game with fifty-fifty odds and double payoff, his strategy was to continue doubling his bet until he wins. In the end, if he had an infinite amount of money to bet, this guarantees that he will win exactly the value of the first bet. For example: lose $1, lose $2, lose $4, win $8, profit=$1. However, with a finite amount of money to bet I tried to persuade him that the strategy does not make any sense. It is risking losing lots of money (with a low probability) and gaining a little (with a high probability). In the end this does not change your expected utility (which is zero for the game I described above). The strategy also doesn't make sense because of the concept of sunk cost. Once he loses money in previous games, it should not affect his future betting strategy. Despite my complaints he ended up making a profit o_o

Kevin Leyton-Brown gave an interesting guest lecture about game theory in my Cognitive Systems 300 class last year. Near the end of class we had several different types of auctions for $5 bills. He let us know that any profits would go to charity. I thought one of the auctions was particularly interesting in which the highest bidder would win the prize as normal but the second highest bidder would also have to pay their bid. This means as soon as there was more than two bids over $2.50 Kevin was guaranteed to make a profit on the $5 bill. I made bids over $2.50 even though I knew it wasn't an optimal strategy (it was for charity after all). Being the second highest bidder you are really tempted to outbid the highest in an attempt to win the prize and avoid a complete loss. Another guy in the class and I continued bidding against eachother until the bids actually got over $5. This means Kevin is getting over $10 for his $5 bill :). I eventually gave up and ended up being the second highest bidder. The highest bidder only lost a few cents while I lost over $5. I thought the auction was fascinating due to the temptation for the two highest bidders to continue outbidding eachother despite going over the actual value of the prize (let alone the optimal maximum of $2.50). I'll keep this auction in mind as a fun thing to try with my friends (except this time I will be the auctioneer).

Wednesday, December 26, 2007


Pictures of my trip can be found here.

December 20:

I left from Vancouver to Las Vegas at 2pm. There was some severe turbulence on the descent into Vegas (enough to start some of the passengers screaming). In Vegas I met my brother, his wife, and her parents. There was a sandstorm when we were driving through town that night so that probably had something to do with the turbulence. The sandstorm was actually interesting to see since I have never been in one before. We were staying at a hotel called Harrah's which was right on The Strip. That night we went to Fremont Street. The massive display on the ceiling was very impressive. The slot machines I used on Fremont Street also turned out to be the only profitable gambling I did in Vegas.

December 21:

We started the day by going to the top of the Stratosphere. This is high enough that you can immediately feel a change in air pressure as you are riding up the elevator. It is way taller than any of the other buildings in Vegas so there are some amazing views. Our next destination was Hoover Dam. On the way there there was some authentic desert with cacti. The dam was a very impressive display of engineering. That night we had dinner at Sam's Town and saw a laser light show.

December 22:

I spent the morning sleeping in while everyone else went to the grand canyon. I had decided not to get tickets to go since it was very pricey. That afternoon we visited a few of the hotels and casinos along The Strip. Each hotel has very unique themes and shows in order to attract visitors. Two shows that I enjoyed were the fountains at the Bellagio and the volcano at the Mirage.

December 23:

We saw a car show in the morning and spent the rest of the day touring The Strip. That night we went to the best part of the trip for me - Cirque du Soliel. We went to Mystère at Treasure Island. This was by far the best circus I have ever seen. The music, theater, and performances combined perfectly to create a magical show. I was so impressed by the quality of it that I now want to see the other Cirque du Soliel shows in hope that they are as good.

December 24:

We went to a few more famous hotels and casinos along The Strip. My favorite building was the Luxor; an Egyption themed hotel/casino in the shape of a pyramid. The MGM had some lions on display. Some other cool places we saw were Caesar's Palace, Paris, New York, The Venetian, and Excalibur.

December 25:

We had a relaxing Christmas, mostly enjoying The Strip and playing some poker. Our hotel had an excellent buffet selection. It was almost overwhelming the number of different food options there were so I inevitably ended up eating way too much. I am fairly sure that I have gained a decent amount of weight in the last six days ;)

December 26:

I had to wake up at 4am to catch a very early flight. I was pleased to see that there was some snow when I returned to Vancouver. Waiting for me at my apartment was the PS2 lens I ordered. I spent about five hours working on the PS2. Although the lens was non-functional when I first installed it, I eventually got it to read original DVDs. It refuses to read any CDs or burnt DVDs however. At least it wasn't a total waste since I can now play a few games in my collection. The fact that it still isn't completely working implies that the lens was not the only problem.

For the rest of vacation I will be splitting my time between Robocup and CIspace. I am also playing the following games right now: Final Fantasy Tactics (on PSP), Grim Fandango, Unreal Tournament 3, and Crysis. Although these are all great games, the game I really want to play is Final Fantasy XII. That is why I have been putting so much effort into getting the PS2 working.

Thursday, December 20, 2007


I found a cool webpage with a collection of detailed images of eyes. Its amazing how complex the patterns are and the amount of variation there is between different people.

I tried photographing my own eye but it turned out to be surprisingly difficult. Not only are reflections hard to avoid but my eye was half closed in most of the pictures:

I eventually got a picture with a full image of my iris and did some photoshoping to get this:

Not quite as interesting as the other eyes on the webpage :(

Wednesday, December 05, 2007

PS2 Frustration

I recently received my old PS2 and a fairly large collection of games shipped here from India. Shipping it here turned out to be a very bad plan. Despite the fact that it was packaged fairly securely, the CD spindle that the games were in was shattered. Luckily the CDs/DVDs were undamaged. However, when I tested the PS2 it would not read any discs. The memory card was also unreadable.

I have been struggling to find a way to fix the disc reader. After a combination of cleaning the laser lens (using alcohol and Q-tips) and cleaning the components which allow the lens to move to different locations on a disc, I have gotten it to reliably read audio CDs and PS2 CDs. It does not read PS2 DVDs or DVD movies however. I have been waiting over a year to play a certain DVD game.

Despite upcoming exams, I have spent several hours adjusting the lens alignment in an attempt to get it to read DVDs. There are many different alignment settings, and testing each setting requires assembling and disassembling the drive (to avoid hazardous laser radiation when the drive is powered up). Every time I make a minor adjustment a completely different set of sounds and vibrations are made when it tries to read a disc. None of the settings successfully read DVDs.

The cost of a replacement lens is $40. I am trying not to let the sunk cost of $67 for shipping the PS2 here play a factor in my decision. I am still not entirely sure if a replacement lens will fix the problem. Despite the fact that the amount of money that I have spent is approaching that of a brand new PS2, I have just finished ordering a new lens. I will post an update on whether it works when it arrives.