On the first day of the year, the hard drive of the email server I am administering failed and I could no longer start the server. If you look at today's picture of the day, you'll see that lovely Blue Screen of Death. So I had to rebuild the server from scratch and try to restore a 20GB information store. Although NT Backup said that my backup was very successful at the time of the backup, now at the time of restore, it found inconsistencies and would not let me restore!!! What a great way to start a new year!! All I can say is that I know the rest of the year is going to be wonderful!
Anyway, I did a poll a few months back asking people which book they'd like me to translate first. The answer was very clear. Therefore, my new year resolution is: I'll put more effort into finishing the translation of SPW as most people requested. So look for small segments of translations, as some wise man once said, "Good things come in small packages!".
Since today is the New Year Day, I wish all of you a great new year! I wish your hard drives will last forever! More importantly, I wish you all to think positively and try to learn from your bad experiences, just like the story I am going to share with you today about my bad luck in Las Vegas a few years back.
[Now here's the story:]
Since we live only 5.5 hours from Las Vegas, I have to say, we are no strangers to the casinos. My wife and I are no gamblers, and we are smart enough to never bet our financial future on gambling, so we always followed a simple rule: lose no more than 200 dollars. As soon as our total loss hits that limit, we play no more games for the rest of the trip. The casinos have many games to offer, however, I'd always spend the majority of my budget on Blackjack ($1 tables), the reasons been: first, I know the rules well; second, the dealer only has very slight advantage over my odds of winning. This means that a good number of times I can actually walk away with handsome winnings with respect to my limited budget, and the budget will always last me a long time, so I get my money's worth of play time.
The dealer would always follow the same rule when dealing for himself/herself: if the current sum is less than 18, then deal another card to self, otherwise, no more card
1 + 2 + 4 + 8 + 16 + 32 + 64 = 127
So that day when I walked in the casino and sat in front of the Blackjack table with $200 in my pocket, I was ready to rumble for a few hours. Putting one dollar on the table, I got my cards: the total was 18 and the dealer got 20. No big deal, I'll just double my bet to two dollars. This time I got 19 and the dealer got 20. Fine, I'll bet $4. Then I got 19 and the dealer got 21.... By the sixth game, I was already betting $32, because I have been losing every single time. And guess what? This time the dealer got a Blackjack and automatically won the game!
At this critical moment (since if I bet $64, I would only have $200-$127=$73 left, which wouldn't allow me to easily make up all my losses if I lose the next round), I started thinking: What's the probability that one would lose 7 games of Blackjack in a row? Let's just say the dealer's winning odds is 0.6 and mine is 0.4, meaning the dealer should win 6 games out of 10, then the probability of me losing 7 games straight in a row would be:
0.4 x 0.4 x 0.4 x 0.4 x 0.4 x 0.4 x 0.4 = 0.0016384
Of course my brain isn't capable of such precision, one thing that I was pretty sure was that the probability of me losing 7 games straight in a row is VERY, VERY low. With that in mind, I placed all of the rest of the $200 on the table, $200 - $63 = $137, like any rational person would have done, and was ready to MAKE SOME PROFIT! The dealer mechanically dealt the cards, as precise and dull as a robot, and my jaw almost dropped. I couldn't believe my eyes! I had 18 and the dealer had 20: I lost again! And I've lost all my $200, in just a little bit over 2 minutes. Hey! What's going on here? How could this have happened??!! Even Clark Griswold could do a better job than me!!
Naturally, that marked the end of it, and we spent the rest of the vacation walking, touring, buffeting, and shopping, never played another game of gambling. However, for many months, I still couldn't believe how bad my luck was in that last game. I made the most logical decision I could think of, but I still failed miserably.
Then it came the time when I took a class about Bayesian Theories, and it finally made sense! Have you figured it out yet?
To better explain this, let's just use the example of a coin flip. With a known fair coin, we know that the probability of the coin landing on head is 0.5, which is exactly identical to the probability of it landing on tail. Now let's flip it and suppose it landed on tail. What is the probability of it landing on tail again in the next flip? "Half and half, of course!", you probably would reply, which is perfectly right. But what if you have already flipped the coin 20 times and it all landed on tail. Now what is the probability that it will land on tail AGAIN in the next flip? You'd probably think the probability of it landing on head is much greater than the probability of it landing on tail now, wouldn't you? If so, you've just made the same mistake I made at the Blackjack table. The correct answer is: the probability of it landing on tail is still 0.5.
So the key idea here is that every flip is an individual trial and the probability is fixed for each trail. It doesn't matter how many times you have flipped it before and how the results turn out. As long as the coin is a fair coin, the probability for head or tail for the next trail is fixed at 0.5. Period. All these trails are independent of each other, so even though the probability of getting 21 tails in a row is VERY, VERY small, with respect to the next trail, the probability is still the same.
You might say, wait a minute, now I don't think the coin is fair. Otherwise how could I get 21 tails in a row? And my answer to that is: either you are just really lucky (or unlucky), or maybe the coin isn't fair at all. And now we tread into the field of Bayesian theories: probability of head at 0.5 is your prior belief before you observed any data. After observing 21 tails in a row, you naturally think your prior belief should be corrected and the real probability of head probably should be much lower than 0.5. So observed data allows us to generate a posterior belief which MIGHT be close to the truth.
Let's go back to the Blackjack case and analyze what really happened that day. If the probability values are what I had expected and are fixed (which I strongly believe was the case), because each round is independent of each other, my probability of winning the last game was still 0.4 (vs. the dealer's 0.6), despite of the fact that I had already lost 6 games in a row. Therefore, betting $137 in this one game was indeed a very risky decision, and I paid dearly for that. At the mean time, me losing 7 games in a row was still a clear indication that luck was not with me on that day.
So what have you learned from this? You shall not gamble? Nah! I think it is okay if you treat it as a game and limit the amount of money involved. What I got out of this is that before relying on your intuition, figure out the dependence (or independence) and conditional dependence (or independence) of things first, then you can make more logical decisions!
Swallow a live frog first thing in the morning, and the rest of the day will be wonderful!!
Picture of the Day: