Monday, December 27, 2010
Investment, Demystified
I started today a new blog: Investment, Demystified. After spending the last 10 years reading about it, arguing about it, making money, losing money and trying to figure the math behind it, I think I know enough to share a bit of the wisdom I learned. I hope you enjoy it too!
Tuesday, December 21, 2010
Pool Night Math
Every Monday night I meet with three friends for a game of pool at Diesel, the Lesbian-owned coffee shop at Davis square. This has become a tradition, in spite of overpriced drinks and under-maintained pool tables. It's a fun place, and it's always interesting to notice the cute boys and how they turn into cute butch girls when they turn around ("a Diesel moment"). But I digress.
We usually play 3 matches, mixing and matching the pairs. This exhausts all the combinations, of course. We noticed something interesting - the last match always creates a team of someone who lost twice with someone who won twice. Thus, after the 3rd game we'd always have either "the biggest winner" (if this team wins) or "the biggest loser" (if this team lost) - someone who either won or lost all 3 games.
How does this happen? Having 3 mathematician out of 4 players meant it would be a fun exercise to figure it out.
Looking at the first two matches, let's check the 4 possibilities for the outcome of the games. First notice that there's exactly one common player between any couple in the first round and any couple in the second round. This is the case since if there were two common players it would mean we played the same combination twice, and if there were no common players it would mean that the other team would be identical to the players in question - again, meaning the same combination was played a second time.
In other words, each team from round one intersects with each team from round two with exactly one player.
Looking at the teams that won in both rounds, it means there's exactly one player who won twice. Similarly, looking at the teams that lost in both rounds, it means there's exactly one player who lost twice.
These players have not played together yet - otherwise, the guy who won twice would have lost when he played with the guy who lost twice. Hence they must be the next and final combination.
And now we can see that the outcome of the last round would show whether one of them is the Biggest Winner (winning all three rounds), or the other guy is the Biggest Loser (losing all three rounds).
QED.
We usually play 3 matches, mixing and matching the pairs. This exhausts all the combinations, of course. We noticed something interesting - the last match always creates a team of someone who lost twice with someone who won twice. Thus, after the 3rd game we'd always have either "the biggest winner" (if this team wins) or "the biggest loser" (if this team lost) - someone who either won or lost all 3 games.
How does this happen? Having 3 mathematician out of 4 players meant it would be a fun exercise to figure it out.
Looking at the first two matches, let's check the 4 possibilities for the outcome of the games. First notice that there's exactly one common player between any couple in the first round and any couple in the second round. This is the case since if there were two common players it would mean we played the same combination twice, and if there were no common players it would mean that the other team would be identical to the players in question - again, meaning the same combination was played a second time.
In other words, each team from round one intersects with each team from round two with exactly one player.
Looking at the teams that won in both rounds, it means there's exactly one player who won twice. Similarly, looking at the teams that lost in both rounds, it means there's exactly one player who lost twice.
These players have not played together yet - otherwise, the guy who won twice would have lost when he played with the guy who lost twice. Hence they must be the next and final combination.
And now we can see that the outcome of the last round would show whether one of them is the Biggest Winner (winning all three rounds), or the other guy is the Biggest Loser (losing all three rounds).
QED.
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