Every once in awhile, I have to go on a streak of public education for the betterment of society. The Monty Hall problem presents such an opportunity and just cause for such evangelism, as this non-intuitive probability problem routinely trips up even sharp-minded folk. So, I present to you a problem:
Suppose you're on a game show. You've made it to the final round, and there are three doors presented. Two of the doors have a goat behind them, meaning you win nothing, and the third holds a new car. Choose the door with the car, and you win that. You make your choice, and before revealing your choice, your host (Monty Hall, hence the name) opens one of the remaining two doors to reveal a goat. He then asks you if you'd like to switch. Is it advantageous to switch doors? What is your probability of winning if you do/do not switch?
...think about it...
...got an answer in mind yet?
The surprising answer is that switching gives you a 2/3 chance of winning. Most people guess 1/2 - there are two doors remaining, and one of them is right. However, let's think of this differently.
When you first choose, you have a 1/3 chance of getting the right door. Then, an incorrect door is revealed. If you were originally right and you switch, you're now wrong. But if you were originally wrong and you now switch, you're right. Because you had an initial chance of 2/3 of being wrong, by switching you now have a 2/3 chance of being right, hence the answer.
Don't believe me? Play a few rounds online and convince yourself.
Wednesday, April 9, 2008
Tuesday, April 8, 2008
Land Prices
Linden Labs announced recently that it would be dropping prices of land sales significantly. New islands, for example, will only cost USD$1,000, down from USD$1,675 as last I recall.
Talk about a way to piss off your most loyal supporters! Everyone currently holding land just took a major hit to their resale value, and my understanding was that land prices had been dropping anyway. While this will certainly encourage new growth, I think there will be a painful period of losses for existing (especially startup) businesses as well. As the new land is sold, those owners can price their rents lower and simply outbid the current ones still paying off their $1,675.
Linden Labs is obviously placing a bet on the elasticity of demand for land. Elasticity, for the uninitiated, is how much the quantity demanded of a good changes with respect to a price change. Some goods, like (some) electronics, are very elastic - small drops in price will produce large sales and vice versa. Other goods, like salt, aren't elastic at all ("inelastic") - you can double the price of salt, and people will still buy about as much as they did before. A few very rare goods, like gasoline, are inelastic in the short run and elastic in the long run...but I'm getting off-topic...
If the demand for new land is elastic, LL will see a large jump in sales for their drop in price. My guess is they're hoping this outweights (a) the amount of anger they're generating, and (b) the amount of extremists who go researching into OpenSim projects.
Let's see how the bet pays off.
Talk about a way to piss off your most loyal supporters! Everyone currently holding land just took a major hit to their resale value, and my understanding was that land prices had been dropping anyway. While this will certainly encourage new growth, I think there will be a painful period of losses for existing (especially startup) businesses as well. As the new land is sold, those owners can price their rents lower and simply outbid the current ones still paying off their $1,675.
Linden Labs is obviously placing a bet on the elasticity of demand for land. Elasticity, for the uninitiated, is how much the quantity demanded of a good changes with respect to a price change. Some goods, like (some) electronics, are very elastic - small drops in price will produce large sales and vice versa. Other goods, like salt, aren't elastic at all ("inelastic") - you can double the price of salt, and people will still buy about as much as they did before. A few very rare goods, like gasoline, are inelastic in the short run and elastic in the long run...but I'm getting off-topic...
If the demand for new land is elastic, LL will see a large jump in sales for their drop in price. My guess is they're hoping this outweights (a) the amount of anger they're generating, and (b) the amount of extremists who go researching into OpenSim projects.
Let's see how the bet pays off.
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