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I recently started eating egg whites regularly, and that meant I needed to start shopping for eggs every week.
My local grocer sells a variety of egg sizes. Can you figure out which one is cheapest?
Here are the prices:
Here is how I approached the problem.
You just received a $100,000 in cash. Do you invest the money all at once, or do you spread it out into equal investments using dollar cost averaging?
Most advisers will say to dollar cost average, but I do not think this is the right answer. Dollar cost averaging has nearly universal support among financial education teachers, banker, brokers, and money advisers. And yet, there has never really been a compelling mathematical case for dollar cost averaging.
To see why, let’s take a step back and understand the reasons people suggest to use dollar cost averaging. Then, we can explore the academic and logical arguments and suggest other alternatives. This article is outlined in 5 parts.
1. The standard explanation of DCA
2. Academic papers showing why DCA is wrong
3. Why the standard explanation is wrong
4. The people who really benefit from DCA
5. Alternatives: better ways to invest
(Standard disclaimers apply: I am not a money expert and you should always consult a professional before making your own decision.)
The numbers 1, 2, 3, and 4 are written on a board.
Alice writes a “+” or “-” sign in front of one of the numbers, and then Bob and Alice take turns.
Once the four signs are written, the arithmetic expression is then evaluated. Bob gets points equal to the absolute value of the result.
What is the best strategy and the value of the game?
Let’s you and I play a game with coins.
You have 100 dimes, and I have 99 pennies. At the same time, we will toss our coins in the air and let them fall on the floor. Then we meticulously count the outcomes of our tosses.
You win if you show more heads than I do. What’s the probability that you will win?
In most American bars, it’s customary to tip a dollar or two per drink. People usually don’t tip for tap water because it’s given for free. But does that make sense?
I thought about a few reasons why one should tip for tap water.
I almost always take a break for meals, even if that means staying late in the office. Meal time is my time, and I want to enjoy my food.
That said, I will occasionally chow down at my desk if I am overwhelmed with meetings, or if I am feeling unusually productive and don’t want to mess up the flow.
So from time to time, I will join the roughly 65 percent of Americans who said they don’t take a lunch break or eat at their desk, according to a survey from Right Management.
When pressed to eat at my desk, I am more selective about my food choices. I won’t eat french fries or pizza or any other greasy food that could mess up my computer. Nor will I pick foods like tuna that are particularly smelly.
In short, I try to pick hearty and healthy foods that can be eaten with utensils and won’t cause a mess at my desk. Here are 8 of my favorite meals to eat while I’m working at my computer.
I recently went to my car dealership for scheduled maintenance.
Now I will already admit this was probably not the best decision. If you are trying to save money, it is often better to avoid overpriced dealerships and go to other mechanics (a former mechanic makes this case of how overpriced dealerships can be.)
But I’ll save that debate for another article. Let’s just say I was convinced I wanted to do servicing at the dealer and look for the second best solution.
So here’s the situation. During the servicing, I got a call suggesting to do other work. I really wanted to get the work done to avoid future hassle so I immediately agreed.
Then I realized I should probably negotiate a little bit. So I said a few words, and amazingly, it worked.
Consider the following game.
Two generals have 5 units each to deploy. Each person decides how many units to send to battle. The general who sends more troops will win, but it’s a draw if they both send the same number.
Each also has the option of “passing” which averts war and ends in a draw.
What’s the best way to play this game?
William Spaniel shows how to solve this game in his video series Game Theory 101. (video after the jump)
This is a nice explanation of the concept of using best responses to find Nash equilibria.
You’re on a two-lane highway and there are cars ahead of you in both lanes. You want to go straight ahead, but some of the cars in front of you might slow down to turn and delay you.
You are in the left lane. In that lane, there are 3 cars, each with an independent 20 percent chance of stopping to turn. If any of the cars stop, you have to stop too.
You see that over in the right lane there is just a lone car. But your experience indicates a 50 percent chance the car will stop to turn.
Which lane are you better off in? Answer is after the jump.
With age comes responsibility. Here is a short observation on how different age groups view the task of having to pack an overnight bag.
Child: “Mom will pack my bag”
Teenager: “I’ll take clothes and a toothbrush”
College student: “I’ll take clothes, a toothbrush, and beer”
First job: “I’ll take clothes, a toothbrush, and a spare set of clothes—in case I spill something at dinner”
First child: “I’ve got to take baby clothes, food, etc. in addition to all of my things.”
Around age 50: “Oh, I better remember to take my prescription meds.”
Cranky old man: “Forget all that, I’m staying in”
I’m somewhere between the stages of first job and first child, as I bring a lot of travel to care for my bald head.
How has your overnight bag changed as you have gotten older and more mature?
I was ordering a beer at a restaurant, and I was asked if I wanted the “tall” or a “pint.”
I suspected the “tall” was a better value, but I always ask to make sure. Occasionally bars will charge a premium on larger quantities, as illustrated in this post on Freakonomics: Happy Hour Fail.
Here were my choices:
The “pint” was $5
The “tall” was $7.50 and contained 23 ounces
I’ll mention a standard U.S. pint is 16 ounces. So quick quiz: which choice is cheaper?
Finding the best savings account is mathematically simple. You should shop around for the best rates at reliable banks, and then pick an account that offers a competitive rate.
But our predictably irrational ways can get in the way. I was reading an interesting example of how something as simple as a smiling face can influence our ability to judge savings accounts.
Flexible Spending Accounts (FSAs) are an incredible way to pay for health expenses. While FSAs can be complicated and require some effort, I now think their rewards are worth the hassle.
I want to explain a bit about how FSAs work, and then I’ll get into the math. Most people know you save money by paying for health expenses pre-tax.
In this article I want to explain why the benefit can be even larger to due some of the details of FSA. In an extreme, extreme example, the benefit can be in the range of a 1,000+ percent of the money used to fund the account.
Last week I released a math puzzles ebook on this blog for sale directly as a pdf. The ebook contains 70 of the best puzzles from this blog.
This is just a short announcement the ebook is now on Amazon in the Kindle store:
Buy at Amazon: http://www.amazon.com/dp/B007ONNCWO
(It’s worth mentioning you can still read the ebook without a Kindle. I personally have downloaded the Kindle apps for both my PC and tablet and they work great.)
And if you like the puzzles on this blog, I have a small favor to ask: please, please add a customer review on Amazon. I really need a couple of reviews to help establish the book’s quality. I’m hoping a few of you can speak up to the high quality of puzzles on this site (even a short sentence like “A great collection of puzzles for the anyone that likes math” would be tremendously helpful.) Thanks.
Imagine you are taking a game theory class, and the professor announces an experiment.
You and another student are called up to the front of the classroom to participate in an auction.
Here is how the auction works:
–the prize money equals the sum of money in both of your wallets
–the winner is determined by an open outcry auction (suppose the professor announces selling prices that increase by $1 increments, and the game goes until someone says “I quit”)
–the winner has to pay the final price in exchange for the prize
Let’s say you are chosen for this game, and you are allowed to peek in your wallet before the auction begins.
You see that you have $10 in your wallet. How much would you be willing to pay in the auction?
Read the rest of this entry »
Buy the pdf from Gumroad: https://gumroad.com/l/pjHS (you pay with a credit card, get it instantly)
Or buy the Kindle version at Amazon http://www.amazon.com/dp/B007ONNCWO
