### Solving IMO 1989 #6 using Probability and Expectation

The state of California is currently holding over $6 billion in unclaimed property belonging to millions of people. What type of property and who are the rightful owners? According to California's official unclaimed property website, these assets fall into the following categories: 1. Bank accounts and safe deposit box contents 2. Stocks, mutual funds, bonds, and dividends 3. Uncashed cashier's checks or money orders 4. Certificates of deposit 5. Matured or terminated insurance policies 6. Estates 7. Mineral interests and royalty payments, trust funds, and escrow accounts People forget, people die, people move around. But$6 billion is a staggering amount of money; some of these amounts have to be really large. Let's try to find some interesting examples.

This is official California UCP search form. Programmer and database types will notice one problem immediately - no fuzzy string matching. If your name or address was misspelled on the assets, or munged in the recording process, tracking down any assets belonging to you could become a difficult to impossible process. Given that this database has at most 18 million rows, there's no excuse for such a basic (and important) feature to be missing.

Leaving aside the flaws and the apparent lack of due diligence on the part of the state of California, let's try to find some interesting examples of owed property.

Strategy - celebrities and the super wealthy with either unusual names and/or known cities (through Forbes or others).
On a personal note, I've found about $40K for friends plus businesses they own (over$20K in one case).

1. You are picking up a commission right?

2. Hah - it'd be nice if some of the wealthier people would donate the money to a charity (assuming someone was able to notify them directly). I'd really like to see California improve the search engine and notification process.

3. I saw an article last week where the government has billions sitting around due to SSN/W2 mismatches.

4. Sounds like an interesting web project as the data is available; it's just a matter of adding some fuzzy logic to a search page.

Not a good idea to depend on 'California' to do this.

5. Thank you! I found some old paychecks (affiliate commissions) from years ago. Only about $30, but I will claim it! 6. Can anybody claim MJ's safe deposit box now? :] 7. Oh hai, thank you for this post... I found my wife has$500 of pending insurance premium refund still to be collected. :)

8. Thanks, I just found that i Have 100+ $worth unclaimed from various sources. I will claim them now :) 9. rich people do not care .. it is a waste of time to take the 4 steps and not worth the$300 to $3000 -_- 10. This comment has been removed by the author. 11. Speaking of unclaimed property.I have a new Facebook page.I enjoyed this blog,and one reason I made my page is this:Every article or blog post,every news segment...none of them tell you to leave the city box blank.By doing this,you increase your search radius by far.And since a lot of money is misdirected because of human error,someone may have sent your money to the wrong place.For Example,notice the address on this account: Date: 2/20/2013 Property ID Number: 011974375 Owner(s) Name:BEVERLY HILLS HOTEL Reported Owner Address:PO BOX 942809 SACRAMENTO CA 94209-0001 Type of Property:Municipal bond earnings Cash Reported:$100,000.00
Reported By:FIRST TRUST OF CALIFORNIA, NATIONAL ASSOCIATION
By entering "Beverly Hills" into the city box,you miss this.
I urge you to try your search again,but this time, LEAVE THE CITY BOX BLANK.
Please check out my page.If you like what you see,please like and share it.
I took the liberty of sharing this blog post on my page.

The national site for searching is: www.unclaimed.org (leave that city box blank!) :)

12. Is there any further reading you would recommend on this?

Amela
Birmingham Safety Deposit Box

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### A Bayes' Solution to Monty Hall

For any problem involving conditional probabilities one of your greatest allies is Bayes' Theorem. Bayes' Theorem says that for two events A and B, the probability of A given B is related to the probability of B given A in a specific way.

Standard notation:

probability of A given B is written $$\Pr(A \mid B)$$
probability of B is written $$\Pr(B)$$

Bayes' Theorem:

Using the notation above, Bayes' Theorem can be written: $\Pr(A \mid B) = \frac{\Pr(B \mid A)\times \Pr(A)}{\Pr(B)}$Let's apply Bayes' Theorem to the Monty Hall problem. If you recall, we're told that behind three doors there are two goats and one car, all randomly placed. We initially choose a door, and then Monty, who knows what's behind the doors, always shows us a goat behind one of the remaining doors. He can always do this as there are two goats; if we chose the car initially, Monty picks one of the two doors with a goat behind it at random.

Assume we pick Door 1 and then Monty sho…

### What's the Value of a Win?

In a previous entry I demonstrated one simple way to estimate an exponent for the Pythagorean win expectation. Another nice consequence of a Pythagorean win expectation formula is that it also makes it simple to estimate the run value of a win in baseball, the point value of a win in basketball, the goal value of a win in hockey etc.

Let our Pythagorean win expectation formula be $w=\frac{P^e}{P^e+1},$ where $$w$$ is the win fraction expectation, $$P$$ is runs/allowed (or similar) and $$e$$ is the Pythagorean exponent. How do we get an estimate for the run value of a win? The expected number of games won in a season with $$g$$ games is $W = g\cdot w = g\cdot \frac{P^e}{P^e+1},$ so for one estimate we only need to compute the value of the partial derivative $$\frac{\partial W}{\partial P}$$ at $$P=1$$. Note that $W = g\left( 1-\frac{1}{P^e+1}\right),$ and so $\frac{\partial W}{\partial P} = g\frac{eP^{e-1}}{(P^e+1)^2}$ and it follows \[ \frac{\partial W}{\partial P}(P=1) = …

### Mixed Models in R - Bigger, Faster, Stronger

When you start doing more advanced sports analytics you'll eventually starting working with what are known as hierarchical, nested or mixed effects models. These are models that contain both fixed and random effects. There are multiple ways of defining fixed vs random random effects, but one way I find particularly useful is that random effects are being "predicted" rather than "estimated", and this in turn involves some "shrinkage" towards the mean.

Here's some R code for NCAA ice hockey power rankings using a nested Poisson model (which can be found in my hockey GitHub repository):
model <- gs ~ year+field+d_div+o_div+game_length+(1|offense)+(1|defense)+(1|game_id) fit <- glmer(model, data=g, verbose=TRUE, family=poisson(link=log) ) The fixed effects are year, field (home/away/neutral), d_div (NCAA division of the defense), o_div (NCAA division of the offense) and game_length (number of overtime periods); off…