The long version:

On a trip to Vegas recently while waiting to enjoy a delicious breakfast at Cafe Bellagio (I highly recommend) I read this flier:

For the uninitiated, in this version of Keno you select 20 number (between 1 to 80) with no repeats (can’t select 12 twice for example) and write them down. Then, after you have selected all your numbers, 20 numbers are randomly chosen by the house (again between 1 and 80 no repeats). On a $5 bet the payout is listed above. If 0 of the numbers you selected are the same as the computers you get $500, if 1 is the same $10, 2 are the same $5, and so on. If all 20 numbers you select are the same as the computer you get a jackpot of $250,000.

I wondered what the odds were of winning the jackpot. Every number the computer selects has to be one of your numbers. The first one has a good chance (as you have all 20 numbers still) so it has a 20/80 chance of selecting a number you have selected. In the next selection it is a little harder, 1 number is already matched so you only have 19 numbers left, and the house only has 79 left to choose from so the chance is 19/79. Next time it is 18/78 and so on. If you write this down the formula, the total chance for getting all 20 is:

You can write this as

where k=20 and n=80 in our case. Some quick work on the calculator tells you the odds are

This is a staggeringly small number. To put this is perspective the age of the known universe is only 4.3*10¹⁷ seconds! In other words you would have had to play Keno 10 times a second for the entire life of the universe up until now to have a decent chance of winning. Needless to say the measly $250,000 you win won’t exactly be profitable.

While I suppose it shouldn’t come as news that you won’t make money gambling in Vegas, I was a bit taken back by how bad the odds were. In fact the most confusing thing about this is why the jackpot isn’t bigger, much much bigger. It is effectively impossible to win, so why not go all out: $10 million, $100 Million, $1 Billion! Think of the headlines that would make. More realistically why not at least $1 million, is has a nice ring to it, everyone wants to win $1 million, what do they have to lose? The only thing I can conclude is the people in charge don’t trust their statisticians.

The astute student of combinatorics (combinatorian?) will have recognized the above formula, it is simply the inverse of the “choose function”.

It describes how many ways you can choose n numbers out of k, or “n choose k” (80 choose 20).

It is also interesting to note that when calculating this, the scientific calculator on the iPhone will frequently overflow and give an error message, round off your number half way though, or even flat out give you the wrong result. If you calculate 80! then divided by 60! it gives 8.946*10³⁶. This is already incorrect, the correct answer is 8.601*10³⁶. If you then hit the “1/x” button to invert it, it gives 1.1*10^-37. This is actually correct (not overall but for the 8.946*10³⁶ that we started with) even if it is rounded off dramatically. I realize that these are very large numbers and that they won’t fit into a float type (not sure why they didn’t use double, it is a scientific calculator after all) but it is a little disingenuous to report 13 significant digits on the first calculation (80!/60!) when there is really only 1 significant digit. The invert function is at least mostly honest with how (in)accurate it is (technically there should be some warning that your answer is rounded off).

So don’t play Keno, and don’t use your iPhone for rocket science.

Feeling Blue? I wonder what is behind that link.

Oh yes, depression counselling. So included with all the other forms and stuff you need to know, a helpful link to the school counselor and what looks like a dedicated support group for PhD students. It is nice to know that depression is a an inevitable consequence of getting a PhD. My only question, is this limited to getting the PhD or does this extend to having a PhD also?

Wikipedia is supposed to be this fount of human knowledge. A huge encyclopedia were you can learn about nearly anything. After all of this effort to create it we find out that people would have been 90% happy with a few pages about human reproduction and some current events.

(By the way I later found this site which lists traffic for individual pages and found out the SWI page gets 400-500 hits a month.)

In case you didn’t catch it the title is a reference to an Asimov book, a great read if you have the time.

I should probably also make one with days spent in Detroit and number of blog posts.  I’m on my way home though so maybe next time I’m in Detroit.

Today I could not print.  Jobs would go to the print queue and fail.  I could access the printer, my drivers were the latest and previously worked, and the printer would work for others, it just wouldn’t work for me. After some thought there was only one conclusion: McAfee.  Sure enough, in all of its wisdom it had seen fit to firewall explorer and a few other normal Windows processes.

I cannot overstate my contempt for McAfee, Norton, and pretty much all other anti-virus software.  They can take a brand new machine and immediately age it a few years by cutting its speed dramatically.  If you are foolish enough to install one of them on an older machine there is a good chance it will be rendered unusable (not from impatience either, we are talking 5 minute boot times and another 5 minutes to get to the Google homepage).  They guarantee nearly all of the detrimental effects of having a virus, and people voluntarily put them on their computers, even paying exorbitant amounts of money for them. I would say without hesitation that this medicine is, if not worse, at least as bad as the disease.

That isn’t to say anti-virus programs don’t have their place, but it is a sad lonely place that shouldn’t be anywhere near your day to day computing.

http://www.reuters.com/article/newsOne/idUSTRE56F5MK20090716

Not is some freak computer power outage, not by someone spilling coffee on it or accidentally  dropping it down a flight of stairs, no, it was erased to save money. Now we are stuck with low quality copies that CBS happened to save.  But don’t worry they assure us, the crappy copies will look better than the originals after they have been restored! Talk about a false dichotomy,  you know what would look even better, the originals digitally restored.

….

I have been cited.  I am pretty sure this is the first one, although I guess there could be many others out there citing my work as instrumental in the fight to cure cancer and stop global warming, but I kind of doubt it.

I didn’t do anything dramatic to hurt my back, I just got out of bed leaned over to do something and kablam incredible pain.  It has been slowly getting better but I have spent some quality time flat on my back in bed.  So back pain sucks, although if you really needed a vacation it might not be a bad gig.