JonMichael is Neither Jon nor Michael

Texas Hold 'em Solitaire

A la Blackjack:

1. Two cards are dealt to the player and two the dealer. 
2. The Player can fold and lose ONE (the base value of the bet).
3. The House will fold if he does NOT have two suited cards, two adjacent cards, two cards that are one position away, a pair of anything or a jack of higher. The player would then gain ONE.
4. The flop is dealt.
5. The Player can fold and lose TWO.
6. The House will fold if it does not have three to a flush, three to a straight (not like signposted, as in 3, 5, 7),  a pair of 6s or better or a queen or higher high card. The player would then gain TWO.
7. The turn is dealt.
8. The Player can fold and lose THREE.
9. The House will fold if it does not have four to a flush, four to a straight (inside or outside),  a pair of 8s or better or a king or higher high card. The player would then gain THREE.
10. The river is dealt.
11. The Player can fold and lose FOUR.
12. The House will fold if it does not have a pair of 10s or better or an ace or higher high card. The player would then gain FOUR.
13. The cards are turned up. If the player wins, the player gains FIVE. If the the House wins, the Player loses FIVE. If they tie, there is no point change.

Last Word on the Electoral College

Three things I predicted right in this election:

1. The five-states that were in play almost to the end (FL fell first like I thought it would).
2. The electoral votes in 49 states and DC (guess which one I got wrong)
3. Ohio is the new Florida.

See you all on the election front in three years.

Five-State Math

Looks like its down to five battleground states: Florida, Ohio, Wisconsin, Iowa and New Mexico.

Here's how the math shows the info.

Kerry: To win
1. FL and (OH, WI, IA or NM).
2. OH and WI
3. OH, IA and NM

Bush: To win
1. FL and OH
2. FL, WI and (IA or NM)
3. OH, WI, IA & NM

The other battlegrounds appear to be breaking this way:
Dem - PA, MI, WA, MN, OR, NH
Rep - MO, TN, AR, NV
Maine looks to give at least 3 to Kerry and maybe 1 to Bush.
I think it's interesting that Kerry brought Ohio onto the table.

Swing States

I saw more reporting on the electoral college and how the battleground states were shaking out. I wanted to compare the battleground states that I defined with the US as a whole to see how our states represent you. BS means battleground states (and something else entriely)

Key (and Fun) Metrics (Source: 2000 Census and 2002 Census projections):
Population- US: 288,368,698 BS: 94,286,157
Female- US: 50.9% BS: 51.1%
High School Diploma- US: 80.4% BS: 82.4%
Bachelor's or Higher- US: 24.4% BS: 22.5%
Homeownership- US: 66.2% BS: 70.0%
Median Income- US: $41,944 BS: $40,912
Mean Travel Time to Work (in mins)- US: 25.5 BS: 23.9
Non-Hispanic/Latino White- US: 69.1% BS: 79.1%

This last results is the most significant difference between observed and expected values. The swing states are less diverse than the nation in general. Of course key states like Florida, Nevada and New Mexico all have significant minority population (in NM, non-Hispanic/Latino whites are the majority-minority). Interesting stuff to think about when you think about what demographics these suits are targeting.

Reality Shows and Voting (Part 1: Intro)

In just six months we will be picking the next President of the United States. But presidential electoral politics has been declining in popularity recently. Out with the old and in with the new. Far more votes were cast for Reuben or Clay than were cast for Al or George. Of course the “American Idol” voters were 1) teens and tweens and 2) allowed to vote several times. But can’t America learn from its reality shows how to give people what they truly want?

Avoiding mainstays like “The Bachelor” and “Joe Millionaire” which award votes via a dictatorship or the “faux” expert oligopolies of “Are You Hot,” “Popstars,” and “The Swan,” there are two grand old mainstays of voting and reality shows: “Survivor” and “American Idol.” This week I’ll be spending two days on “Survivor” (one in a party machine method and one in a truly public opinion method) and one day on the “American Idol” method.

Point Nine Repeating

A lot of people have problems with infinity. They think that infinity never happens and therefore anything that happens at infinity must be false. In calculus, we talk about limits that go to infinity and some people can't except that something infinite as being bounded in any way because you can never get to infinity there for any thing associated with infinity must be zero.

I remember these indeterminate forms from calculus. Anything that can be expressed as ∞ - ∞ or ∞ / ∞ or 0/0 is an indeterminate form. Just because ∞ - ∞ looks like zero, doesn't mean it is. Look at it this way.

Let X = ∞ - ∞, then X + ∞ = ∞. This is true for all real X. So we can't make the most intuitive guess, we have to settle for the fact we don't know.

So this leads me to the old boondoggle about .999999...=1.

I have had so many arguments with people that think that BOAT = SHIP, but can't accept .999999...=1. (Different sets of symbols representing the same concept.) And my opponents' argument is that 1 divided by ∞ > 0. Given that 1 - .99999... = .0000...01, which implies termination (which is impossible, but bear with me). So that the difference between the two numbers is 1 divided by some infinitely large difference. Of course, 1/∞ = 0, which means that 1=.99999....

Now you can say that there is always a little piece between the two numbers, but the numbers do meet at infinity and infinity is right where it should be: everywhere. So free yourself: accept that point nine repeating equals one.

The Lottery and Voting

I don't write about technology in my blog because in general I don't understand it. I am a concpetual pereson who understands how software and hardware are supposed to work but not how they actually do. But it is with reluctance that I weigh in on the issue of electronic voting machines. I do this precisely because my job (which has been keeping me from blogging) is for the Lottery. And the Lottery and voting are very similar.

Ways in which the Lottery and Voting are similar:
1. Both have anonymous transactions. There should be no way to track who voted for what in the same way the Lottery system doesn't know who purchased what ticket.
2. Both systems should be secure. Hacking into a Lottery system would be the end of the Lottery; voting is the same.
3. Both require synching many small subsidiary systems to a master host. Voting results in minutes instead of hours.

My lottery (Wisconsin) is installing 3,600 touch screen terminals in as many locations. Every day these terminals are required to transmit tons of data to a host center in Madison via a dedicated redundant satellite telecommunications system. These transactions are logged (including failed attempts and anything that happens on every machine) and reports are run either via GTECH, the vendor, or by the lottery. In addition to being fully redundant, a back-up system at the Lottery (called ICS) maintained by a third-party vendor also tracks the same transactions and MUST balance with the main system before the Lottery will pay dollar one in prizes to anyone.

Ostensibly, GTECH has built a multi-million dollar satellite-networked counting machine. Sounds like what we could use for voting.

Diebold has run into some problems in California. They have also had issue with hacking (Act One in this episode of TAL, Real) and they couldn't produce a paper record of the vote. So Lottery systems, running the most base and profane (at least according to some that I worship with) form of government, gambling, is more secure than voting! Voting! And think of how many pieces of paper that those machines generate! Voting!

Why is this?

1. As the O'Jays said, "Money, Money, Money... MONEY!" Just in the US, lotteries make over $45 billion. And while that's peanuts compared to the trillions of dollars that our President or the billions that over Governors throw around, voting is not high budget priority (at least not compared to jailing pot smokers, building better ways to kill our enemies or providing health care to the old while forcing the young to pay for it AND their own.)
2. Democrats don't want to fix the system. Where are the worst cases of voter fraud? Cities. Where are the largest stronghold of Democratic voters? Cities. Why is this? In close races (Nixon/Kennedy and Bush/Gore to name two) democrats want to go into a big city (Chicago, Miami) and claim that there were disenfranchised voters and that every vote should be counted. And suddenly, new Democrat votes appear. Huh?
3. Who wants a race that's over when the poles close? When a Lottery closes sales on a game. It knows immediately, how much sales there were. When the balls are drawn, the numbers are entered into the system at two separate locations. The system checks the numbers against the wagers played and -- BING! -- you know if you've had a winner. There is no recount. The computer will simply run the same program again. No recount = no recourse for close races. This is what We, the People want but Them, the Politicians don't. And who runs this country anyway?
4. A lot of people on BOTH sides of the aisle don't want to say "Hey look! Gambling technology could make a big difference in voting." Because gambling is seen as dirty. There are still many organizations (like the NFL) that don't want anything to do with gambling because there worried about the impression it will give. HEY PEOPLE! People gamble ALL THE TIME! Because it's fun! Who are you to tell other people what they can do with their fun money? [And do not say "tax on the poor". If you think the poor pick lottery tickets over food for their families, you've obviously never been hungry.] And at least the lottery (as opposed to other types of gambling) is transparent in its operations and tells you what your odds are before you buy.

So, a dual-redundant vote counting system already exists. And it's available at a retailer near you (unless you live in OK, AK, HI, NV, UT, AL, AR, MS, NC or WY). Will the government truly ever give people the option to use a secure method of selecting candidates via a redundant communications system with bipartisan auditors? Probably not. But its not a technology problem as I'm sure Diebold knows. The real problem keeps showing up on the ballot.

OK, I'll get back to writing about 50's music as soon as I can.

March Madness

As usual, I love March Madness for the Math of it.

After Day 1 (16 games), my random number generator method produced my best bracket with 15 out of 16 games correctly picked.

Method: In each game I assume that there n balls in a bag where n is the sum of the "ranks" of the two teams. So for each of the first 32 games, the value is 17. So out of these 17 balls, each team gets the other team's rank-number of balls. So in this year's contest when St. Joe's played Liberty, there were 17 "balls" in the bag and 16 of them said St. Joe's and 1 said Liberty. The random generator picked St. Joe's, who won.

This is the then repeated throughout all the games.

For the record, the random number generator picked "Stanford".

Next year, I'm going to try to make this into an downloadable Excel file so you can make your own bracket.

Electoral College

In the last election 16 states were decided by less than 3% (the usual error in a poll). These are the real battlegrounds of the next election. Leading these in electoral votes is Florida, of course, with 27. Other hotbed battlegrounds include Minnesota, Iowa and Wisconsin; Ohio and Michigan, and Pennsylvania.

With these sixteen states essentially toss-ups, the other 34 states are pretty much locked in to vote the way they did in '00. This gives the Republicans 194 EVs and the Democrats 168 EVs.

I constructed a random number generator in Excel to assume each of these 16 states decided the president by flipping a coin. Of course, the news is that out of 500 trials, the Dems won only 156 times. This means they have a 31% chance of reclaiming the White House, based on my assumptions. Of course, the Democratic nominee could bring more states into play or could lose more states to the Republicans. But right now it looks like the Republicans are about 2 times as likely to win the presidency.

How important is Florida to the Democrats? In the 156 scenarios where they win, 116 have Florida in the victory column. This means that nearly 75% of the Dems chances of victory require a win in Florida.

My home state of Wisconsin only shows up in 54% of the winning outcomes.

Nine of the 500 outcomes (1.8%) have the field ending in a tie broken by the (currently) largely Republican House of Representatives.

Here's the list with Electoral votes and % observed in winning combination.
Florida - 27 votes - 75%
Pennsylvania - 21 votes - 71%
Ohio - 20 votes - 76%
Michigan - 17 votes - 75%
Missouri - 11 votes - 60%
Tennessee - 11 votes - 62%
Washington - 11 votes - 59%
Minnesota - 10 votes - 61%
Wisconsin - 10 votes - 54%
Oregon - 7 votes - 58%
Iowa - 7 votes - 58%
Arkansas - 6 votes - 52%
Nevada - 5 votes - 64%
New Mexico - 5 votes - 58%
Maine - 4 votes - 55%
New Hampshire - 4 votes - 49%

I should also point out that New Mexico has the best track record picking presidential winners.

Clue

On a lark, I did some calculations on the game Clue. Enjoy!

Longest distance between two rooms by most direct route: Library to Dining Room (16 moves)
Runner-up: Hall to Billiard Room (15 moves)

Most geographically isolated room (as calculated by total number of steps to all other rooms): Library (79 moves)
Most geographically connected room: Conservatory (56 moves)

Total number of distinct Room/Person/Weapon combos: 324

Room with most entrances: Ball Room (4)
Total number of entrances: 17

7-7-7

One of the great and simple remaining mathematical mysteries is the way that the primes are arranged. No one has yet determined formulas that even provide information on the density of primes (no matter what this bear says.)

So when looking at a natural number, it is critical to determine what primes divide into it. Which brings us to you. Everyone should know whether any number is divisible (when I say "divisible" I mean "divisible without remainder" as do most mathematicians) by any number 1-10. Here are the shortcuts:

Everything is divisible by 1 (1 is not prime by the way)

2, 5 and 10 are the ending tests. If it's divisible by 2 it ends with 2, 4, 6, 8 or 0. If it's divisible by 5 it ends with 5 or 0. And if it's divisible by 10 it ends with 0.

4 and 8 are slightly constructed. If the last two digits are divisible by 4, the the entire number is divisible by 4. The same holds for the last three digits and 8. If this is too hard, simply divide the last three digits in half and then check it is still divisible by 4.

3 and 9's are fun. Add all the individual numbers of the number together and if they are then divisible by 3, the number is divisible by 3. If they are divisible by 9, then the number is divisible by 9.

For 6, simply check if the number is divisible by 2 AND 3. If it is, then it is divisible by 6.

7... what a stupid number. It took me years to learn the sevens tests, and then (because I discovered it on my own without the help of a computer) I had to prove. I shan't prove it for you (the math isn't interesting enough) but I shall state the conclusion. To find if a number is divisible by 7 simply take the digit in the ones place and double it. Then subtract it from the remaining number. Continue doing this until you have a number you know is divisible by 7.

Example:
8,675,309
9x2=18 867,530-18 = 867,512
2x2=4 86,751-4 = 86,747
7x2=14 8,674-14=8,660
Zeros can simply be removed.
6x2=12 86-12 = 74 which is between 7x10 and 7x11.
So 8,675,309 is not divisible by seven.

Also of note:
My dad taught me the wheel of 7s for division.

Draw a circle. Start at the top and place these numbers clockwise around the circle evenly: 1, 4, 2, 8, 5, 7. Then, inside the circle, write these numbers respectively: 1/7, 3/7, 2/7, 6/7, 4/7, 5/7. Now to create a decimal representation of any fraction with 7 in the denominator, simply start at the number of sevenths left over on the wheel and proceed around it clockwise.
1/7 = .142857142857...
5/7 = .714285714285...

Two frightening uses of 7's in your everyday life. Think about it, won't you.