Why Has Fairview's Exempt Percent Increased?

To contact us Click HERE
The Fairview Fire District has the highest fire tax rate in Dutchess County, and possibly the highest fire tax rate in New York State. One of the reasons for Fairview's high tax rate is that roughly half of Fairview's market value is exempt from paying fire taxes, but the exempt half still accounts for half the fire and emergency service calls to the Fairview Fire District. Fairview's taxable property owners pay not only their own share of fire tax, but also pay for service to the exempt properties. Fairview residents and property owners have had a longstanding interest in knowing exactly what percent of Fairview is exempt, and how Fairview's exempt percent may be changing over time. Unfortunately, there has been a history of misstatement of Fairview's exempt percent, which I have attempted to correct. See Fairview Fire District's Exempt Percent Is Misstated — Again.

Fairview's Exempt Percent

The following table shows a 5-year history of Fairview's exempt percent, according to my calculations:

Year of Tax Bill	Exempt Percent
2008	47.9*
2009	47.5
2010	47.9
2011	50.8
2012	51.7

* Listed exempt percent for 2008 is after correcting for a blunder by the Town of Poughkeepsie Assessor's Office.

Note that the 2008 “land” tax bill (including the fire, town, county, and other taxes) corresponds to the 2007 assessment roll, and so forth. This table shows that for the years 2008 — 2010, Fairview's exempt percent has been 47.7 plus or minus 0.2 percent. However, beginning in 2011, Fairview's exempt percent has noticeably increased, standing at 51.7 percent for 2012 tax bills. What accounts for this 4 percent increase in Fairview's exempt percent over two years? This post will examine this question.

Exempt Value has Increased While Taxable Value Decreased

Property values have been falling every year in Dutchess County since the 2008 economic meltdown. Fairview's taxable market value fell 11.8 percent between the 2010 and 2012 tax bills. If Fairview's exempt market value had also fallen 11.8 percent during this period, Fairview's exempt percent would have stayed the same as 2010, at 47.9 percent. But Fairview's exempt market value did not fall 11.8 percent — it actually increased by 2.5 percent! In terms of dollars, Fairview's exempt market value for the 2012 tax bill was about $74 million greater than it would have been if Fairview's exempt percent had remained constant. This $74 million caused Fairview's exempt percent to increase from 47.9 to 51.7 in two years. The $74 million arises from two sources:

1. Four exempt parcels saw dramatic increases in assessed value, for a total of about $41 million. 
2. Fairview's other exempt parcels fell in value by only about 4 percent on average, rather than by the 11.8 percent decrease for taxable parcels. These exempt parcels are assessed at approximately $33 million more than they would have been if they'd depreciated in proportion to taxable parcels.

Why did four exempt parcels dramatically increase in assessed value?

One might assume that the dramatic increases in four parcels simply reflect major construction projects on these parcels. Surprisingly, this assumption is true only for one of the four parcels. Marist College's parcel at 30 Fulton Street (Parcel number 134689-6162-05-035776-0000) increased in value from $240,000 in 2010 to $17,760,000 in 2012 because student residence halls were constructed on that property between those years.

The other three parcels, detailed in the following table, are part of the water and sewer systems for the City and Town of Poughkeepsie:

Parcel number 134689-6062-02 -xxxxxx-0000	827844	835560	818562
Address	3431 North Rd	Kittredge Pl	173 Kittredge Pl
Land use class	822 (water supply)	853 (Sewage)	853 (Sewage)
Owner	City of Poughkeepsie and Town	City of Poughkeepsie	Town of Poughkeepsie
2008 tax bill	$4,274,000	$111,400*	$159,300
2009 tax bill	$4,274,000	$235,000*	$316,000
2010 tax bill	$4,274,000	Not in roll	$316,000
2011 tax bill	Not in roll	Not in roll	$300,500
2012 tax bill	$12,000,000	$10,000,000	$5,250,000

The above three parcels have had no significant construction or other actual increase in market value in many years. These parcels have just been improperly assessed for at least 5 years:

• The 835569 property was erroneously listed as taxable rather than exempt for the 2008 and 2009 tax bills, as indicated by * after its assessed value.
• This same property was erroneously listed with land use class 340 (Vacant land located in industrial areas) for these same years.
• Two of the three parcels were erroneously omitted from the assessment roll corresponding to the 2011 tax bill. One was erroneously omitted from the assessment roll for the 2010 tax bill.
• None of the assessed values for any of these three parcels for any of the 5 years is remotely correct. Even for the 2012 tax bill, the total assessed value is $27,250,000 — only a fraction of the true value of these three properties.

According to my discussion with Town of Poughkeepsie Assessor Kathleen Taber, the 2012 values are only the beginning of an attempt to correct the assessments for these parcels. A realistic correction will not be in place until the 2013 land tax bill, which is based on assessments being finalized this month. The current Parcel Access database, applicable to 2013, shows a tentative total assessed value for these parcels of $125,000,000 — nearly $100 million more than this year's assessment.

Why did exempt parcels decrease in value less than taxable parcels?

While taxable parcels fell in value 11.8 percent in two years, most exempt parcels fell only about 4 percent. As I understand Taber's explanation for this, many exempt properties are difficult to assess because they don't generally appear on the open market. People don't generally buy or sell municipal sewage treatment plants, college academic buildings, or hospital atriums. Changes in the market value of these properties are difficult to gauge because there really isn't a market for these properties. Taber also mentioned that “commercial” properties tend to decrease in value more slowly than residential properties.

It may also be that less attention is given to properly assessing exempt properties simply because the stakes are lower. For taxable parcels, property owners pay real money proportional to the assessment. Taxpayers want assurance that they are paying no more than necessary, while municipal governments receiving taxes want assurance that they are collecting the full amount of money from every taxable parcel. Therefore, tax assessors are under considerable pressure to make assessments of taxable properties that are neither too high nor too low. For exempt properties, these incentives are not present. Inaccurate — apparently even wildly inaccurate — assessments aren't so much noticed.

Summary

There isn't one simple answer as to why Fairview's exempt percent has increased in the last two years. According to my analysis, there are three contributors, in order of decreasing importance:

1. Although Fairview's taxable market value fell by 11.8 percent, Fairview's exempt market value fell by only about 4 percent. The difference means that Fairview's exempt properties were valued $33 million higher than they would have been if they had tracked the taxable decline.
2. Three municipal water and sewer parcels were grossly under-assessed. The assessor made a correction of $23 million.
3. Marist College built student residences, increasing the value of one parcel by $18 million.

These three factors contribute 45%, 31%, and 24%, respectively, to Fairview's increase in exempt percent. Thus, all three factors contribute significantly to Fairview's increase.

Pattern of Under-Assessment of Exempt Properties

The careful reader will have noticed two reasons why Fairview's exempt percent may not be as meaningful as one would like. The first is that gross under-assessment of high-value exempt properties is a bigger issue than previously assumed. Two years ago, I found that the St. Frances Hospital complex had been under-assessed by over $100 million. At the time, I assumed this blunder was a one-time event that would be unlikely to be repeated. Now there's a second instance:  Municipal water and sewer parcels have been under-assessed by over $100 million. Most of this under-assessment will not be corrected until Fairview's 2013 tax bill. This pattern will continue: The recent construction of dormitories at Dutchess Community College — worth tens of millions of dollars — will not be reflected in Fairview's 2013 exempt percent. Taber told me she didn't have time to add the DCC dorms to the current assessment roll, the basis for Fairview's 2013 tax. The omission of such major contributors to exempt value results in underestimation of the true exempt percent.

Unequal Depreciation

The second reason why Fairview's exempt percent may not be so meaningful is that market forces apparently do not affect taxable and exempt properties equally. Nearly half (45 percent) of the increase in Fairview's exempt percent in the last two years is due to the fact that the average exempt property lost only one third as much value as the average taxable property did. At least, that's what the assessment rolls say. Do the assessment rolls accurately reflect exempt property values? There is some reason to wonder. If exempt properties have been overvalued in the last few years, Fairview's corresponding exempt percent is artificially high.

Pace Study's Analysis of Fairview Fire Tax Rate is Flawed

To contact us Click HERE
Pace University's Michaelian Institute for Public Policy and Management released its 189 page Fairview Fire District Consolidation and Efficiency Study final report on June 12. This work, known locally as the Pace Study, examines the feasibility of Fairview consolidating with one or more neighboring fire districts. Pace Study Principal Investigator Michael Genito will present this work at a public meeting this evening, according to the Pace Study website.

In spite of the central importance of tax rates to fiscal analysis, the final report devotes only three sentences and one chart to Fairview's past and future tax rates. Unfortunately, these three sentences, which pertain to average yearly tax rate increase and projection to 2017, are incorrect. Also, the chart contains some incorrect data and an incorrect linear approximation. When I presented my analysis to Genito, he readily concurred that all these statements and the chart are flawed.

Flawed Final Report Passage

The flawed information, on page 175 of the final report PDF (labeled page 167), is as follows:

The Fairview Fire District tax rate has increased on average 4.4% each year from 2008 through 2012. A linear regression of the past five years going forward indicates that by 2017 the tax rate would approximate $6.50 per $1,000 taxable assessed valuation. As such, and all things being equal, the median home would expect to see their fire service property tax to rise from $1,321 per year to $1,502 in 2017.

The above chart, copied from the final report, is confusingly labeled “Tax Rate per $1,000 Assessed Value”, but it is clear from context that this data is really tax rate per thousand dollars of market value, otherwise known as true value tax rate. This is the appropriate kind of tax rate for this analysis.

2008 Fairview Fire Tax Rate Is Incorrect

The key flaw is that the 2008 tax rate in the above chart is incorrect. Fairview's effective 2008 tax rate is $5.16, whereas the above chart shows it to be approximately $4.83. The final report's error in Fairview's 2008 tax rate leads to all the other errors in this passage, as will be explained below.

Genito's Blunder

How did Genito come to make this error? He apparently took an unwarranted shortcut. Instead of dividing Fairview's tax levy by Fairview's market value (the correct method, and the definition of true value tax rate), he took the Poughkeepsie portion of Fairview's tax levy and divided it by the Poughkeepsie portion of Fairview's market value. Under ordinary circumstances, such as between 2009 and 2012, Genito's method would give the same — or nearly the same — result as the correct method. Unfortunately, Fairview's circumstances in 2008 were far from ordinary.

Inequitable Apportionment

Long-time followers of my work know that for every year from 2001 to 2008, apportionment of Fairview's fire tax levy between Poughkeepsie and Hyde Park has been inequitable, resulting in different true value tax rates for the Poughkeepsie and Hyde  Park segments, in violation of New York State Real Property Tax Law. In 2008, the Poughkeepsie segment had a true value tax rate of $4.83 — the number on Genito's chart — but the Hyde Park segment had a whopping true value tax rate of $5.96. All these facts were documented in detail four years ago here, and especially here.

Corrected Chart

In order to fairly graph tax rates, the Y-axis should ordinarily begin at zero dollars. Genito's chart begins the Y-axis at $2, presumably to better visualize small changes in tax rate. The following chart, using the corrected 2008 value, takes this decision further, beginning the Y-axis at $5. This way, small changes in tax rate can be seen even better.


Although the final report's chart includes a straight line approximation to the data and an extrapolation to 2017, such analyses are not appropriate to the corrected data. That's because the corrected data simply does not fit a straight line well enough to justify such an approximation. The corrected data cannot meaningfully be used to linearly extrapolate Fairview fire tax rate out even one year — let alone five years. Once again, Genito concurs with this judgement, which is supported by generally accepted criteria for goodness of fit to a straight line. What this means is that there is simply no basis to support the second and third sentences in the final report's passage, which project 2017 values.

Fairview's Tax Rate Has Been Trending Down Until 2012

We know that taxes are always going up, right? Well, not in Fairview. Examination of the corrected chart between 2008 and 2011 shows that Fairview's yearly tax rate change has been downward twice and upward only once. Even the single upward change from 2010 to 2011 leaves Fairview's tax rate lower than it was in 2008. A standard linear approximation to Fairview's 2008—2011 tax rate would show a decreasing tax rate, not an increasing one.

Fairview's Tax Rate Has Been Approximately Constant — Until 2012

Fairview's downward trend in the 2008—2011 time period is actually quite small. It would probably make more sense to approximate Fairview's tax rate during this time period as a constant value. With such an approximation, Fairview's 2008—2011 tax rate is $5.10 plus or minus 1.2 percent for every year in this interval. The 2011 tax rate is equal to this constant value to within 0.2 percent.

Fairview's 2012 Tax Rate Breaks the Pattern

This pattern of constant tax rate is broken in 2012, where the tax rate soars 12 percent from its historical value of $5.10. It is this break from the pattern that makes it infeasible to predict future tax rates. Another way to look at it is that there is no way one could have predicted Fairview's 2012 tax rate by extrapolation from the previous 4 years.

Average Yearly Tax Rate Increase Is Misleading

What about the first sentence in the final report's passage (average tax rate increase of 4.4 percent per year)? This statistic depends crucially on the 2008 value. With the corrected value, the average tax rate increase is only 2.6 percent per year, not 4.4 percent. Thus the passage's first sentence is incorrect.

Of course, even the corrected sentence is of dubious value. Averages can be deceiving. Why mention a formally correct “average increase” when the tax rate actually decreases as often as it increases. A man drowned in a river whose “average” depth was 6 inches. But he was in the 10-foot part. For the average yearly tax rate increase, essentially all of the tax rate increase during the 5-year period occurred in the last year.

Flawed Passage Is Best Removed

According to Genito, the report's inclusion of the above-quoted passage stemmed from a request by Fairview officials (the “Study Committee”) for a projection based on a 5-year history. Now that Genito has accepted my correction, he and I seem to agree that no future projection can be justified by the data. As I see it, the average tax rate increase is misleading as well, and is best omitted. The only part of the flawed passage that could be of positive value is the corrected chart. This chart is certainly useful for understanding Fairview's fiscal situation, but such an understanding appears to be outside the scope of this report.

Dutchess County Gov't 2013 Tax Rate Likely To Be Highest in Millennium

To contact us Click HERE
Newly elected County Executive Marcus Molinaro is many weeks away from announcing a proposed 2013 budget. After that, the county legislature must deliberate on adjustments before approving a final budget in December. Nevertheless, I can already predict with some confidence that the final 2013 county budget will result in the highest tax rate in this millennium, and the highest tax levy in the history of Dutchess County. In other words, properties will be taxed more steeply by Dutchess County Government than ever before in this millennium. These predictions are based on two tax trends:

1. Dutchess County's taxable market value continues to fall — for the fifth year in a row.
2. Dutchess County Government's tax levy has never significantly fallen, year-to-year.

Taxable Market Value

Dutchess County's taxable market value and tax levy for each year from 2001 through 2012 are derived from the tax rate pamphlets published by the Dutchess County Real Property Tax Service Agency (RPTSA).


For the 2013 tax bill, only an initial estimate of Dutchess County's taxable market value is available (shown in yellow), based on the July 1, 2012, assessment rolls. This value is shown as $30.7 billion on page 23 of a fiscal presentation by the Dutchess County Budget Office. The downward trend in property values since the beginning of the economic meltdown in 2008 is evident in the following chart:


The 2013 taxable market value is shown in yellow to indicate that it is only a preliminary value. The final value, which will not be available until late January 2013, is most likely to be somewhat lower than this value for a variety of reasons explained in detail here.

Note that taxable market value is a net value, including both the value of new construction and improvements, and the current value of existing construction. Dutchess County's taxable market value surged in the first part of the last decade. In 2008 it was 2.5 times larger than in 2001. But from 2008 to 2013 it fell 20 percent. Once again, this 20 percent includes the effects of both the value of new construction and the current value of existing construction. Since there has been some new construction, the value of existing construction must have dropped more than 20 percent since 2008. 

Year to year increases in the taxable market value are shown  below:


When I performed this analysis last year, it appeared as if the property value free-fall was nearly over, since the 2012 taxable market value decrease was the smallest since the meltdown. But the 2013 estimate clearly contradicts that conclusion. Although the 2013 decrease is only an initial estimate, the final decrease will most likely be somewhat greater. Note that all these market values lag tax bills by a year and a half. For example, for tax bills to be paid in February 2013, the corresponding market values are as of July 1, 2011.

Tax Levy

To reason about the 2013 tax levy, let's consider Dutchess County's tax levy history:




The above charts show that Dutchess County's tax levy has increased by a significant amount almost every year. Only in 2002 and 2011 has the tax levy been essentially unchanged from the previous year. Accordingly, I've made the most conservative assumption, that Dutchess County's 2013 tax levy increase will be zero. Based on history, it's unlikely that Dutchess County's 2013 tax levy will be lower than the 2012 levy. The yellow bar indicates that this data point is speculative.

Tax Rate

The 2013 true value tax rate, which is calculated by dividing the assumed 2013 tax levy by the 2013 taxable market value, is $3.38 per thousand dollars of market value: 

The above chart shows that this projected 2013 tax rate for Dutchess County (in yellow) is higher than in any previous year. This projection is almost certainly a low estimate. That's because the final 2013 taxable market value and the 2013 tax levy are both likely to move in a direction to increase this tax rate even further. The tax rate increase chart gives a third reason to conclude that the $3.38 estimate is conservative:

If Dutchess County's 2013 tax rate turns out to be “only” $3.38 — the highest in this millennium — it will still represent the lowest tax rate increase since the meltdown.

Will My Predictions Stand the Test of Time?

What would it take for my tax rate prediction of at least $3.38 or my prediction of the largest tax levy in Dutchess County's history to be wrong? Well, perhaps Molinaro will propose an especially frugal budget with a lower tax levy than last year's. But this won't be easy to do. Former County Executive William Steinhaus was known for shrinking county government and implementing other austerity measures in the years since the meltdown. It's unlikely there's a lot of fat to cut. Meanwhile, the costs of everything are continuing to increase. The effects of the 2008 economic meltdown are still being felt all over, despite allegations of a “recovery”.

How Will We Know Whether My Predictions Are Correct?

The first and most significant indication of whether my predictions are correct will occur next month, when Molinero announces his proposed budget. The second and probably less significant indication will be when the County Legislature approves the budget, possibly with modifications, in December. But the final word will not be out until January, when the 2013 tax rate pamphlet is released by the RPTSA, possibly with slight adjustments as described here. It is these tax rates that are used to generate property tax bills. Ultimately, it is the property tax bills that define how steeply taxpayers are being taxed.

I Hope I'm Wrong

It would be great if my predictions turn out to be wrong. Property taxpayers have been suffering more every year since the meltdown, and of course not just from Dutchess County Government taxes. Only time will tell whether my prediction of Dutchess County's 2013 tax rate of $3.38 turns out to be low-ball.

UPDATE 10/6/2012 — Budget May Exceed 2% Tax Cap

Just a day after publication of this post, it already looks like my caution that my predictions might be wrong may be unwarranted. A front page story in yesterday's Poughkeepsie Journal describes Molinaro's intent to replenish  the County's rainy-day fund. The story quotes Dutchess County Legislative Chairman Robert Rolison as saying that Molinaro's plan would probably require exceeding the State's 2 percent tax cap. Nevertheless, Rolison signaled his intent to support such an increase. As I see it, the stage is already being set to increase the County's 2013 tax levy by at least 2 percent over 2012. Even at just 2 percent, the 2013 tax rate would be $3.45, a 6.1 percent increase over 2012. Such a result would easily confirm my predictions.

Krugman's Keynesian "Trickle-Down" Economics: Washington, D.C., as an Experiment

To contact us Click HERE
According to Paul Krugman and other Keynesians (not to mention almost all so-called political Progressives), endorsing a relatively free economy in which governments do not set or regulate prices and permit owners of factors of production to bargain in free markets is also to endorse what they call "Trickle-Down Economics." This "theory," according to the Progressives, operates like this: If we "help" the "rich," (that is, do not confiscate all or nearly all of their wealth), then by so doing, the spending of the rich will "trickle down" benefits to everyone beneath.

Obviously, this is presented with the belief that the "theory" is false on its face, or at least the results of the "theory." The rich, as Krugman and others will tell you, don't spend all of their income, which means that not everyone beneath them will receive enough income to survive. The better way to do things, according to the Krugmanites, is for the government to confiscate most of the earnings and wealth of the rich and distribute them to everyone else. This will result in equal incomes, which then assure enough spending to keep the Big Circle of the Economy moving and result in economic Nirvana.

For the past four years, we have had a major Keynesian experiment in Washington, D.C., as huge amounts of money have been transferred from elsewhere in the USA to the D.C. area, and especially the nation's capital itself. The outlying counties have become considerably wealthier, and especially wealthier relative to the rest of the USA. But what about Washington, itself? If the Keynesian theory is correct, then the wealth absorbed by government should have "trickled down" to the other residents of D.C. who are not directly connected to high-paying government jobs, political office, or lobbying firms or companies that have major government contracts.

Certainly the economy of D.C. has received enough new money to have gained "traction" (as Krugman likes to call it) to be engaged in a boom. Well, it turns out that unless one is well-connected politically, the Keynesian "stimulus" just might not have as much staying power as Krugman claims.

It turns out that income and living inequality in the District are worse than ever, according to recent reports:

Two decades of record federal spending and expanding regulation have fostered a growing upper class of federal contractors, lobbyists and lawyers in the District of Columbia area. The federal government funneled $83.5 billion their way in defense and other work in 2010 - an increase of more than 300 percent since 1989, even after adjusting for inflation. Private industry poured more than $3 billion into lobbying toinfluence the government, nearly double what it spent a decade ago.

Like spokes on a wheel, the high-rise offices of this elite radiate out from Capitol Hill along major arteries deep into suburban Maryland and Virginia. The latest Census figures placed 10 of the capital's surrounding counties in the top 20 nationwide for median household income - up from six in 1990.

The article lays out the rise of Lani Hay from military officer to out-and-out Washington tycoon whose wealth has come about solely from the income transfers from private individuals and businesses to the government. And her $120 million in government-awarded income pales next to the income that others gain at the government troughs.

Yet, at the same time, the regular people in Washington are not taking part in this orgy of new governmental wealth. This article lays out what the "other" people experience, as the blogger Glenn Reynolds received this from a D.C. council member:

"I really think you should reconsider your article about how Washington, DC was not affected by the recession and is doing so much better than the rest of the country. . . . I am not sure if you have ever been to the DC area, but I live here and there is a lot of poverty. The capital area might be doing great and the 2 wards where congresspeople live might be doing well, but the rest of the city is affected by poverty. Wards 7 and 8 have an average income of less than $30,000 and there are boarded up stores all over the city, just not in the 2 mile radius that tourists and outsiders see. . . . Maybe your next article could be about how DC has the largest income margin in the nation? About how the congresspeople and lobbyists make over $100,000 a year and the rest of city is living in poverty?"

 That is not all. The Reuters article lays out a few gems that would contradict the Keynesian Gospel:

Inequality has increased in 49 of 50 states since 1989. (See accompanying box on how inequality was measured.)

The poverty rate increased in 43 states, most sharply in Nevada, ravaged by the housing bust, and in Indiana, which saw a rise in low-paying jobs.

Twenty-eight states saw all three metrics of socioeconomic well-being worsen. There, inequality and poverty rose and median income fell.

In all 50 states, the richest 20 percent of households made far greater income gains than any other quintile - up 12 percent nationally.

The five largest increases in inequality all were in New England: Connecticut first, followed by Massachusetts, New Hampshire, Rhode Island and Vermont. The decline in manufacturing jobs hit New England's poor and middle hard, while the highly educated benefited from expansionin the biotech and finance industries.

And then there is this: 

Massachusetts boasts the country's finest public education system, but that has failed to slow a sharp increase in the income divide. Indiana has revamped the state's welfare system, but the number of people in poverty has soared. And in the District of Columbia, the federal government's hand in rising inequality is visible locally and nationwide.

This is not possible under Krugman's Keynesian Trickle-Down Theory. More money for public education means inequality disappears. The New England states vote heavily Democratic, and very liberal Democrats at that (no Republican holds statewide office in New England), so there can be no question that the policies that govern these states are correct, according to Krugman's views. Furthermore, there is no more Democratic political entity in the country than Washington, D.C., so there can be no doubt that the city is following "proper" political and economic policies.

So, if all of the claims that Krugman has been making the past several years are true, then there is little or no economic inequality in Massachusetts and in Washington, D.C., and they are the two most "liberal" political entities in the country. Inequality cannot be happening there because Paul Krugman always is correct.

Random Walks and Gambler's Ruin

To contact us Click HERE
Suppose you have $100 and you decide to go to a casino to try to double your money. Are you better off putting the whole $100 on a single bet, or should you make a lot of smaller bets? Maybe you should adjust the size of your bet as the evening progresses? Should you stop as soon as you reach $200 (if you ever do), or keep going?

Lots of people have opinions about questions like these. Today, I will show you how to calculate the correct answers yourself with just a few lines of code in R. Even better, you will understand the approach, which means you can do your own analysis of whatever strategy you want to test. And best of all, it's free: no need to spend real money at an actual casino to find out.

First, you need a copy of R. This is the free, high quality,open source statistical programming language that has become astandard for statisticians in industry and academia because it is botheasy and powerful. Download the latest version for Windows, Mac, orLinux from The R Project forStatistical Computing. Click on "Download R" and select a mirror(meaning, pick a site located close to you, to speed up the downloadprocess - there are mirrors all over the world), then click "DownloadR for Windows" (or Mac or Linux). Then just double click the installerand accept the default selections. You should now have a desktop iconor Start menu entry for starting R. You can copy and paste the samplecode from this blog post right into the R console window, and it willprint answers and draw graphs right on your computer screen.

We are going to answer the questions by running simulations. Not thegiant computer-game kind of simulations, with photo-realistic images ofblackjack tables, just a simple mathematical simulation of theessential elements of the process.

What do we need to know to set up the simulation? Not very much. Wedon't even need to know the details of any particular casino game,just your probability of winning and your payoff if you dowin. These vary depending on the game you choose to play.

So, let's assume the following situation:

• You start with some initial amount of money.
• You choose a size for your next bet.
• With probability w, you win back your bet plus more.
• With probability 1-w, you lose your bet.
• You decide whether to play again or to stop.
• You have to stop if you cannot make a minimum bet.

Let 'm' represent how much money you have to play with. Let 'b'represent the amount you choose to bet, which must be between 0 and'm'. Let 'w' be the probability of winning, and let 's' be themultiple of your bet that you get if you win. In symbols:

• With probability 'w', you now have 'm+b*s', because you get back your bet, bringing your total back to 'm', but then on top of that you get 's*b' as a prize.
• With probability '1-w', you now have 'm-b', because you lose the amount 'b' that you bet.

We can code this up using R without difficulty. We have only tospecify the strategy you want to test. We can encapsulate yourstrategy into a function that returns the size of your nextbet, as long as we interpret a zero or negative bet size as meaningyou choose to end the game and walk away without further betting.

However, the questions at the beginning of this article asked whetheryou would be "better off" under certain strategies. This is trickierto decide, since it depends on your personal values (both moral andfinancial). In other words, the answer depends on you.

In order to have something to discuss here, I will rank orderthe strategies according to the probability that you do not losemoney. However, you can choose to rank them by other criteria, ifyou want, such as the average amount of money you walk away with. Happily,the results of our simulation will provide a complete picture of thepossible outcomes, so you can decide for yourself which strategy youprefer.

Here's the code. You can copy and paste this into R now.

w <- 0.48s <- 1f <- 0.5nextBet <- function(m) {  if(m >= 200) 0  else m*f}oneNight <- function() {  m <- 100  b <- nextBet(m)  while(b >= 1 & m >= b) {    if(runif(1) < w) m <- m + b*s    else m <- m - b    b <- nextBet(m)  }  m}score <- function() {  n <- 1e4  x <- 0  for(i in 1:n)    if(oneNight() >= 100) x <- x+1  x/n}print(score())

This should only take a second or two to run, after which it shouldprint a number around 0.37, which means that in about 37% of the testcases, the strategy did allow you to leave with at least as much moneyas you started with. But what exactly is the strategy we are testinghere?

Let's examine the code. The first line sets the probability of winningto be 48%. That's because in R, the two characters '<' and '-'together act like an arrow pointing left, and they mean "assign".

The next line sets s=1, which means you are playingdouble-or-nothing.

Finally, the strategy: 'f' represents the fraction of your currentbalance that you will bet each turn. In this example, 'f' is 1/2,which means that on your first turn, you bet $50, which is half yourbalance. If you lose, you will only have $50 left, so your second betwill be half of that, or $25. If you win, you will have $150, so yoursecond bet will be $75. And so on.

How does 'f' come to mean 'fraction to bet'? The answer is in the'nextBet' function. This function receives as an input your currentmoney balance 'm'. If you have reached $200, it returns zero, meaningtime to go home. Otherwise, it returns 'm*f', which is fraction 'f' ofyour current balance.

You can modify the code to test other strategies by changing the'nextBet' function. We will look at an example toward the end. Firstthough, let's see how 'nextBet' gets used. The 'oneNight' functionstarts you off with m=100 dollars. Then it calculates your initialbet. As long as that bet is positive, it draws a random number betweenzero and one using 'runif(1)', and if that is less than 'w', youwin. Winning raises your balance to 'm+b*s', while losing lowers it to'm-b'. Finally, you get to decide the size of your next bet; choosingzero means you exit the loop and are done. I have imposed a minimum bet of$1 here, so actually, if your balance drops below $2, half of it willbe below $1, so you will stop. I have also insisted that you haveenough money to cover the bet (that's the 'm >= b' condition in thewhile loop).

Calling the 'oneNight' function simulates a single night at thecasino. However, any one night could be lucky or unlucky, purely bychance, irrespective of the strategy you want to test. So the 'score'function calls 'oneNight' ten thousand times, to give a very thoroughevaluation of the possible results.

You can modify the 'score' function to reflect whatever metric youwant to use for ranking strategies. I have made it count up the numberof nights in which you walk out with at least the $100 you startedwith, but you could instead ask it to compute the average dollaramount that you end up with each night, by writing something like

score <- function() {  n <- 1e4  x <- 0  for(i in 1:n)    x <- x + oneNight()  x/n}

If you copy and paste that in and run 'print(score())' again, R willprint a number around 89, meaning that on average you take home $89each night. In fact, in this specific example, you actually takehome either at least $200 (in 37% of the cases) or something close tozero (in 63% of the cases), which simply happen to average to $89:in no case do you ever take home an intermediate value like $89.

Notice that $89 is less than your initial $100 balance. Thisis bad: it means that on average, you lose $11 each night. The morenights you play this game, the more you lose. Yes, on any given night,you might win, and temporarily reverse the trend, but if you play manynights, you will find your money draining away, slowly and not quitesteadily, but inescapably.

If you like, you can even see a histogram or density plot showing thevariety of outcomes:

score <- function() {  n <- 1e4  x <- c()  for(i in 1:n)    x <- c(x,oneNight())  plot(density(x))  mean(x)}print(score())

Here's the result:

You see a large peak near zero (you never really go negative, that'sjust an artifact of the smoothing process inherent in drawing thecurve), and a smaller peak at and above $200. If you win the first twobets, you walk away with $225, but other combinations of wins andlosses can lead to a variety of other winning outcomes between $200and $300.

I've been saying you will get an answer "close" to $89, because eachtime you run the program, you will get different random numbers, andso get a slightly different final answer. That's why we simulate10,000 different nights: it helps average out the noise, so that youwind up with a pretty consistent analysis, regardless of the specificroll of the dice. If you want to always get the same answer each time,put 'set.seed(123)' at the start of the code instead.

Mathematicians call this sort of situation a "random walk", becauseyour balance staggers randomly up and down over time, and it has"absorbing barriers" at $2 and $200, because once you reach (or pass)those values, you stop. Here is a picture of one particular night,showing your balance over time:

In this example, you won the first bet, but then lost the nexttwo. Then you won again, but then you lost 5 times in a row, whichforced you to stop.

So far, so good (or bad). Whether you like the odds reflected in these pictures or not, they are the results of betting half your cash each time, in a double-or-nothing game with a 48% chance of winning, given that you stop if you double your initial cash. But the real question is, "compared to what?" We need to try some alternative strategies to see if they are better or worse.

We assume you cannot change 'w' and 's', because those arefixed characteristics of the game you are playing. In reality, youcould go look for a different, more favorable game, but 48%double-or-nothing is about as favorable as typical casino games get,actually.

So what can you change? You can change 'f', or you can modify the'nextBet' function to do something else, such as bet a fixed dollaramount each time, rather than a fixed percentage. This is easy enough:type in

f <- 25nextBet <- function(m) {  if(m >= 200) 0  else f}

and now 'f' is the fixed dollar amount of each bet, in this case $25each time.

So, try some experiments. Change 'f' to reflect different fractions ordifferent fixed size bets, and see what happens. Draw the densitycurves to see the whole story, or just pick the strategy with thehighest score. Let me know in the comment section if you find astrategy you think is really good - but be warned, ultimately, acasino exists to take your money, so stick with computer simulationsand stay out of actual casinos. One can in fact prove, mathematically,that in this sort of game there is NO "winning" strategy, meaning onethat returns on average more than your original $100. You can keepyour original $100 by not going to the casino at all, but the moreoften you bet, the more likely you are to lose.

To demonstrate that last remark, here are the results if you bet yourfull balance in one big bet: you get a 48% chance of walking away with$200, making this strategy "better" (by my scoring definition) thanthe first one we looked at, since that only gave you a 37% chance ofwinning. This raises your average payout to $96, still less than the$100 you started with (as I said, this is unavoidable), but betterthan the $89. Of course, you don't have as much "fun", since theevening is over after just one bet, either way. The distribution ofoutcomes is very sharply peaked, at zero and at $200, since these arethe only two possible outcomes.

Conversely, if you decide to make the evening last by making smallerbets, you wind up hurting your chances of winning: the more often youbet, the more likely it is that the casino takes your money, becausethe odds are in its favor. If we set 'f <- 0.1' in our originalcode, so that you bet only 10% of your balance each time, you win onlyabout 26% of nights, and your average balance is $61. The distribution ofoutcomes is also more skewed: more probability of losing everything,less of reaching, let alone exceeding, $200, as shown in the image atthe very beginning of this post.

Similarly, if we make a fixed size small bet, say $10 each time, weget a 30% chance of winning, and a $62 payout. Again, the results areworse financially than just betting your whole $100 in one shot,although they might provide more "entertainment value" since you getto keep playing longer.

Now it's your turn. Think up some new strategies you would like tocompare, code them up and see what you can discover! What happens,for instance, if you limit yourself to 20 bets rather than continuingto play indefinitely until you reach zero or $200? (Hint: modify the'oneNight' function to count the number of bets 'n', then add '& n<= 20' in the condition of the 'while' loop.) (Warning: nostrategy, no matter how clever, will prevent you from losing money atthis game, so don't try it with real money!)

If you liked this article, you may also like Supply, Demand and Market Microstructure for a more elaborate, "agent based" simulation of economic activity, or check out the Contents page for a complete list of past topics.

Please post questions, comments and other suggestions using the box below, or email me directly at the address given by the clues at the end of the Welcome post. Remember that you can sign up for email alerts about new posts by entering your address in the widget on the sidebar. If you prefer, you can follow @ingThruMath on Twitter, where I will tweet about each new post to this blog. The Contents page has a complete list of previous articles in historical order. Now that there are starting to be a lot of articles, you may also want to use the 'Topic', 'Search' or 'Archive' widgets in the side-bar to find other articles of related interest.

I hope you enjoyed this discussion. You can click the "M"button below to email this post to a friend, or the "t" button toTweet it, or the "f" button to share it on Facebook, and so on. Seeyou next time!

Joel Miller's Flawed Legislation for Fire District Budget Empowerment

To contact us Click HERE
New York State Assemblyman Joel Miller has introduced legislation to provide for public vote on fire district budgets in the November general election. Under current New York State law, fire district budgets are controlled by the district's board of fire commissioners. Miller's legislation A9762A, called the Fire District Budget Empowerment Act, shifts the approval of fire district budgets from the fire commissioners to the general public. Miller announced his popular vote initiative in an April 22, 2012, Valley Views article in the Poughkeepsie Journal.

Popular Vote on Budget Is Inconsistent With Other Local Governments

As I see it, popular vote on fire district budgets is a risky departure from most governance in this country. There is no public vote on the federal budget, there is no public vote on the New York State budget, there is no public vote on the Dutchess County budget, or on city or village budgets. Instead, the general public votes for representatives (government officials such as legislators, councilmen, etc.) who in turn decide on agency budgets. This is the principle of representative democracy, one of the foundations of this country. In the case of fire districts, the people vote for fire commissioners, who in turn control the budget.

Direct Democracy Is Seldom Used But Often Problematic

Miller's initiative is an example of direct democracy, in which policy decisions are made by popular vote, bypassing or overriding government officials. Direct democracy for economic decisions is used only sparingly in the United States. In California, many major economic decisions beginning with the infamous Proposition 13 have been made by popular vote, with disastrous results.

The founding fathers were very much opposed to direct democracy (also called “pure democracy”), according to Wikipedia. John Witherspoon, a signer of the Declaration of Independence, said, “Pure democracy cannot subsist long nor be carried far into the departments of state – it is very subject to caprice and the madness of popular rage.” The American colonists favored representative democracy — not direct democracy. That's why they said “No taxation without representation.” They didn't say “No taxation without popular vote.”

Why should fire districts be any different from other local governments?

Fire districts are just one more kind of local government taxing authority in New York State, along with Towns, cities, villages, and counties. I know of no reason why fire districts should be governed differently than any of these other taxing authorities. In my view, fire districts should continue to use the same budget approval process as most other local taxing authorities.

Incorrect and Misleading Statements in Valley View Article

Miller's Valley View article contains misleading statements, and at least one statement that is just plain wrong. In the context of the Fairview Fire District's high fire tax rate, Miller writes:

Fairview alone had fire district tax rates nearly 10 times higher than 27 other towns in Dutchess County in 2010.

This statement is absurd, since there are only 20 towns in Dutchess County. Well, perhaps Miller meant “fire districts” instead of “towns”, since there are about 31 fire districts in Dutchess County. I checked with Miller's office, and was assured that yes, that's what he meant. Well, wrong again! My tax rate analysis from 2009 shows (page 14) that Fairview's tax rate was 10 times higher than 13 other fire districts — not 27 other fire districts. Miller's research staffer has conceded that the Valley Views statement — even after changing “towns” to fire districts” — is incorrect.

Miller misleadingly writes, “This legislation will permit public participation in fire district budgets ...,” as if public participation in the fire district budget process doesn't already exist. But New York State law already requires a fire district to publicize its tentative budget and to hold a public hearing on the budget, during which public input is received. In this way again, state law provides for public participation in the fire district budget process just as it does in most other kinds of local government, including counties, cities, villages, and schools.

This Is My Opinion

Most of my previous posts have been nonpartisan, focusing on objective facts. This post (except for the last section) is clearly my own opinion. Therefore, it's marked with an “Opinion” label. As always, I welcome your reasoned comments.

Joel Miller Just Can't Get Fairview Facts Straight

To contact us Click HERE
“Everyone is entitled to his own opinion, but not his own facts.” Daniel Patrick Moynihan
Try as he might, New York State Assemblyman Joel Miller just can't get his facts right regarding the Fairview Fire District. On his first try, in a Poughkeepsie Journal Valley Views article on April 22, 2012, he wrote

Fairview alone had fire district tax rates nearly 10 times higher than 27 other towns in Dutchess County in 2010.

I pointed out in Joel Miller's Flawed Legislation for Fire District Budget Empowerment that there are only 20 towns in Dutchess County, and that even if he meant “fire districts” instead of “towns” (which would have made more sense), his statement is still not even close to correct.

Flawed Staff Work

In preparation for that blog post, I spoke with the staffer for Miller who had generated this misstatement. This staffer had already reviewed some of my own reports, including The Big Three Fire Districts of Dutchess County. It became clear to me that this staffer was not well prepared to interpret quantitative information, and the staffer readily conceded as much. My instinct was that if Miller were to release a corrected statement, it might also be wrong. Because I genuinely wanted facts to be correctly stated, I suggested a corrected statement, and I offered to preview any proposed new statement about Fairview. I never heard from Miller or any of his staffers about this matter.

My instinct turned out to be correct. On April 26, Miller sent a press release to each Fairview Fire Commissioner. This press release was essentially a rewording of his Valley Views article, except that the incorrect statement about Fairview was replaced by a new incorrect statement about Fairview:

Fairview alone had fire district tax rates nearly eight times higher than 30 other fire districts in Dutchess County in 2010.

The irony is that the above statement appears to be a mis-quote of a statement in my own report, which reads

Fairview’s tax rate is nearly eight times the average of the non-big-three districts.

Apparently the staffer thought the word “average” in my statement didn't really mean anything important, and could just be omitted! But as most European high school students know, an average of a bunch of numbers must be smaller than some of the numbers being averaged. In fact, for ordinary data like tax rates, roughly half the numbers can be expected to be greater than the average. Maybe even much greater.

And so it is in this case. Half the non-big-three fire districts had tax rates greater than the average of the non-big-three, and half had tax rates less than the average. So Fairview's tax rate was eight times higher than only 14 other fire districts — not 30 other fire districts.

Incidentally, “30 other fire districts” in Miller's statement is wrong too. There were only 30 fire districts in the whole analysis, and the big three fire districts were excluded from this average, so there could only be 27 non-big-three districts. The (weighted) average of these 27 was greater than 14 of these districts, and smaller than 13 of these districts, as one would expect. For five of these districts, Fairview was only about four times higher — not 8 times higher as Miller claimed.

Miller Has Been Ambivalent About Accuracy

This post isn't about flawed staff work. The principal is responsible for the work of his staff. If Miller had any doubt whether his staff could handle the fire tax rate issue, the doubt was resolved the first time the mistake was made. At that point, Miller knew — or should have known — that his staff didn't know what they were doing on this issue, and so were unlikely to make a proper correction on their own. Miller could have arranged for an independent review of his proposed “correction” before it was released. (I would have been glad to accommodate.)

But this post isn't just about fire taxes either. Joel Miller represents 6 of Dutchess County's 20 towns in the New York State Assembly. Yet he allowed himself to write “27 other towns in Dutchess County,” a gaffe that he or any member of his staff could easily have corrected without knowing anything about fire tax rates.

Taken together, these mistakes show Miller to have been ambivalent about the accuracy of his factual statements. Such lapses affect his credibility.